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. 1). Horizontal-dipole sources can create strong SH modes in onshore programs. No effective seismic horizontal-dipole sources exist for marine applications.

• 

  Fig. 1 – Basic elements of ocean-bottom cable data acquisition. P denotes a seismic compressional wave; SV is a converted shear mode.

Seismic wave model

A principal difference among P, SV, and SH wavefields is the manner in which they cause rock particles to oscillate. Fig. 2 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.

• 

  Fig. 2 – Distinction between the three components of an elastic wavefield.

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 V_p in consolidated rocks, which is approximately two times faster than velocity V_s of either the SH or SV wave. In carbonates, the velocity ratio (V_p/V_s) tends to be approximately 1.7 or 1.8. In siliciclastics, V_p/V_s 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).

The P, SH, and SV particle displacements shown in Fig. 2 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. 3). 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. 3).

• 

  Fig. 3 – Particle motions produced by the two principal seismic surface-wave noise modes: the Love wave and the Rayleigh wave.

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

....................(1)

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 V_p if the wave mode of interest is a P wave; it is set to V_s 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.

Reflection coefficients

Seismic reflectivity is best explained with a simple two-layer Earth model in which Layer 1 is above Layer 2 (Fig. 4). The seismic reflection coefficient, R, for a downgoing particle-velocity wave mode that arrives perpendicular to the interface between the two layers is

....................(2)

A negative algebraic sign has to be inserted on the right side of Eq. 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 (ρ₁V₁ – ρ₂V₂) across the interface.

• 

  Fig. 4 – Two-layer Earth model describing seismic reflectivity parameters.

A seismic reflection/transmission process is indicated in Fig. 4 by the raypaths labeled A_o, A_r, and A_t. 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. Aki and Richards gives a detailed mathematical treatment. The seismic reflection, A_r, is given by

....................(3)

and the transmitted seismic event, A_t, is given by

....................(4)

The magnitude and algebraic sign of A_r depends on R and, in turn, the basic control on R is the variation of impedance ρV across the interface (Eq. 2). Table 1- Geological influences on acoustic impedance. 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. 5 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. 5). 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.

• 

  Fig. 5 – Relationships between petrophysical conditions that occur at an impedance boundary and the existence of P and S reflections at that 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.)

Nomenclature

Ao	=	incident seismic amplitude
Ar	=	seismic reflection amplitude
At	=	transmitted seismic amplitude
I	=	seismic impedance, (g•m)/(cm3•sec)
R	=	seismic reflection coefficient or seismic receiver
V	=	velocity of seismic wave propagation, L/t
ρ	=	bulk density of the rock, m/L3, g/cm3

Noteworthy papers in OnePetro

Use this section to list papers in OnePetro that a reader who wants to learn more should definitely read

External links

Use this section to provide links to relevant material on websites other than PetroWiki and OnePetro

See also

Vibration theory

Seismic imaging and inversion

Seismic data acquisition equipment

Seismic interpretation

Geological influences on acoustic impedance

PEH:Fundamentals_of_Geophysics