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PEH:Fundamentals of Geophysics

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Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume V – Reservoir Engineering and Petrophysics

Edward D. Holstein, Editor

Chapter 2 – Fundamentals of Geophysics

Bob A. Hardage, U. of Texas at Austin

Pgs. 25-75

ISBN 978-1-55563-120-8
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Geophysics is a broad subject that encompasses potential field theory (gravity and electromagnetic fields) and seismic technology. Potential field data are valuable in many studies, but seismic data are used in more reservoir characterization and reservoir management applications. This chapter focuses on seismic fundamentals and does not consider gravity, magnetic, or electrical concepts.

Seismic data have been used for many years to guide exploration. More recently, seismic data have been used to support reservoir characterization in field development planning and subsequent reservoir management. As the technology in equipment and interpretation techniques has advanced, so has the ability to define the size, shape, fluid content, and variation of some petrophysical properties of reservoirs. This chapter provides insight into the fundamentals of seismic data acquisition, interpretation techniques, and the types of information that can be derived. See the chapter on reservoir geophysics in the Emerging and Peripheral Technologies section of this Handbook for information on emerging technologies that apply geophysical data.

Most seismic data are acquired with surface-positioned sources and receivers. For the first 4 or 5 decades that seismic-reflection data were acquired, sources and receivers were deployed along the same straight line to create 2D seismic profiles. Two-dimensional seismic data do not yield a correct image of subsurface stratigraphy when a 2D seismic line crosses a complex subsurface structure because the acquisition geometry cannot distinguish reflections that originate from outside the profile plane from reflections that occur within the 2D vertical image plane.

This imaging deficiency of 2D seismic profiling has been remedied by the implementation of 3D seismic data acquisition, which allows data processing to migrate reflections to their correct image coordinates in 3D space. Industry largely abandoned 2D seismic profiling in the 1990s and now relies almost entirely on 3D seismic data acquisition. This chapter covers the basics of 3D seismic technology, but does not consider 2D seismic technology involving surface-positioned equipment.

In some reservoir applications, seismic data are acquired with downhole sources and receivers. If the receiver is stationed at various depth levels in a well and the source remains on the surface, the measurement is called vertical seismic profiling (VSP). This technique produces a high-resolution, 2D image that begins at the receiver well and extends a short distance (a few tens of meters or a few hundred meters, depending on the source offset distance) toward the source station. This image, a 2D profile restricted to the vertical plane passing through the source and receiver coordinates, is useful in tying seismic responses to subsurface geologic and engineering control.

If the source is deployed at various depth levels in one well and the receiver is placed at several depth stations in a second well, the measurement is called crosswell seismic profiling (CSP). Images made from CSP data have the best spatial resolution of any seismic measurement used in reservoir characterization because a wide range of frequencies is recorded. CSP data are useful for creating high-resolution images of interwell spaces and for monitoring fluid movements between wells. However, a CSP image is also a 2D profile with the image limited to the vertical plane that passes through the source and receiver coordinates. This chapter includes brief descriptions of the fundamentals of subsurface VSP and CSP technologies to complement the descriptions of surface-positioned seismic technology.

Impulsive Sources

A variety of seismic sources exist that can apply vertical impulse forces to the surface of the ground. These devices are viable energy sources for onshore seismic work. Included in this source category are gravity-driven weight droppers and other devices that use explosive gases or compressed air to drive a heavy pad vertically downward. Multiple references[1][2][3] describe these types of sources.

Chemical-explosive energy sources are popular for onshore seismic surveys but are prohibited at some sites because of environmental conditions, cultural restrictions, or federal and state regulations. Chemical explosives are no longer used as marine energy sources for environmental and ecological reasons.

Field tests should always be made before an extensive seismic program is implemented. First, it should be determined whether the selected impulsive source creates adequate energy input to provide data with an appropriate signal-to-noise ratio and a satisfactory signal bandwidth at appropriate offset distances. Second, it is important to determine whether an impulsive source causes unwanted reverberations in shallow strata.


Vibroseis™ energy sources are some of the more popular seismic source options for onshore hydrocarbon exploration. The generic term vibrator refers to these types of seismic sources. Vibrators have several features that make them attractive for seismic data acquisition. They are quite mobile and allow efficient and expeditious illumination of subsurface targets from many different shotpoint locations. Also, the frequency content of a vibrator signal often can be adjusted to better meet resolution requirements needed for a particular target. In addition, the magnitude of the energy input into the Earth can be tailored for optimal signal-to-noise conditions by varying the size and number of vibrators or by altering the output drive of individual vibrators. For these reasons, vibrators are one of the most versatile onshore seismic energy sources.

Vibrators work on the principle of introducing a user-specified band of frequencies, known as the sweep, into the Earth and then crosscorrelating that sweep function with the recorded data to define reflection events. The parameters of a vibrator sweep are start frequency, stop frequency, sweep rate, and sweep length. A vibrator can do an upsweep that starts with a frequency as low as 8 to 10 Hz and stops at a high value of 80, 100, or 120 Hz. Alternatively, vibrators can do a downsweep that starts with a high frequency and finishes with a low frequency. Most Vibroseis data are generated with upsweeps.

Sweep rate can be linear or nonlinear. A linear rate causes the vibrator to dwell for the same length of time at each frequency component. Nonlinear sweeps are used to emphasize higher frequencies because the vibrator dwells longer at higher frequencies than it does at lower frequencies.

Sweep length defines the amount of time required for the vibrator to transverse the frequency range between the start and stop frequencies. As sweep length is increased, more energy is put into the Earth because the vibrator dwells longer at each frequency component. Sweep length is usually in the range of 8 to 14 seconds.

If a vibrator sweep is 12 seconds long, then each reflection event also spans 12 seconds in the raw, uncorrelated data. It is not possible to interpret uncorrelated Vibroseis data because all reflection events overlay each other and individual reflections cannot be recognized. The data are reduced to an interpretable form by a crosscorrelation of the known input sweep with the raw data recorded at the receiver stations. Each time the correlation process finds a replication of the input sweep, it produces a compact symmetrical correlation wavelet centered on the long reflection event. In this correlated form, Vibroseis data exhibit a high signal-to-noise ratio, and reflection events are robust wavelets spanning only a few tens of milliseconds.

As a general observation, if an area is plagued by random noise, vibrators are an excellent energy source because the correlation process used to reduce the vibrator sweep to an interpretable form discriminates against noise frequencies that are outside the source sweep range. If several sweeps are summed, unorganized noise within the sweep range is attenuated. However, if coherent noise with frequencies within the vibrator sweep frequency range is present, then the correlation process may accentuate these noise modes. The references section contains[4][5][6][7][8][9][10][11][12][13] a portion of the available literature that describes the operating characteristics of vibrators and their ability to optimize signal-to-noise ratios.

Probably the most important improvement in vibrator operations has been the development of ground-force phase-locking technology.[13] Application of this technology results in the same ground-force function (i.e., the same basic seismic wavelet) being generated during hundreds of successive sweeps by vibrators positioned over a wide range of ground-surface and soil conditions and by all vibrators in a multivibrator array. All aspects of seismic data processing benefit when a source generates consistent output wavelets throughout a seismic survey, hence the appeal of vibrators as the source of choice for most onshore surveys.

Shear Wave Sources

All seismic energy sources generate compressional (P) and shear (S) body waves. To study the physics and exploration applications of S-waves, it is often necessary to increase the amount of S-wave energy in the downgoing wavefield and to produce a shear wavefield that has a known vector polarization. These objectives can be accomplished with sources that apply horizontally directed impulses to the Earth or by vibrators that oscillate their baseplates horizontally rather than vertically. In either case, a heavy metal pad is used to impart horizontal movement to the Earth by means of cleats on the bottom side of the pad that project into the Earth. A specific design for a horizontal shear-wave vibrator can be found in a patent issued to Fair.[14]

Horizontal vibrators have also been improved with the introduction of ground-force phase-locking technology that results in more consistent shear wavelets from sweep to sweep as horizontal vibrators move across a prospect. Surface damage has been minimized by reducing the size of the cleats underneath the baseplate so that they make only shallow ground depressions.

Marine Air Guns

Air guns are now the primary energy sources used in offshore seismic profiling. Chemical explosives are no longer used for safety reasons and because of their adverse effects on marine biology. Modern seismic vessels tow multiple arrays of air guns, and each array sometimes has 10 or more air guns. The size and position of each air gun in the array are engineered so that the output wavelet has minimal bubble oscillations and optimal peak-to-peak amplitude. Fig. 2.1 shows map and section views of the deployment of air guns from a seismic vessel. The air guns and hydrophone cable are positioned at proper lateral offsets from each other by steering vanes. Combinations of depth-control vanes and surface buoys keep the air guns and hydrophones at a constant depth as they are towed across a survey area.

The air-gun arrays are powered by large onboard compressors that allow the guns to fire and repressure (to approximately 2,000 psi) at intervals of 8 to 10 seconds as the vessel steams along a prescribed course at constant speed. These high-repetition firing rates create shotpoints at regular spacings of 20 to 100 m, depending on boat speed, along the length of the source line. In wide-line profiling, a vessel tows several air-gun arrays spaced 50 to 100 m apart laterally to create parallel source lines in one traverse of the vessel across a prospect area (Fig. 2.1).

Fig. 2.2 shows the raypaths involved in air-gun illumination of a geologic target. The seismic energy produced by an air-gun shot propagates up and down from the source array. The downgoing raypath creates the primary arrival. The upgoing raypath reflects from the water surface (where the reflection coefficient is –1 for an upgoing pressure wave) and travels downward as a time-delayed ghost event. Reduced-amplitude versions of the primary and ghost events follow at later times as the air bubble created by the shot oscillates and decays. These three components—primary arrival, ghost arrival, and bubble oscillations—combine to form the air-gun source wavelet.

The effectiveness of air-gun array parameters is tested in deepwater environments in which a hydrophone can be positioned at a deep, far-field station to record the source output wavelet, as shown in Fig. 2.2. The term far field refers to that part of wavefield propagation space that is several seismic wavelengths away from the source. This far-field requirement means that the hydrophone depth, D, shown in Fig. 2.2 is several hundreds of meters.

Air-gun arrays are designed to create source wavelets that are as compact in time as possible and that have minimal bubble oscillations. Compact wavelets are desired because such wavelets have wide signal-frequency spectra; minimal bubble oscillations are desired so that the signal spectrum will be as smooth as possible.

Fig. 2.3 shows an ideal source wavelet. The vertical dash line marks the arrival time of the bulk of the energy that travels the primary raypath (Fig. 2.2). The energy that travels the ghost raypath (Fig. 2.2) arrives at a time delay, 2d/v, where v is the velocity of the pressure pulse in seawater and d is the depth of the air-gun array. The ghost event has a polarity opposite that of the primary arrival because the reflection coefficient for an upgoing pressure wave at the air/water interface is –1. The primary and ghost arrivals define the peak-to-peak amplitude of the source wavelet. Small-amplitude events occur at later times in the source wavelet because the air bubble produced by the air-gun discharge oscillates as it decays (Fig. 2.3). The number, sizes, and relative separations of the guns in the array control the amplitude of these residual bubble oscillations.

The two wavelet properties of greatest interest are its peak-to-peak strength (PTP) and its primary-to-bubble ratio (PBR). The objectives of air-gun array design are to maximize the PTP property of an air-gun wavelet, which is the difference, A–B, in Fig. 2.4, and to minimize the PBR parameter, which is the ratio (A–B)/(C–D).

Many factors, such as the number of guns in the array, the volume of the guns, and the depth of the guns, affect the amplitude, phase, and frequency character of an air-gun array wavelet. Table 2.1 summarizes Dragoset’s[15] analysis of air-gun array parameters and their effects on the fundamental PTP and PBR properties of air-gun wavelets. A key point in this table is that the number of guns in an array has a greater impact on the peak-to-peak amplitude (or wavelet energy) than does the volume of the guns.

Seismic Sensors

Two classes of seismic sensors are used to acquire seismic data: scalar sensors and vector sensors. A scalar sensor measures the magnitude of Earth motion created by a seismic disturbance but does not indicate the direction of that motion. A hydrophone is an example of a popular scalar sensor used throughout the seismic industry. Hydrophones measure pressure variations (scalar quantities) associated with a seismic disturbance. A hydrophone cannot distinguish a pressure variation caused by a downgoing wavefield from a pressure change created by an upgoing wavefield. Hydrophones provide no directional (vector) information about a propagating seismic event.

A vector sensor indicates the direction that a seismic event causes the Earth to move. The classic example of a vector sensor is the moving-coil geophone that has been used for decades to record onshore seismic data. The principal of a moving-coil geophone is that a lightweight coil, with several hundred turns of thin copper wire, is suspended by springs that are, in turn, attached to the case of the geophone. The springs are designed to allow the geophone case and the lightweight coil to move independently of each other over a frequency band of interest. Permanent magnets are attached to the geophone case to create a strong internal magnetic field. When the case is moved by a seismic disturbance, an electrical voltage is created as the coils cut the magnetic lines of force. The magnitude of the voltage output is proportional to the number of magnetic lines of force cut per unit time; thus, geophone response indicates the velocity of the geophone case, which, in turn, is proportional to Earth particle velocity at the geophone station.

The polarity of the geophone output voltage depends on the direction that the electrical conductors are moving as they cut across the magnetic lines of force. If an upward movement creates a positive voltage, a downward movement produces a negative voltage. Thus, a geophone is a vector sensor that defines not only the magnitude of Earth motion, but also the direction of that motion.

Because geophones are directional sensors and can distinguish between vertical and horizontal Earth motions, they are used to record multicomponent seismic data. Three-component (3C) geophones are used to record compressional and shear seismic data onshore. Shear waves do not propagate in fluids. In marine environments, geophones have to be placed in direct contact with the Earth sediment on the seafloor, with data-recording cables connected to surface-positioned ships or telemetry buoys. Four-component (4C) sensors used for this service are encased in large, robust, watertight enclosures that include a hydrophone and a 3C geophone. Fig. 2.5 illustrates a segment of an ocean-bottom cable (OBC) used for deploying 4C marine seismic sensors. In this cable design, a 4C sensor station is positioned at intervals of 50 m along the 150-m cable segment. A large number of these segments, each containing three receiver stations, are connected end to end to make a continuous OBC receiver line several kilometers long. The exact length of the receiver line is determined by the depth of the target that is to be imaged.

Fig. 2.6 shows an OBC line deployed on the seafloor and connected to a stationary data-recording vessel. A second boat towing an air-gun array traverses predesigned source lines either parallel to, or orthogonal to, the OBC cable. The 4C sensors remain motionless on the seafloor as data are recorded, just as onshore geophones do when onshore seismic data are acquired. Seafloor sensors are not towed as are the conventional marine hydrophone cables shown in Fig. 2.1.

Seismic Wave Propagation

The full elastic seismic wavefield that propagates through an isotropic Earth consists of a P-wave component and two shear (SV and SH) wave components. Marine air guns and vertical onshore sources produce reflected wavefields that are dominated by P and SV modes. Much of the SV energy in these wavefields is created by P-to-SV-mode conversions when the downgoing P wavefield arrives at stratal interfaces at nonnormal angles of incidence (Fig. 2.6). Horizontal-dipole sources can create strong SH modes in onshore programs. No effective seismic horizontal-dipole sources exist for marine applications.

A principal difference among P, SV, and SH wavefields is the manner in which they cause rock particles to oscillate. Fig. 2.7 illustrates the relationships between propagation direction and particle-displacement direction for these three wave modes. A compressional wave causes rock particles to oscillate in the direction that the wavefront is propagating. In other words, a P-wave particle displacement vector is perpendicular to its associated P-wave wavefront. In contrast, SV and SH waves cause rock particles to oscillate perpendicular to the direction that the wavefront is moving, with the SH and SV displacement vectors orthogonal to each other. A shear-wave particle-displacement vector is thus tangent to its associated wavefront. In a flat-layered isotropic Earth, the SH displacement vector is parallel to stratal bedding, and SV displacement is in the plane that is perpendicular to bedding.

To create optimal images of subsurface targets, a seismic wavefield must be segregated into its P, SV, and SH component parts so that a P-wave image can be made that has minimal contamination from interfering SV and SH modes. Likewise, an SV image must have no interfering P and SH modes, and an SH image must be devoid of P and SV contamination.

A P wave travels at velocity Vp in consolidated rocks, which is approximately two times faster than velocity Vs of either the SH or SV wave. In carbonates, the velocity ratio (Vp/Vs) tends to be approximately 1.7 or 1.8. In siliciclastics, Vp/Vs varies from approximately 1.6 in hard sandstones to approximately 3 in some shales. This velocity difference aids in separating interfering P and S wave modes during data processing. An equally powerful technique for separating a seismic wavefield into its component parts is to use data-processing techniques that concentrate on the distinctions in the particle displacements associated with the P, SH, and SV modes (Fig. 2.7).

The P, SH, and SV particle displacements shown in Fig. 2.7 form an orthogonal coordinate system. The fundamental requirement of multicomponent seismic imaging is that reflection wavefields must be recorded with orthogonal 3C sensors that allow these P, SH, and SV particle motions to be recognized. To date, most exploration seismic data have been recorded with single-component sensors that emphasize P-wave modes and do not capture SH or SV wave modes.

Body Waves and Surface Waves

Seismic wavefields propagate through the Earth in two ways: body waves and surface waves. Body waves propagate in the interior (body) of the Earth and illuminate deep geologic targets. These waves generate the reflected P, SH, and SV signals that are needed to evaluate prospects and to characterize reservoirs. Reflected (or scattered) body waves are the fundamental signals sought in seismic data-acquisition programs.

Surface waves travel along the Earth/air interface and do not illuminate geologic targets in the interior of the Earth. Surface waves are noise modes that overlay the desired body-wave reflections. Surface waves can be a serious problem in onshore seismic surveys. Surface waves do not affect towed-cable marine data because they require some shear-wave component to propagate, and shear waves cannot propagate along the air/water interface. An exception in the marine case is sometimes encountered when data are recorded with ocean-bottom sensors (OBS) because interface waves can propagate along the water/sediment boundary and become a type of surface-wave noise that degrades OBS marine seismic data.

There are two principal surface waves: Love waves and Rayleigh waves (Fig. 2.8). Love waves are an SH-mode surface wave and do not affect conventional P-wave seismic data. Love waves are a serious noise mode only when the objective is to record reflected SH wavefields. The more common surface wave is the Rayleigh wave, which combines P and SV motions and is referred to as ground roll on P-wave seismic field records. Love waves create particle displacements in the horizontal plane; Rayleigh wave displacements are in the vertical plane (Fig. 2.8).

Much of the field effort in onshore seismic programs concentrates on designing and deploying receiver arrays that can attenuate horizontally traveling surface waves (ground-roll noise) and, at the same time, amplify upward-traveling reflection signals. The most effective field technique is to deploy 10, 12, 16, or more geophones at a uniform spacing at each receiver station so that the distance from the first geophone to the last geophone is the same as the dominant wavelength of the ground-roll event. All geophone responses are then summed to create a single output response at that receiver station. The idea is to create a sensor array length such that half of the geophones are moving up and half are moving down as the horizontally traveling ground roll passes the receiver station. The summed output of the geophone array is essentially zero because of the passage of the ground-roll event. In contrast, upward-traveling reflections arriving at this same receiver array are not attenuated because such events cause all geophones to move up and down in unison. The summed output of the array for an upward-traveling reflection wavefield is thus a strong voltage signal.

Seismic Impedance

The concept of acoustic (or seismic) impedance is critical to understanding seismic reflectivity. Seismic impedance controls the seismic reflection process in the sense that seismic energy is reflected only at rock interfaces in which there are changes in impedance across the interface. Seismic impedance is defined as


where I = impedance, ρ = the bulk density of the rock, and V = the velocity of seismic wave propagation through the rock. V is set to Vp if the wave mode of interest is a P wave; it is set to Vs if S-wave reflectivity is being considered. Any alteration in rock properties that causes ρ and/or V to change can be the genesis of a seismic reflection event; therefore, areal and vertical variations in seismic reflectivity can be used to infer spatial distributions of rock types and porosity trends.

Reflections Coefficients

Seismic reflectivity is best explained with a simple two-layer Earth model in which Layer 1 is above Layer 2 (Fig. 2.9). The seismic reflection coefficient, R, for a downgoing particle-velocity wave mode that arrives perpendicular to the interface between the two layers is

RTENOTITLE ....................(2.2)

A negative algebraic sign has to be inserted on the right side of Eq. 2.2 if the downgoing wavefield is a pressure wavefield (hydrophone measurement) rather than a particle-velocity wavefield (geophone measurement). The velocity parameters, V1 and V2, are P-wave velocities if P-wave reflectivity is being calculated; they are S-wave velocities if S-wave reflectivity is to be determined. At any interface, R can be positive, negative, or zero, depending on the impedance contrast (ρ1V1ρ2V2) across the interface.

A seismic reflection/transmission process is indicated in Fig. 2.9 by the raypaths labeled Ao, Ar, and At. For nonnormal incidence angles, the expression for reflection coefficient involves trigonometric functions that ensure that horizontal slowness (the inverse of horizontal velocity) is conserved and is a more complex expression than that given in Eq. 2.2. Aki and Richards[16] gives a detailed mathematical treatment. The seismic reflection, Ar, is given by

RTENOTITLE ....................(2.3)

and the transmitted seismic event, At, is given by

RTENOTITLE ....................(2.4)

The magnitude and algebraic sign of Ar depends on R and, in turn, the basic control on R is the variation of impedance ρV across the interface (Eq. 2.2). Table 2.2 lists the common geologic conditions that often create impedance contrasts that result in nonzero reflection coefficients at rock interfaces.

Two types of petrophysical properties control the value of acoustic impedance in individual rock layers: elastic properties of the rock matrix and properties of the fluid in the pore spaces of the rock. P-waves travel through elastic materials and fluids; thus, any change in either the rock matrix (such as a change in mineralogy or porosity) or in the type of fluid occupying the pore spaces will create a discontinuity in the P-wave seismic impedance of the rock system.

Fig. 2.10[17] illustrates the relationships between petrophysical conditions that occur at an impendance boundary and the existence of P and S reflections at that boundary. A P-wave reflection will occur at boundaries at which there is a change in either the rock matrix or the pore fluid, or both. In constrast, S-waves are not affected by changes in pore fluid or are only weakly affected. Consequently, a change in the properties of the rock matrix can create a reflecting boundary for S-waves, but a change in pore fluid will create only a small (usually negligible) S-wave reflection boundary (Fig. 2.10). If a small, nonzero S-wave reflection coefficient occurs at a fluid boundary, that reflection coefficient usually exists because the bulk density of the rock system varies across the fluid boundary.

These wave physics provide valuable geologic insights when both P and S reflection data are acquired across a prospect area. When P and S reflections occur at the same depth coordinate, the reflecting boundary at that depth is associated with a change in the rock matrix (that is, with a lithological change). There may or may not be a change in pore fluid at that boundary. When a P reflection occurs at a boundary but there is no S reflection, that boundary quite likely marks a change in pore fluid and not a change in rock matrix. (That is, the lithology probably does not change at that depth, but the type of pore fluid does.)

Seismic Attributes

The fundamental properties of processed seismic data that are used in interpretation are temporal and spatial variations of reflection amplitude, reflection phase, and wavelet frequency. Structural and stratigraphic interpretations of 3D seismic data are inferences of geologic conditions made by analyzing areal patterns of these three seismic attributes—amplitude, phase, and frequency—across selected seismic time surfaces. Any procedure that extracts and displays these seismic parameters in a convenient, understandable format is an invaluable interpretation tool.

Taner and Sheriff[18] and Taner et al.[19] began using the Hilbert transform to calculate seismic amplitude, phase, and frequency instantaneously, meaning that a value of amplitude, phase, and frequency is calculated for each time sample of a seismic trace. Since that introduction, numerous Hilbert transform algorithms have been implemented to calculate these useful seismic attributes (e.g., Hardage[20]).

Complex Seismic Trace

Fig. 2.11 illustrates the concept of a complex seismic trace in which x(t) represents the real seismic trace and y(t) is the Hilbert transform of x(t). In this discussion, we ignore what a Hilbert transform is and how the function y(t) is calculated. Most modern seismic data-processing software packages provide Hilbert transform algorithms and allow processors to create the function y(t) shown in Fig. 2.11 easily. These two data vectors are displayed in a 3D (x, y, t) space in which t is seismic traveltime, x is the real data plane, and y is the imaginary plane. In this complex trace format, the actual seismic trace, x(t), is confined to the real x plane, and y(t), the Hilbert transform of x(t), is confined to the imaginary y plane. When x(t) and y(t) are added vectorally, the result is a complex seismic trace, z(t), in the shape of a helical spiral extending along, and centered about, the time axis t. The projection of this complex function z(t) onto the real plane is the real seismic trace, x(t), and the projection of z(t) onto the imaginary plane is y(t), the calculated Hilbert transform of x(t).

Fig. 2.12 illustrates the reason for converting the real seismic trace, x(t), into what first appears to be a more mysterious complex seismic trace, z(t), in which the attributes known as instantaneous seismic amplitude, instantaneous phase, and instantaneous frequency are introduced. At any point on the time axis of this complex seismic trace, a vector a (t) can be calculated that extends away from the t axis in a perpendicular plane to intersect the helically shaped complex seismic trace, z(t). The length of this vector is the amplitude of the complex trace at that particular instant, hence the term instantaneous amplitude. This amplitude value is calculated with the equation for a (t) shown in Fig. 2.12.

The orientation angle, ϕ(t), of the amplitude vector, a(t), at time t, which is generally measured relative to the positive axis of the real x-plane, is defined as the phase of z(t) at that moment in time. Numerically, the phase angle is calculated from the equation for ϕ(t) defined in Fig. 2.12. As seismic time progresses, vector a(t) moves along the time axis and rotates continually about the time axis to maintain contact with the spiraling complex trace, z(t). Each full rotation of the vector around the time axis increases the phase value by 360°.

In any oscillating system, and specifically for a seismic trace, frequency can be defined as the time rate of change of the phase angle. This fundamental definition describes the frequency of the complex seismic trace so that the instantaneous frequency, ω(t), at any seismic time sample is given by the time derivative of the phase function specified by the equation in Fig. 2.12.

Instantaneous Phase and Instantaneous Frequency Calculations

Fig. 2.13 illustrates calculations of the instantaneous phase associated with a typical seismic trace. The figure’s bottom panel shows the actual seismic trace, and the center panel shows the real and imaginary components of the associated complex trace. Applying the second equation of Fig. 2.12 to the real and imaginary components of the complex seismic trace (center panel) produces the instantaneous phase function at the top of Fig. 2.13. The phase behavior at times t1, t2, t3 is critical to understanding the geologic significance of anomalous frequencies. Although phase is a positive function that monotonically increases in magnitude with seismic time, it is customarily plotted as a repetitive, wraparound function with plot limits of 0 to 360° (or –180° to +180°). Each wraparound of 360° corresponds to a full rotation of vector a(t) around the seismic time axis while the vector stays in contact with the spiraling complex seismic trace z(t) (see Fig. 2.12).

The top panel of Fig. 2.14 shows the instantaneous frequencies calculated for the seismic trace presented in Fig. 2.13. Although the calculated frequency values at times t1 and t2 shown by the solid-line curve are physically impossible because they are negative, these anomalous frequency behaviors are some of the most useful seismic attributes that an interpreter can use. They should be preserved because, when displayed in an eye-catching, contrasting color, they serve to shift an interpreter’s attention quickly to subtle structural and stratigraphic discontinuities in a seismic image.

Comparing the time coordinates of these anomalous frequency values with the time coordinates of the instantaneous phase function in Fig. 2.13 shows that rather than exhibiting its typical, monotonically increasing behavior in these time intervals, the phase momentarily decreases in magnitude. This causes the time rate of change of phase (or the slope of the phase function), which is the instantaneous frequency, to be negative at time samples t1 and t2. Numerical algorithms should not camouflage these unrealistic frequency values, which some algorithms do by arbitrarily reversing the algebraic sign of any negative frequency. The dashed-curve segments in the enlargement show how some software algorithms change the algebraic sign of negative frequency values to positive values. Although this seems like a logical correction, it should be avoided because it reduces the interpretive value of a 3D volume of instantaneous frequencies.

At times t1, t2, and t3, some type of wavelet interference (that is, a wavelet distortion) occurs in the seismic trace (bottom panel). As a result, the reflection waveform at times t1, t2, and t3 is slightly distorted (bottom panel) because of the destructive interference of two or more overlapping wavelets, demonstrating that anomalous frequencies tend to coincide with, and emphasize, distorted wavelets such as are produced at structural and stratigraphic discontinuities. High positive frequency values also occur at 1580, 1650, 1740, and 1840 milliseconds, but these values are not anomalous in the sense that they do not exceed the Nyquist limit (125 Hz). However, they too coincide with distorted wavelets (bottom panel).[21]

Applications of Seismic Attributes

All instantaneous seismic attributes (amplitude, phase, frequency) can be used in interpretation. In practice, most interpreters use instantaneous amplitude, or some variation of an amplitude attribute, as their primary diagnostic tool. Amplitude is related to reflectivity, which in turn is related to subsurface impedance contrasts. Thus, amplitude attributes provide information about all the rock, fluid, and formation-pressure conditions listed in Table 2.2.

Instantaneous phase is useful for tracking reflection continuity and stratal surfaces across low-amplitude areas where it is difficult to see details of reflection waveform character. In general, instantaneous phase is the least used of the seismic attributes.

Instantaneous frequency sometimes aids in recognizing changes in bed thickness and bed spacing. Anomalous values of instantaneous frequency (negative values or unbelievably high positive values) are particularly useful for recognizing edges of reservoir compartments, subtle faults, and stratigraphic pinchouts. Hardage[22] demonstrated these applications of instantaneous frequency.

Seismic Interpretation

A stratal surface is a depositional bedding plane: a depositional surface that defines a fixed geologic time. A siliciclastic rock deposited in a high-accommodation environment contains numerous vertically stacked stratal surfaces. A fundamental thesis of seismic stratigraphy is that a seismic reflection event follows an impedance contrast associated with a stratal surface; that is, a seismic reflection is a surface that represents a fixed point in geologic time.[23][24] The term chronostratigraphic defines this type of seismic reflection event. Because lithology varies across the area spanned by a large depositional surface, the implication of this interpretation principle is that an areally pervasive seismic reflection event does not necessarily mark an impedance contrast boundary between two fixed rock types as that reflection traverses an area of interest. The application of this fundamental concept about the genetic origin of seismic reflections to seismic interpretation is referred to as stratal-surface seismic interpretation.

Tipper[25] illustrated and discussed situations in which a seismic reflection can be either chronostratigraphic or diachronous (meaning that the event moves across depositional time surfaces), depending on the vertical spacings between beds, the lateral discontinuity between diachronous beds, and bed thickness. The conclusion that a seismic reflection is chronostratigraphic or diachronous needs to be made with caution because the answer depends on the local stratigraphy, the seismic bandwidth, and the horizontal and vertical resolution of the seismic data.

If two seismic reflection events, A and B, are separated by an appreciable seismic time interval (a few hundred milliseconds) yet are conformable to each other (that is, they parallel each other), then the uniform seismic time thickness between these two events represents a constant and fixed period of geologic time throughout the seismic image space spanned by reflectors A and B. An implication of seismic stratigraphy that can be invoked in such an instance is that any seismic surface intermediate to A and B, which is also conformable to A and B, is also a stratal surface.

A key first step in seismic interpretation is to use well logs and cores to identify the three types of stratal interfaces that exist in geologic intervals of interest: flooding surfaces, maximum flooding surfaces, and erosion surfaces. Flooding surfaces are widespread interfaces that contain evidence of an upward, water-deepening facies dislocation, such as contact between rooted, unfossiliferous floodplain mudstones and overlying fossiliferous marine shale. A ravinement surface is a specific type of flooding surface that suggests that transgressive passage of a surf zone has eroded underlying shallower-water facies.

Maximum flooding surfaces are interfaces that contain evidence of a widespread, upward, water-deepening facies dislocation that is associated with the inferred, deepest water facies encountered in a succession of strata. A maximum flooding surface is commonly represented by a thin condensed section, typically a black, organic-rich shale with a low-diversity fossil assemblage representing deepwater, sediment-starved conditions.

Maximum flooding surfaces bound and define upward-coarsening facies successions that are called genetic sequences by Galloway.[26] These genetic sequences are similar to cycles or cyclothems in other terminology.[27][28]

An erosion surface is an interface in which there is evidence of a facies offset that indicates that an abrupt decrease in water depth occurred. If an erosion surface is widespread, truncation of older strata can be documented on well log cross sections. Some of these surfaces may be disconformities representing downcutting during periods of subaerial exposure caused by allocyclic (extrabasinal) mechanisms, such as eustatic sea-level changes. These major chronostratigraphic surfaces are often manifested as mappable seismic reflections. All 3D seismic data volumes should be calibrated with mappable, key surfaces recognized from cores and well logs, with priority given to flooding surfaces, maximum flooding surfaces, and erosion surfaces. See the chapter on reservoir geology in this volume for more discussion on sequence stratigraphy and depositional environments.

Structural Interpretation

The original use of seismic reflection data (circa 1930 through 1960) was to create maps depicting the geometry of a subsurface structure. Because many of the world’s largest oil and gas fields are positioned on structural highs, structural mapping has been, in a historical sense, the most important application of exploration seismic data. When the seismic industry converted from analog to digital data recording in the mid-1960s, digital technology increased the dynamic range of reflected seismic signals and allowed seismic data to be used for applications other than structural mapping, such as stratigraphic imaging, pore-fluid estimation, and lithofacies mapping. These expanded seismic applications have led to the discovery of huge oil and gas reserves confined in subtle stratigraphic traps, and seismic exploration is now no longer limited to just "mapping the structural highs." However, even with the advances in seismic technology, structural mapping is still the first and most fundamental step in interpretation. When 3D seismic data are interpreted with modern computer workstations and interpretation software, structural mapping can be done quickly and accurately.

Different seismic interpreters use different approaches and philosophies in their structural interpretations. The technique described here is particularly robust and well documented.[29] The first step of the procedure is to convert the 3D seismic data volume that has to be interpreted to a 3D coherency volume. Coherency is a numerical measure of the lateral uniformity of seismic reflection character in a selected data window. As the waveform character of side-by-side seismic traces becomes more similar, the coherency value for the traces approaches a value of +1.0; as the traces become more dissimilar, the coherency of the traces approaches zero. All modern seismic interpretation software can perform the numerical transform that converts 3D seismic wiggle-trace data into a 3D coherency volume.

Fig. 2.15 shows an example of a horizontal time slice through a 3D coherency volume from the Gulf of Mexico. This figure is also discussed in the chapter on reservoir geophysics in the Emerging Technologies volume of this Handbook. The narrow bands of low coherency values that extend across this time slice are created by faults that disrupt the lateral continuity of reflection events. Fault mapping is a major component of structural mapping, and this type of coherency display can be used to create fast, accurate fault maps. Coherency technology has evolved into the optimal methodology for detecting and mapping structural faults in 3D seismic image space.

The second step of the structural interpretation procedure is to transfer the fault pattern defined by coherency data to the associated 3D seismic wiggle-trace data volume. Fig. 2.16 illustrates the projection of the faults in Fig. 2.15 onto a vertical profile through 3D seismic image space. The coherency time slice in Fig. 2.15 defines the X, Y coordinates of each intersected fault at one constant, image-time coordinate across the image space. Additional coherency time slices are made at image-time intervals of 100 or 200 milliseconds to define the X, Y coordinates of each fault as a function of imaging depth. This procedure causes the orientations and vertical extents of faults transferred to a 3D seismic wiggle-trace volume to be quite accurate.

The first-order fault labeled in Fig. 2.16 extends through the entire stratigraphic column and create large vertical displacements of strata. The second-order faults have less vertical extent and cause less vertical displacement than the first-order faults. Other structural and stratigraphic features that are common in Gulf of Mexico geology are labeled. These features are identified to indicate the imaging capabilities of seismic data. Rollover indicates fault-related flexing of bedding, which results in structural trapping of hydrocarbons. The bright spot is an example of reflection amplitude reacting as a direct hydrocarbon indicator (see changes in pore fluid in Table 2.2). The velocity sag feature is a false structural effect caused by anomalously low seismic propagation velocity that delays reflection arrival times, leaving the misleading appearance of a structural sag.

The third step of this approach to structural mapping is to interpret a series of chronostratigraphic surfaces across the seismic image space. These surfaces can be any of the chronostratigraphic surfaces (flooding surfaces, maximum flooding surfaces, and erosion surfaces) described in Sec. 2.15, depending on the amount and quality of subsurface well control available to the interpreter. If there is no well control, interpreters must use their best judgment as to how to correlate equivalent strata across a seismic image space and then adjust their interpretation, if necessary, as wells are drilled.

When a selected stratal surface is extended across the complete seismic image space, the geometrical configuration of that chronostratigraphic surface can be displayed as a structure map. The structure map in Fig. 2.17 is one of the chronostratigraphic surfaces interpreted across this Gulf of Mexico prospect with the fault geometry information defined by coherency slices (Fig. 2.15) and vertical slices (Fig. 2.16). The producing fields shown in the map are positioned on local structural highs associated with one or more first-order faults.

In the lower left of the map in Fig. 2.17, an arbitrary profile XX′ is shown crossing the fault swarm. Fig. 2.18 displays a vertical section along this profile to demonstrate the degree to which faults compartmentalize producing strata. This expanded view of the seismic reflection character also reveals critical stratigraphic features, such as lowstand wedges, that are embedded in the faulted structure. (A lowstand wedge is a sedimentary wedge deposited during a period of low sea level.) This type of seismic interpretation allows stratigraphers to construct detailed models of the internal architecture of targeted reservoir systems.

Fig. 2.19 shows a second structural map constructed from a shallower chronostratigraphic surface to illustrate that less fault compartmentalization is in shallow reservoirs than in the deeper reservoirs associated with the structure shown in Fig. 2.17. The first-order faults still displace strata at this shallow level, but most second-order faults have terminated at deeper depths and no longer cause reservoir compartmentalization.

The structure maps shown in Figs. 2.17 and 2.19 are time-structure maps. These maps can be converted to depth maps once seismic propagation velocities are determined through the stratigraphic column.

Imaging Reservoir Targets

Fig. 2.20 shows a data window from a vertical slice of a 3D seismic data volume that is centered on a targeted channel system. These data include a good-quality reflection peak labeled "reference surface." The reference surface is a reference seismic stratal surface used to construct additional stratal surfaces that pass through the targeted thin-bed interval.[30] The fluvial system is embedded in the reflection peak that occurs at 0.73 seconds at inline coordinate 120. This particular reflection peak satisfies the fundamental criteria required of a reference stratal surface used to study thin-bed sequences: the event extends over the total 3D image space and has a high signal-to-noise character; the event is reasonably close to the targeted thin-bed sequences that need to be studied (i.e., the strata related to the anomalous reflection waveforms labeled "Channel 1" approximately 90 milliseconds above the reference surface); and the event is conformable to (i.e., parallel to) this targeted thin-bed sequence. The third criterion is the most important requirement for any seismic stratal surface that is to be used as a reference surface. Because this reference surface follows the apex of an areally continuous reflection peak, the basic premise of seismic stratigraphy is that this reference surface follows an impedance contrast that coincides with a stratal surface.

Fig. 2.21 displays this crossline section view with four conformable surfaces (A, B, C, and D) that pass through the targeted thin-bed interval added to the profile. These four surfaces are, respectively, 92, 90, 88, and 86 milliseconds above—and conformable to—the reference surface. Visual inspection of the reflection events above and below surfaces A, B, C, and D shows that all these reflection peaks and/or troughs are reasonably conformable to the reference surface event. Surfaces A, B, C, and D can thus be assumed to be stratal surfaces, or constant-depositional-time surfaces, because they are conformable to a known stratal surface (the reference surface) and are embedded in a 200-millisecond seismic window in which all reflection events are approximately conformable to the selected reference surface. The highlighted data window encircles subtle changes in reflection waveform that identify the seismic channel facies.[30]

The circled features in Fig. 2.21 identify locations where stratal surfaces A, B, C, and D intersect obvious variations in reflection waveform. These waveshape changes are the critical seismic reflection character that distinguishes channel facies from nonchannel facies, as can be verified by comparing the inline coordinates spanned by the circled features (coordinates 60 to 70) with these same inline coordinates where this crossline (number 174) intersects the channel features labeled "Channel 1" in Fig. 2.22.

Fig. 2.22 shows reflection-amplitude behavior on stratal surface B, which is 90 milliseconds above, and conformable to, the selected seismic reference surface. This surface shows portions of the Channel 1 system in the lower right quadrant of the image. A second channel system (Channel 2) is located in the upper right quadrant.[30] The channel-system image shown in Fig. 2.22 is a surface-based image; that is, the seismic attribute that is displayed (which is reflection amplitude in this instance) is limited to a data window that vertically spans only one data sample. When a 1-point-thick data window is a good approximation of a stratal surface that passes through the interior of a targeted thin-bed sequence, then the seismic attributes defined on that surface can be important depictions of facies distributions within the sequence, as the image in this figure demonstrates.

An alternate, and usually more rigorous, way of determining facies distributions within a thin-bed sequence is to calculate seismic attributes in a data window that spans several data points vertically, yet is still confined (approximately) to only the thin-bed interval that needs to be studied. The bottom stratal surface of this data window must reasonably coincide with the onset depositional time of the sequence, and the top stratal surface must be a good approximation of the shutoff depositional time of the sequence. Such a data window is called a stratal-bounded seismic analysis window.

Stratal surfaces A and D shown in the section view in Fig. 2.21 are examples of surfaces that define a stratal-bounded data analysis window that spans a targeted thin-bed sequence, specifically a thin-bed fluvial channel system that was the interpretation objective of this 3D seismic program. In this instance, the analysis window is 4 data points (8 milliseconds) thick. As stated in the discussion of Fig. 2.21, surfaces A, B, C, and D are good-quality stratal surfaces because each horizon images a significant part of the thin-bed fluvial system that was deposited over a "short" geological time period. Because each of these four seismic horizons is a good approximation of a constant-depositional-time surface, the four surfaces collectively are a good representation of the facies distribution within the total thin-bed sequence that they span.

One way to evaluate facies-sensitive seismic information spanned by surfaces A and D is to calculate some type of an averaged seismic attribute in each stacking bin (the concept of a stacking bin is described in Sec. 2.18.1) of the 4-point-thick data analysis window bounded by horizons A and D. For example, the average peak amplitude between A and D could be used to show an alternate image of the total channel system.

In thin-bed interpretations such as the fluvial channel system considered here, it is important to try to define two seismic reference surfaces that bracket the thin-bed system to be interpreted: one reference surface below the interpretation target and the second reference surface above the target. By creating conformable reference stratal surfaces above and below a thin-bed system, an interpreter can extend a series of conformable seismic stratal surfaces from two directions to sweep across a thin-bed target. A set of seismic stratal surfaces extended across an interval from above the interval is often a better approximation of constant-depositional-time surfaces within a targeted thin-bed sequence than is a set of stratal surfaces extended across the interval from below the interval (or vice versa). The more accurate set of surfaces will produce more reliable images of facies patterns within the thin-bed unit.

To illustrate the advantage of this opposite-direction convergence of seismic stratal surfaces onto a thin-bed target, a second reference surface was interpreted above (and, in this case, closer to) the targeted fluvial system studied in Figs. 2.20 through 2.22. Specifically, this second stratal reference surface followed the apex of the reflection troughs immediately above the thin-bed channels. Fig. 2.23 shows the location of reference surface 2 on a second vertical slice (crossline 200) through the 3D seismic data volume. Reference surface 1 is the horizon labeled "reference surface" in Fig. 2.20. Reference surface 2 is an alternate seismic stratal surface positioned above the Channel 1 thin-bed target.[30] The targeted fluvial system referred to as Channel 1 is approximately 24 to 30 milliseconds below this second reference surface.

Fig. 2.24 displays the reflection-amplitude response across the channel systems observed on a stratal surface 26 milliseconds below and conformable to reference surface 2, as defined in Fig. 2.23. An improved channel image occurs, when compared with the image in Fig. 2.22, because in this case stratal surfaces that are conformable to the overlying seismic stratal surface happen to be better approximations of constant-depositional-time surfaces for this channel system than are stratal surfaces that are conformable to the deeper reference surface. This result illustrates that the combination of upward and downward extrapolations of conformable stratal surfaces across a thin-bed target is a good interpretation procedure, especially in those instances in which valid stratal reference surfaces can be interpreted both above and below the targeted thin bed.

In summary, a good technique for interpreting thin-bed targets in 3D seismic data volumes is to interpret a reference surface that is conformable to the areal geometry of the thin-bed sequence and then to create seismic stratal surfaces conformable to this reference surface that pass through the thin-bed target. If the seismic stratal surfaces constructed according to this logic are satisfactory approximations of constant-depositional-time surfaces that existed during the deposition of the thin-bed sequence, the seismic attributes across these stratal surfaces are usually valuable indicators of facies distributions within the sequence.

A second technique is to expand the application of this stratal-surface concept by calculating seismic attributes inside a thin, stratal-bounded analysis window that is centered vertically on the thin-bed target. Facies-sensitive attributes extracted from carefully constructed stratal-bounded windows are often better indicators of facies distributions within a thin-bed target than are attributes that are restricted to a 1-point-thick stratal surface that passes through the target. This fact implies that the geologic time interval during which a thin-bed sequence is deposited can sometimes be portrayed satisfactorily by a stratal-bounded data window, whereas a fixed geologic time during the thin-bed deposition is not well approximated by a 1-point-thick seismic stratal surface. Interpreters have to try both approaches to determine an optimal procedure.

A third technique is to extend a series of conformable seismic stratal surfaces and stratal-bounded windows onto the thin-bed target from opposite directions, that is, from both below and above the thin-bed target. The logic in this dual-direction approach is that one of the seismic reference surfaces may be more conformable to the thin-bed sequence than the other reference surface and that this improved conformability will lead to improved attribute imaging of facies distributions within the thin bed.

Three-Dimensional Seismic Survey Design

Stacking Bins

The horizontal resolution a 3D seismic image provides is a function of the trace spacing within the 3D data volume. As the separation between adjacent traces decreases, horizontal resolution increases. At the conclusion of 3D data processing, the area spanned by a 3D seismic image is divided into a grid of small, abutted subareas called stacking bins. Each trace in a 3D seismic data volume is positioned so that it passes vertically through the midpoint of a stacking bin.

In Fig. 2.25, each stacking bin has lateral dimensions of Δx and Δy. The horizontal separations between adjacent processed traces in the 3D data volume are also Δx and Δy. The term inline is defined as the direction in which receiver cables are deployed, which is north/south in this example. Inline coordinates increase from west to east as shown. Crossline refers to the direction that is perpendicular to the orientation of receiver cables; thus, the crossline coordinates increase from south to north.[31] These stacking bins can be square or rectangular, depending on an interpreter’s preferences. The dimension of the trace spacing in a given direction across a 3D image is the same as the horizontal dimension of the stacking bin in that direction. As a result, horizontal resolution is controlled by the areal size of the stacking bin.[32]

The imaging objective dictates how small a stacking bin should be. Smaller stacking bins are required if the resolution of small stratigraphic features is the primary imaging requirement. As a general rule, there should be a minimum of three stacking bins, and preferably at least four bins, across the narrowest stratigraphic feature that needs to be resolved in the 3D data volume. This imaging principle causes the targeted stratigraphic anomaly to be expressed on three or four adjacent seismic traces.

As Fig. 2.26 illustrates, the critical parameter to be defined in 3D seismic design is the smallest (narrowest) horizontal dimension of a stratigraphic feature that must be seen in the 3D data volume. For purposes of illustration, it is assumed that the narrowest feature to be interpreted is a meander channel. At least three, and ideally four, stacking bins (that is, seismic traces) must lie within the narrowest dimension, W, of this channel if the channel is to be reliably seen in the seismic image during workstation interpretation. Once W is defined, the dimensions of the stacking bins are also defined. The bin dimensions should be no wider than W/3. Ideally, they should be approximately W/4.[31] A variation in seismic reflection character on three to four adjacent traces is usually noticed by most interpreters, whereas anomalous behavior on fewer traces tends to be ignored or may not even be seen when a 3D data volume is viewed.

For example, if the interpretation objective is to image meandering channels that are as narrow as 200 ft, then the stacking bins should have lateral dimensions of approximately 50 ft (Fig. 2.26). This would cause a 200-ft channel to affect four adjacent traces. One of the first 3D design parameters to define, therefore, is the physical size of the stacking bin to be created. The bin size, in turn, can be determined by developing a stratigraphic model of the target that is to be imaged and then using that model to define the narrowest feature that needs to be seen. Once this minimum target dimension is defined, stacking bins with lengths and widths that are approximately one-fourth the minimum target width must be created if the target is to be recognized in a 3D data volume. Conversely, once a stacking-bin size is established, the narrowest stratigraphic feature that most interpreters can recognize will be a facies condition that spans at least three or four adjacent stacking bins.

Station Spacings

The distance between adjacent source points along a seismic line is the source-station spacing; the distance between adjacent receiver arrays along that same line is the receiver-station spacing. Previous publications on the topic of seismic acquisition[33][34] show that the trace spacing (i.e., the stacking-bin dimension) along a 2D seismic profile is one-half the receiver-station spacing (assuming the usual condition that the source-station spacing along the line is equal to or greater than the receiver-station spacing). Applying this principle to 3D seismic design leads to the following: the dimension of a 3D stacking bin in the direction in which receiver lines are deployed in a 3D grid is one-half the receiver-station spacing along these receiver lines, and the dimension of the stacking bin in the direction in which source lines are oriented is one-half the source-station spacing along the source lines.

As stated previously, once a decision has been made about the narrowest target that must be imaged, the required size of a stacking bin is automatically set at one-third or one-fourth that target dimension (Fig. 2.26). As a result, the source-station and receiver-station spacings are also defined because source-station spacing is twice the horizontal dimension of the chosen stacking bin in the source-line direction, and receiver-station spacing is twice the dimension of the stacking bin in the receiver-line direction. Stated another way, the source-station and receiver-station spacings should be one-half the narrowest horizontal dimension that needs to be interpreted from the 3D data.

When the geology involves steep dips or large changes in rock velocity across a fixed horizontal plane, rigorous calculations of station spacing (or bin size) should be made with commercial 3D seismic design software rather than by following the simple relationships described here.

Stacking Fold

The stacking fold associated with a particular 3D stacking bin is the number of field traces that are summed during data processing to create the single image trace positioned at the center of that bin (Fig. 2.25). In other words, the stacking fold is the number of distinct reflection points that are positioned inside a bin because of the particular source-receiver grid that is used.

At any given stacking-bin coordinate, the stacking fold inside that bin varies with depth. Fig. 2.27 illustrates vertical variation in stacking fold. The source-station and receiver-station spacings along this 2D profile both have the same value for Δx, which results in a stacking bin width of Δx/2. The vertical column shows the coordinate position of one particular stacking bin. For a deep target at depth Z2, the stacking fold in this bin is a high number because there is a large number, N2, of source-receiver pairs that each produce a raypath that reflects from subsurface point B. Only one of these raypaths, CBG, is shown. For a shallow target depth, Z1 , the stacking fold is low because there is only a small number, N1, of source-receiver pairs that can produce individual raypaths that reflect from point A. One of these shallow raypaths, DAF, is shown. When a 3D seismic data volume is described as a 20-fold or 30-fold volume, the designers are usually referring to the maximum stacking fold created by the 3D geometry, which is the stacking fold at the deepest target.[31]

In Fig. 2.27, when the stacking bin is centered around deep reflection point B, the stacking fold is at its maximum because the largest number of source and receiver pairs can be used to produce individual reflection field traces that pass through the bin. The number of source-receiver pairs that can contribute to the image at B is typically confined to those source and receiver stations that are offset horizontally from B by a distance that is no larger than depth Z2 to reflection point B. Thus, the distances CE and EG are each equal to Z2.

With this offset criterion to determine the number of source-receiver pairs that can contribute to the seismic image at any subsurface point, we see that the stacking fold at depth Z2 would be N2 , as Fig. 2.27 shows, because N2 unique source-receiver pairs can be found that produce N2 distinct field traces that reflect from point B. When the stacking bin is kept at the same x and y coordinates but moved to shallower depth, Z1, the stacking fold decreases to the smaller number, N1. Only N1 source-receiver pairs generate field traces that reflect from A and still satisfy the geometrical constraint that these pairs are offset by distance DE (or EF) that does not result in critical wavefield refractions at interfaces above A. When critical refraction occurs, the transmitted raypath, bent at an angle of 90°, follows a horizontal interface rather than continuing to propagate downward and illuminating deeper targets.

In 2D acquisition geometry, the inline stacking fold, FIL, is a function of two geometrical properties: the number of active receiver channels and the ratio between the source-station interval and the receiver-station interval. The raypath diagrams in Figs. 2.28 and 2.29 illustrate the manner in which each of these geometrical parameters affects inline stacking fold. Fig. 2.28 establishes the principle that inline stacking fold is one-half of the active receiver stations when the source-station interval equals the receiver-station interval.

RTENOTITLE ....................(2.5)

The raypaths in Fig. 2.28a show the distribution of reflection points (the solid circles on the subsurface interface) when there are four active receiver channels and the source-station interval is the same as the receiver-station interval. The vertical dashed lines pass through successive reflection points. The stacking-fold numbers at the bottom of the diagram define the number of distinct source-receiver pairs that create a reflection image at each subsurface point, that is, the number of reflection points that each vertical dashed line intersects.

The maximum stacking-fold for this four-receiver situation is 2. The raypaths in Fig. 2.28b show the distribution of reflection points and the stacking fold that results when there are six-receiver channels. The maximum stacking fold for this six-receiver geometry is 3.[31]

Fig. 2.29 expands the inline stacking-fold analysis to show that for geometries in which the source-station interval does not equal the receiver-station interval, then

RTENOTITLE ....................(2.6)

where ~ means "is proportional to."

The raypath diagram in Fig. 2.29a shows the distribution of subsurface reflection points (the solid circles on the subsurface interface) when there are four active receiver channels and the source-station spacing equals the receiver-station spacing. The inline stacking fold is the number of independent reflection points that occur at the same subsurface coordinates, which is the same as the number of reflection points intersected by each vertical dashed line. The stacking fold is shown by the sequence of numbers at the base of the diagram and, in this geometry, the maximum fold is 2.

The raypath picture in Fig. 2.29b shows the distribution of reflection points when the number of active receiver channels is the same as in Fig. 2.29a; that is, there are four receiver groups, but the source-station spacing is now twice the receiver-station spacing. (Note that the incremental movement of the source-station flag in Fig. 2.29b is two times greater than the flag movement in Fig. 2.29a.) The resulting stacking fold is shown by the number written below each vertical dashed line, which is the number of reflection points intersected by each of those lines. The maximum stacking fold in this geometry is only 1. These two diagrams establish the principle that inline stacking fold is proportional to the ratio of the receiver-station interval to the source-station interval.

Combining Eqs. 2.5 and 2.6 leads to the design equation for inline stacking fold:

RTENOTITLE ....................(2.7)

In 2D seismic profiling, the source-station interval is usually the same as the receiver-station interval, making the ratio term in the brackets in Eq. 2.7 equal to 1. However, in 3D profiling, the source-station spacing along a receiver line is the same as the source-line spacing, which is several times larger than the receiver-station spacing. Crossline fold, FXL, is given by

RTENOTITLE ....................(2.8)

In a 3D context, the stacking fold is the product of the inline stacking fold (the fold in the direction in which the receiver cables are deployed) and the crossline stacking fold (the fold perpendicular to the direction in which the receiver cables are positioned). This principle leads to the important design equation:

RTENOTITLE ....................(2.9)

To build a high-quality 3D image, it is critical not only to create the proper stacking fold across the image space but also to ensure that the traces involved in that fold have a wide range of offset distances and azimuths. Eq. 2.9 provides no information about the distribution of either the source-to-receiver offset distances or azimuths that are involved in the stacking fold. When it is critical to know the magnitudes and azimuth orientations of these offsets, commercial 3D seismic design software must be used. Offset analysis is a technical topic that goes beyond the scope of this discussion. Galbraith[35] describes the parameters involved in onshore 3D seismic survey design.

Vertical Seismic Profiling

In vertical seismic profiling (VSP), a seismic sensor is lowered to a sequence of selected depths in a well by wireline. Fig. 2.30 shows the source-receiver geometry involved in VSP. A wall-locked seismic sensor is manipulated downhole by wireline so that the receiver occupies a succession of closely spaced vertical stations. This receiver records the total seismic wavefield, both downgoing and upgoing events, produced by a surface-positioned energy source. Only 6 receiver stations are indicated here for simplicity, but a typical VSP consists of 75 to 100 receiver stations. The vertical spacing between successive stations is a few tens of feet. A common receiver spacing is 50 ft (15 m). The horizontal distance, X, between the surface source and the downhole receiver is the offset and can assume different magnitudes, depending on the specific VSP imaging application. Fig. 2.30 depicts a VSP measurement made in a vertical wellbore, but the VSP technique can also be implemented in deviated wells.[36]

Because the receiver stations are aligned vertically, the data-recording procedure is called VSP to distinguish the technique from conventional horizontal seismic profiling, in which seismic receivers are deployed across the surface of the Earth. In horizontal seismic profiling along the Earth surface, only upgoing seismic wavefields are recorded. The crucial information of the downgoing wavefields is not available to assist seismic data processors and interpreters. Seismic data recorded with a vertical receiver array have many valuable applications,[38][36] but the only uses stressed here are the abilities of such data to calibrate stratigraphic depth to specific waveform features of surface-recorded seismic reflection data and to provide an independent, high-resolution image of the subsurface in close proximity to the VSP receiver well.

Velocity check-shot data are recorded with the same source-receiver geometry used for VSP data recording (Fig. 2.30). However, the vertical distance between successive receiver stations is on the order of 500 ft (150 m) or more, compared with a smaller station spacing of approximately 50 ft (15 m) used to record VSP data. This order-of-magnitude difference in the spatial sampling of subsurface seismic wavefields is the principal difference between VSP and velocity check-shot data. The primary use of velocity check-shot data is to create a rigorous relationship between stratigraphic depth coordinates and seismic image-time coordinates. These depth-to-time relationships are critical for transforming log data and engineering data from the depth domain to the seismic image-time domain. This coordinate transformation allows critical geologic and engineering information to be associated with proper data windows in the seismic image.

Because equivalent source-receiver recording geometries are used, velocity check-shot data can provide a rigorous relationship between stratigraphic depth and seismic travel-time, just as VSP data do. One shortcoming of check-shot data, however, is that they do not provide an independent seismic image that can be correlated with surface-recorded seismic reflection images. Such a correlation can verify the precise amount of time shift that should be imposed to bring subsurface stratigraphy into exact phase agreement with a surface-recorded 3D seismic image. To a seismic interpreter, two images are in phase agreement when the peaks and troughs of the two sets of wiggle-trace data occur at the same time coordinates over a window of interest and the waveshapes of key events in the two images are similar over that window. In contrast to check-shot data, VSP data provide an independent seismic image, and this VSP image is the unique feature of the VSP technique that allows subsurface stratigraphy to be inserted into 3D seismic image volumes at precise seismic travel-time coordinates.[37]

Synthetic Seismograms

Some seismic interpreters argue that a synthetic seismogram made from sonic and density log data can provide an independent image that can be used to determine the proper time shift between surface-recorded seismic data and check-shot-positioned stratigraphy encountered in the check-shot well. Fig. 2.31 illustrates the steps taken to create a synthetic seismogram and to use that synthetic model in interpretation.

First, sonic log data and density log data recorded in a chosen calibration well are multiplied to create a log of the layer impedances penetrated by the well (left three curves of Fig. 2.31). Eq. 2.1 describes this calculation. Either before or after this multiplication, these log data have to be converted from functions of depth to functions of vertical seismic travel time. Such a transformation is done with a simple equation:

RTENOTITLE ....................(2.10)

The velocity function in this equation is provided by the sonic log used in the calculation. Sonic log data usually have to be adjusted by small percentage amounts so that the integrated sonic log time agrees with seismic check-shot time. With Eq. 2.2, the time-based layer impedance wave is converted to a time series of reflection coefficients, and an estimated seismic wavelet is convolved with this reflectivity series. The result is the synthetic seismogram trace shown in Fig. 2.31. The interpretation step is done by comparing the synthetic seismogram with real seismic traces near the calibration well (last step of Fig. 2.31). During this comparison, the synthetic trace is shifted up and down in time to determine what time shift, if any, is required to create an optimal alignment of reflection peaks and troughs between the synthetic and real traces. Most geophysicists would describe the wiggle-trace alignment shown in Fig. 2.31 as a good phase tie.

There are instances in which synthetic seismograms are a poor match to seismic data. When there are only a few well penetrations, this can be a problem best addressed with VSP data. As the number of wells increase and greater areal coverage is provided, poor synthetic data can be eliminated and reliable synthetic seismograms can be used to leverage a limited number of VSP surveys. There are several reasons that synthetic seismograms sometimes fail to provide the reliability needed for calibrating thin-bed stratigraphy with seismic reflection character.[39] The more common failures are usually related to one or more of the following factors:
  • The log-determined velocity and density values used in a synthetic seismogram calculation represent petrophysical properties of rocks that have been mechanically damaged by drilling and altered by the invasion of drilling fluids. In addition, irregular changes in borehole diameter sometimes induce false log responses. As a result, well log determinations of rock velocity and density, which are the fundamental data used to produce the reflection coefficients needed for a synthetic seismogram calculation, may not represent the velocity and density values in undrilled rocks near the logged well, which are the fundamental rock properties that determine the reflection waveshape character of seismic data recorded at the wellsite.
  • A synthetic seismogram represents an estimate of the seismic image that would result if the imaging raypath traveled vertically downward from a source and then reflected vertically upward along that same travel path to a receiver located exactly at the source position. In contrast, each trace of an actual seismic profile is a composite of many field traces that represent wavefield propagation along a series of oblique raypaths between sources and receivers that are laterally displaced from each other, with each of these raypaths reflecting from the same subsurface point. These two images (synthetic seismogram and actual seismic trace) thus involve raypaths that travel through different portions of the Earth.
  • Even when log-determined velocity and density values (and any synthetically calculated seismic reflectivity derived from these log data) represent the correct acoustic impedances of a stratigraphic succession, that stratigraphy may be localized around the logged well and not be areally large enough to be a reflection boundary for a surface-generated seismic wavefield. This situation may be more common in heterogeneous rock systems than many interpreters may appreciate.
  • The effects of the near surface are not included in a synthetic seismogram calculation because logs are not recorded over shallow depths. At some wellsites, the near surface can induce significant effects into the waveform character of surface-recorded seismic data. In contrast, near-surface effects, such as peg-leg multiples, frequency absorption, and phase shifting, are included in VSP data because VSP wavefields propagate through the total stratigraphic section, including the near surface, just as surface-recorded seismic wavefields do.

Calibrating Seismic Image Time to Depth

VSP recording geometry causes the stratigraphy at the VSP well, where sequence boundaries are known as a function of depth from well log and core control, to be locked to the VSP image. This stratigraphy, in turn, is also known as a function of VSP reflection time. This fixed relationship between stratigraphy and the VSP image results because VSP receivers are distributed vertically through the seismic image space. This data-recording geometry allows both stratigraphic depth and seismic traveltime to be known at each receiver station. The dual-coordinate domain (depth and time) involved in a VSP measurement means that any geologic property known as a function of depth at the VSP well can be accurately positioned on, and rigidly welded to, the time-coordinate axis of the VSP image.

Fig. 2.32 illustrates the VSP depth-to-time calibration. VSP data are unique in that they are the only seismic data that are recorded simultaneously in the two domains critical to geologic interpretation: stratigraphic depth and seismic reflection time (Fig. 2.32a). As a result, specific stratigraphic units, known as a function of depth from well log data, can be positioned precisely in their correct VSP-image time windows (Fig. 2.32b). Each numbered stratigraphic unit shown in Fig. 2.32b is a thin-bed reservoir penetrated by the VSP well. When the VSP image is shifted up or down to correlate better with a surface-recorded seismic reflection image that crosses the VSP well, the VSP-defined time window that spans each stratigraphic unit should be considered to be welded to the VSP data. This causes the stratigraphy to move up and down in concert with the VSP image during the VSP-to-surface seismic correlation process. The seismic time scale involved in the depth-to-time calibration illustrated here is VSP image time, which may be different from the image time for surface-recorded reflection data. Fig. 2.33 illustrates the transformation of stratigraphy from VSP image time to 3D seismic image time.

The reverse situation is also true; that is, the VSP image could be positioned on, and welded to, the depth-coordinate axis of the stratigraphic column at the VSP wellsite. This option of transforming a VSP image to the stratigraphic depth domain is not often done because the common objective of seismic interpretation is to insert stratigraphy into 3D seismic data volumes that are defined as functions of seismic traveltime, not as functions of stratigraphic depth.

The concept of a welded bond between a VSP image and the stratigraphy at the VSP wellsite means that whenever a VSP image is moved up to better correlate with a 3D seismic image, the stratigraphy moves up by that same amount of time in the 3D image. If the VSP image has to be moved down to create a better waveform character match with the 3D data, then the stratigraphy shifts down by the same amount in the 3D data volume. The fact that VSP data provide an independent image that can be moved up and down to find an optimal match between VSP and 3D reflection character is the fundamental property of the VSP-to-seismic calibration technique, which establishes the correct time shift between 3D seismic reflection time and VSP reflection time.

When the time shift between these two images is determined, the correct time shift between the 3D seismic image and the stratigraphy at the VSP-calibration well is also defined because that stratigraphy is welded to the VSP traveltime scale and moves up and down in concert with the VSP image time coordinate. Fig. 2.33 shows a specific example of a VSP-based stratigraphic calibration of a 3D data volume. The rigid welding of stratigraphic depth to VSP traveltime as described in Fig. 2.32 is repeated here as Fig. 2.33a. In this example, the VSP image must be advanced (moved up) by 18 milliseconds to optimally align with the 3D seismic image at the VSP well (Fig. 2.33b). Because the stratigraphy penetrated by the VSP well is welded to the VSP image, the positions of the targeted thin-bed time windows in the 3D image also move up by 18 milliseconds to align with their positions in the VSP image. The VSP technique provides not only a time-vs.-depth calibration function but also an independent reflection image that can be time shifted to correlate with a surface-recorded image in the manner shown here. This is the unique feature that makes a VSP calibration of stratigraphy to 3D seismic image time more reliable than a check-shot-based stratigraphic calibration.[37]

This VSP image was produced from a large-offset VSP survey in which the offset distance, X (Fig. 2.30), was a little more than 2,000 ft (600 m). In Fig. 2.33, the VSP-based interpretation procedure leads to the conclusion that although the tops of thin-bed reservoirs 19C and 15 are positioned at VSP travel times of 1.432 and 1.333 seconds, they have to be inserted into the 3D data volume at 3D seismic travel times of 1.414 and 1.315 seconds.

Three-dimensional VSP data can be acquired when many source stations encircle a receiver well. Technically, there is no barrier to 3D VSP imaging. The major industry objection to 3D VSP technology is the relatively high cost of data acquisition and processing compared with the cost of conventional 3D surface-based seismic imaging. In special cases that have justified the cost, 3D VSP imaging has been done to create high-resolution images around a receiver well. To date, only a few such surveys have been done worldwide.

Crosswell Seismic Profiling

Fig. 2.34[40] shows distinctions among the source-receiver geometries involved in vertical seismic profiling (VSP), reverse vertical seismic profiling (RVSP), and crosswell seismic profiling (CSP). Fig. 2.34a shows the field geometry used in conventional VSP. Source S is positioned on the surface of the Earth, and seismic receiver R is lowered into the well where the data are to be recorded. The direct arrival path is SR, and the reflected travel path is SPR. The position of reflection point P can be varied by moving either source S or receiver R. If the source is directly above the receiver, the measurement is called a zero-offset VSP. If the source is not directly above the receiver, the measurement is called an offset VSP.

In RVSP, the positions of the source and receiver are exchanged. As Fig. 2.34b shows, receiver R is on the surface for an RVSP, and source S is located in the well. The offset in this diagram has the same meaning as it does for a conventional VSP. (Offset is the lateral distance between a vertical line passing through the source position and a vertical line passing through the receiver position.) In a vertical well, offset can be measured relative to the wellhead, if desired. In nonvertical wells, offset must be measured strictly between the coordinates of the source and the receiver. Three-dimensional RVSP data can be acquired at rather low cost because it is not difficult to distribute a large number of receiver stations on the Earth’s surface in an areal pattern around a source well.

In a CSP measurement, both the source and the receiver are below the surface and in separate wells, as Fig. 2.34c shows. The direct travel path is again SR, and the reflected path is SPR. One of the attractions of CSP data is that no part of either path SR or path SPR passes through the near-surface weathered layer, as occurs when VSP and RVSP data are recorded. As a result, crosswell data do not suffer a significant loss of the higher-frequency components of the source wavefield. These components are usually attenuated as they pass through the surface weathered layer to complete any of the VSP-type travel paths. Because spatial resolution improves as the frequency content of the signal is increased, crosswell data reveal greater reservoir detail than do either type of VSP measurement.

In crosswell data acquisition, two types of source-receiver offsets can be considered, depending on whether the direct or the reflected wavefield is being analyzed. These two offsets are transmission offset and reflection offset, respectively. Transmission offset in a crosswell geometry (Fig. 2.34c) is measured orthogonal to the direction in which reflection offset (Figs. 2.34a and 2.34b) is measured and can be defined as the vertical distance between a horizontal line passing through the source position and a horizontal line passing through the receiver position.

There are three techniques by which the interwell space of a reservoir system can be investigated using CSP data: attenuation tomography, for which the basic measurement is the amplitude of the direct seismic arrival wavelet; velocity tomography, for which the principal measurement is the traveltime required for the direct seismic arrival to propagate across the interwell space; and elastic wavefield imaging.

In velocity and attenuation tomography, the only information in the crosswell wavefield that is used are the travel times and amplitudes of the seismic direct arrival. In elastic wavefield imaging, the complete seismic wavefield is used. The major imaging contributions come from the scattered wavefield that occurs after the direct arrival.

Tomographic data are used to infer spatial distributions of rock and fluid properties in interwell spaces. Velocity tomograms are more widely used than are attenuation tomograms. Table 2.2 lists several reservoir properties (lithological variations, porosity, pore fluid) that affect seismic wave velocity. In concept, crosswell velocity tomograms can define the spatial patterns of these properties in the 2D vertical plane passing through the source and receiver wells.

Elastic wavefield imaging of CSP data provides more information about interwell conditions than do velocity tomograms because the images are presented in wiggle-trace format similar to surface-recorded seismic data. Interpreters can use standard seismic interpretation software to analyze these images, calculate amplitude and frequency attributes, and map stratal surfaces.

Because CSP technology provides data with signal frequencies as high as 1000 to 2000 Hz, some CSP data have dominant wavelengths as short as 3 m [10 ft]. Thus, CSP technology provides a better spatial resolution of reservoir properties than does surface-based seismic technology. By acquiring CSP data in a time-lapse sequence (usually 12 to 15 months between surveys), engineers can often track fluid movements in interwell spaces to determine if secondary recovery processes are performing as planned.

Fig. 2.35 gives a visualization of the portions of a crosswell wavefield that are involved in these approaches to CSP imaging. In this measurement, a source was kept at the depth labeled "Source" in a well that was 1,800 ft [550 m] away from the receiver well in which the data were recorded. A wall-clamped 3C geophone was then positioned in the receiver well at depth stations 25 ft apart, starting at a depth of 6,100 ft and extending up to a depth of 500 ft. Fig. 2.35 displays the response of the vertical geophone in the top wavefield, and the bottom wavefield shows the summed response of both horizontal geophones. It is probably not wise to sum the responses of the two horizontal geophones into a single wavefield because then the SV and SH shear modes (see Fig. 2.7) cannot be distinguished. As a result of this summation, all shear events in Fig. 2.35 are labeled as S, not as SH or SV.

The compressional (P) wavefield arrives first and is followed by the shear (S) wavefield. The arrival times of these wavefields are labeled on the shallow geophone trace. The S wavefront has more curvature than the P wavefront because S velocity is less than P velocity. CSP data record both downgoing reflection events (when the reflecting interface is above the receiver depth) and upgoing reflection events (when the reflecting interface is below the receiver depth). The opposite traveling reflection events create a crisscross pattern in the data, an effect that is pronounced in the S wavefield. The depth at which each S reflection occurs can be determined by extending each of these crisscrossing events back to its point of origin on the S first-arrival wavefront. Many P reflection events exist in the data at times later than the P first-arrival wavefront, but they are difficult to see in these unprocessed data. The labeled linear events sloping up and down behind the P first-arrival wavefront are SV events created by P-to-SV mode conversions at stratal interfaces. These events are better seen on the display of the horizontal-geophone data. The depth at which a reflection occurs can be determined by extrapolating a linear event to intersect the P-wave first arrival. The interpreted reflector depths can then be compared with the depths of rock and fluid interfaces defined by logs recorded in the receiver well and with the formation depths calculated from surface-recorded seismic data.

For a velocity tomography analysis of the interwell space illuminated by the wavefields in Fig. 2.35, the P and S first-arrival times can be picked at each depth station. These travel times then can be used to synthesize the interwell velocity structure by some type of iterative travel-path reconstruction technique. The particular downhole source used in this instance was a vibrator that produced a symmetrical wavelet. In this example, the data are not deconvolved to reduce the wavelet side lobes; thus, the arrival times would be the center point of the long, ringing, symmetrical direct arrivals.

To produce an estimate of the spatial distribution of seismic attenuation properties of the interwell space, amplitudes of the P and S direct arrivals have to be analyzed with other factors such as the consistency of the receiver couplings, the shot-to-shot energy levels, and the geometric shapes of the source radiation and receiver antenna patterns.

To produce P and S seismic images of the interwell space, the reflection portions of the wavefields that are noted need to be processed with interwell velocities determined by the velocity tomography analysis to position each reflection wavelet at its subsurface point of origin. The vertical axis of images created from CSP data is true stratigraphic depth, not image time, because the source and receiver stations are distributed over known depth coordinates. CSP images can be correlated to surface-based seismic images only if the surface data are transformed from the image-time domain to the depth domain.


a(t) = seismic trace amplitude value
Ao = incident seismic amplitude
Ar = seismic reflection amplitude
At = transmitted seismic amplitude
d = depth of air-gun array, L, ft or m
D = depth, L, ft or m
F = 3D stacking fold
FIL = inline stacking fold
FXL = crossline stacking fold
ir = receiver-station interval, L, ft or m
is = source-station interval, L, ft or m
I = seismic impedance, (g•m)/(cm3•sec)
nc = number of receiving channels
nl = number of receiver lines in the recording patch
N1 = number of source-receiver pairs that image target at depth Z1
N2 = number of source-receiver pairs that image target at depth Z2
R = seismic reflection coefficient or seismic receiver
t = seismic traveltime, t, second
v = velocity, L/t
V = velocity of seismic wave propagation, L/t
Vp = propagation velocity of a compressional (P) wave, L/t
Vs = propagation velocity of a shear (S) wave, L/t
W = minimum target width, L, ft or m
x = real data plane
x(t) = real seismic trace
X = offset distance, L, ft or m
y = imaginary plane
y(t) = Hilbert transform of x(t)
z(t) = complex seismic trace
Z1 = shallow target depth, L, ft or m
Z2 = deep target depth, L, ft or m
Δx = inline dimension of stacking bin, L, ft or m
Δy = crossline dimension of stacking bin, L, ft or m
ρ = bulk density of the rock, m/L3, g/cm3
ϕ(t) = phase angle
ω(t) = instantaneous frequency, cycles/sec


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2D (two-dimensional) is an adjective used to describe seismic data acquisition when a single vertical plane can pass through all source and receiver stations. The resulting image is restricted to the vertical plane passing through the source and receiver stations.

3D (three-dimensional) is an adjective used when seismic receivers are distributed across an expansive area surrounding a seismic source station. The point of origin of a reflection event recorded by this areal receiver patch can then be positioned correctly in x, y, z space.

3C (three-component) is an adjective used to describe seismic data acquired with three orthogonal sensors at each receiver station. These sensors measure Earth movement as a vector quantity in x, y, z coordinate space.

4C (four-component) is an adjective used to describe seismic data acquired on the seafloor. These seafloor receivers consist of a 3C geophone that measures vector movement of the seafloor in x, y, z space plus a hydrophone that measures scalar pressure variations at the seafloor.

Air gun is a marine seismic energy source that releases a high-pressure (~2,000 psi) pulse of compressed air to produce a robust, high-resolution seismic wavelet.

Body wave is a seismic wave that propagates in the interior (body) of the Earth. See surface wave.

Bright spot is a dramatic increase in seismic reflection amplitude that makes a subsurface object the dominant feature on any amplitude-based data display. A "true" bright spot is caused by gas replacing liquid in the pore spaces of a reservoir rock. A "false" bright spot is caused by a change in the rock matrix, such as a lateral transition from sand to coal.

Check-hot survey is a seismic measurement involving a seismic source on the Earth surface and a seismic sensor suspended by wireline in a well. The objective is to measure the travel time required for a seismic wavelet to travel from the Earth’s surface to the downhole receiver. Check-shot data allow interpreters to convert seismic image times to stratigraphic depth (or vice versa).

Chronostratigraphic is an adjective meaning "time layer" (chrono=time, strata=layer). Interpreters must define the context in which they are using the term "time" (i.e., geologic time or seismic image time).

Coherency is a numerical measure of the similarity of reflection wave shapes in a user-specified data window. Coherency values are scaled to the numerical range +1 to –1. A value near +1 means the comparison wave shapes are identical; a value near –1 means the wave shapes are identical but have opposite polarities. A value near zero means the comparison wave shapes have little similarity.

Complex seismic trace is the result of applying a Hilbert transform to a seismic trace. A complex seismic trace consists of a real part (the input seismic trace) and an imaginary part produced by the Hilbert transform. The reason for transforming seismic data from the "real" domain to the "complex" domain is that reflection amplitude, phase, and frequency can then be calculated at each time sample point of the seismic wiggle trace.

Crossline is the direction that is perpendicular to seismic receiver lines. See inline.

Crisswell seismic profiling (CSP) data are acquired with a downhole seismic source in one well and downhole seismic sensors in a second well. CSP data provide high-resolution 2D images of geologic conditions across interwell spaces.

Depth-structure map is a seismic-derived map showing the geometry of subsurface structure in terms of depth coordinates. See time-structure map.

Diachronous is a term used to describe a surface or a seismic reflection that cuts across geologic time (dia=across, chrono=time). See chronostratigraphic and stratal surface.

Erosion surface (ES) is a subsurface interface marking an ancient erosional event that has removed portions of one or more stratigraphic units.

Far field is that portion of a seismic propagation medium that is a distance of at least 3 or 4 wavelengths away from a source station.

Flooding surface is a depositional surface marking the transgression of a flooding event across an area. Deeper-water fauna occur above a flooding surface; shallower-water fauna exist below that surface.

Genetic sequence is a package of stratigraphic units that are genetically related. Genetic sequences are bounded by erosional surfaces, flooding surfaces, or maximum flooding surfaces.

Ground force phase locking is a technology that ensures each vibrator in an array of vibrators generates the same source wavelet regardless of variations in soil conditions beneath the vibrator base plates.

Ground roll is a robust, high-amplitude wave produced by onshore seismic sources that travels along the Earth/air interface. A ground-roll wave does not propagate in the interior (body) of the Earth. See Rayleigh wave.

Impedance is the product of bulk density and seismic propagation velocity in the medium in which the wavefield propagates.

Inline is the direction in which receiver lines are deployed. See crossline.

Instantaneous amplitude is the amplitude of a complex seismic trace at a specified time coordinate along that trace. Instantaneous amplitude is not the same as trace amplitude. See complex seismic trace.

Instantaneous frequency is the frequency of a complex seismic trace at a specified time coordinate along that trace. Instantaneous frequency is the time derivative of instantaneous phase. See complex seismic trace.

Instantaneous phase is the phase of a complex seismic trace at a specified time coordinate along that trace. Instantaneous phase is the inverse tangent of the ratio: real part of the complex trace divided by imaginary part of the complex trace. See complex seismic trace.

Love wave is a surface wave that propagates along the Earth/air interface and creates a particle displacement that is tangent to the Earth surface and also perpendicular to the direction of wave propagation. A Love wave does not propagate in the interior of the Earth. See body wave, ground roll, Rayleigh wave, and surface wave.

Low-stand wedge is an asymmetrical accumulation of sediment and strata occurring during a period of lower sea level.

Maximum flooding surface (MFS) is a depositional surface that marks conditions associated with the deepest water depth occurring in a geologic time period of interest.

Ocean-bottom cable (OBC) is a cable-based seismic receiver system that is positioned on the seafloor so shear-wave data can be acquired in addition to compressional wave data. OBC technology usually involves 4C sensors. See 4C.

P wave is a compressional wave. It is sometimes called a primary (P) wave because it is the portion of a seismic wavefield that arrives first at an observation point. A P wave causes rock particles to oscillate in a direction that is perpendicular to its wavefront.

Peak-to-peak (PTP) is a parameter used to describe air-gun performance. An air-gun wavelet consists of a high-amplitude peak followed by a high-amplitude trough. The parameter PTP defines the magnitude of the source wavelet amplitude measured from the apex of the leading peak of the wavelet to the apex of the following trough. A high PTP value indicates a high energy output.

Primary-to-bubble ratio (PBR) is a parameter used to define the performance of a marine airgun array. "Primary" refers to the amplitude of the wavelet created by the output pulse of high-pressure air. "Bubble" refers to the amplitude of the wavelet created by the subsequent collapse of the air bubble in the water column. A high PBR value (~30) is desired.

Rayleigh wave is the correct name for a ground-roll wave. A Rayleigh wave is a surface wave that propagates along the Earth/air interface, not in the body of the Earth. A Rayleigh wave creates an elliptical motion of Earth particles along its propagation path. The horizontal particle displacement associated with this ellipse is oriented in the direction of wave propagation. The horizontal displacements associated with Love waves and Rayleigh waves are orthogonal to each other.

Reflection coefficient is a parameter that defines the amplitude of the wave that reflects from an interface. The magnitude of a reflection coefficient at an interface is linearly proportional to the difference in seismic impedance across that interface. The algebraic sign of a reflection coefficient defines the polarity of the reflection event.

Rollover is a downward bending of strata that often forms a structural trap for oil and gas. The bending movement is initiated by tectonic forces.

S wave is a shear wave. It is sometimes called a secondary (S) wave because it arrives later than the primary wave (see P wave). The term S wave needs to be used carefully because there are several types of shear waves. S waves include SH and SV modes and, in a complex anisotropic Earth, each of these modes (SH and SV) divides into a fast and slow component. Converted SV waves (called C waves) that result when P waves arrive at interfaces at nonnormal angles of incidence are another type of S wave. The term "S wave" spans a large family of distinct wave types.

SH is a shear wave mode that has its particle-displacement vector oriented perpendicular to the vertical plane passing through the source and receiver stations. In a flat-layered isotropic Earth, an SH mode has its particle-displacement vector oriented parallel to horizontal interfaces. See SV.

Stacking bin is the smallest definable area within a 3D seismic image space. The number of stacking bins in a 3D seismic volume is the same as the number of seismic traces in that volume. At the conclusion of 3D data processing, one image trace passes vertically through the center of each stacking bin. The lateral dimension of a stacking bin is the same as the spacing between adjacent traces in the 3D volume.

Stacking fold is a number that specifies how many seismic field traces are summed to create a final image trace in a 3D seismic volume. A stacking fold of 20 means that 20 field traces were summed to create one stacked trace.

Stratal surface is a depositional surface associated with a fixed geologic time. Geologic time is constant along a stratal surface, but the rock types above and below the surface can vary.

Surface wave is a seismic wave that trends along an interface, particularly along the Earth/air interface. Surface waves do not enter the body of the Earth and image deep targets. See ground roll, Love wave, and Rayleigh wave.

SV is a shear-wave mode that has its particle-displacement vector oriented in the vertical plane passing through the source and receiver stations. An SV displacement vector is orthogonal to an SH displacement vector. See SH.

Synthetic seismogram is a mathematical construction of a seismic wavefield. Synthetic seismograms can be calculated in 1D, 2D, or 3D data space. Either downgoing wavefields, upgoing wavefields, or both can be included in the calculation.

Thin bed is a sedimentary layer with a thickness less than one-fourth of the length of the dominant wavelength in the illuminating seismic wavefield. Typical dominant wavelengths can be 200 to 300 ft (~65 to 100 m); therefore, many thin beds have thicknesses of 50 to 75 ft (~15 to 22 m). The top and base of a thin bed cannot be resolved in a seismic image.

Time slice is a horizontal slice through a 3D seismic data volume. Seismic image time is constant across a time slice, but geologic time is not, unless the stratigraphy is perfectly flat.

Time-structure map is a map identifying the seismic image times at which subsurface structure is located. Time-structure maps can be converted into depth-structure maps if seismic propagation velocity can be defined throughout 3D seismic image space. See depth-structure maps.

Tomograms are popular products produced by crosswell seismic profiling. A CSP velocity tomogram shows the spatial distribution of seismic propagation velocities in the interwell space between a source well and a receiver well.

Vibrator is a popular onshore seismic energy source. Vibrators are large vehicles weighing 60,000 lbs or more. They transmit seismic energy into the Earth through a heavy baseplate that is pressed to the ground and then vibrated over a prescribed frequency range.

Vertical seismic profile (VSP) data are acquired with an energy source on the Earth’s surface and a vertical array of closely spaced receiver stations in a well. VSP receiver stations are positioned vertically at increments of approximately 50 ft (15 m). This small spatial sampling allows all wave modes (downgoing, upgoing, shear, compressional) to be separated from the raw data.

SI Metric Conversion Factors

ft × 3.048* E − 01 = m
mile × 1.609 344* E + 00 = km
psi × 6.894 757 E + 00 = kPa


Conversion factor is exact.