PEH:Reservoir Geophysics

Publication Information

Petroleum Engineering Handbook

Larry W. Lake, Editor-in-Chief

Volume VI – Emerging and Peripheral Technologies

H.R. Warner Jr., Editor

Copyright 2007, Society of Petroleum Engineers

Chapter 1 – Reservoir Geophysics

By Wayne D. Pennington, Michigan Technological U.

Pgs. 9-58

ISBN 978-1-55563-122-2
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Introduction

Reservoir geophysics, in contrast to exploration and development geophysics, is a relatively new field. Rather than being limited to assisting in the identification and delineation of prospects, geophysics is now increasingly being used for the characterization of the internal geometry and quality of reservoirs themselves and is often used as a means of monitoring reservoir changes between wells during production. Advances in the reliability of seismic observations and in methods for interpreting these observations in terms of reservoir properties have, together with economic considerations, provided the driving forces for the development of reservoir geophysics. The chapter on Fundamentals of Geophysics in the Reservoir Engineering and Petrophysics section of this Handbook addresses the concepts used in seismic studies and is a useful introduction to the general topic. This chapter expands on the applications of geophysical technologies to reservoir characterization and monitoring for improved production.

Overview

Differences from Exploration Geophysics

There are several specific differences between exploration geophysics and reservoir geophysics, as the term is usually intended. The differences include: the assumption that well control is available within the area of the geophysical survey; a carefully designed geophysical survey can be conducted at a level of detail that will be useful; some understanding of the rock physics is available for interpretation; 3D seismic (or other geophysical) data can be collected; and geostatistical techniques can be applied to it. The reservoir geophysicist should be familiar with the usefulness and limitations of petrophysical and reservoir-engineering studies and should be able to ask intelligent questions of the experts in those fields. However, the reservoir geophysicist typically is not an expert in those areas and works with the appropriate specialists to interpret the data or to design a new experiment to solve reservoir problems.

Well Control

In exploration, extrapolation of well data from far outside the area of interest is often necessary, and the interpretation is required to cross faults, sequence boundaries, pressure compartments, and other discontinuities that may or may not be recognized. The interpreter resorts to analogs in the absence of hard data, and local calibration of the geophysical response is generally poor. In reservoir geophysics, it can often be assumed that a reservoir is already under production or at a late stage of development; therefore, wells are available for analysis, providing a variety of information. The interpreter has access to edited and interpreted well-log data, descriptions of the lithology (including the mineralogy, porosity, and perhaps even the morphology of the pore spaces), and the fluid content (sometimes related to either logged conditions or virgin reservoir conditions). In addition, detailed depth constraints for geologic horizons are available, whereas exploration-based seismic data is limited to estimates of time-to-depth conversions that are inaccurate without well ties. If a well has been tested, there may be estimates of the proximity to boundaries, aquifers, or other features of interest. If the reservoir has been under production, good estimates of the total volume of the reservoir are also available. The asset team can relate these observations to the geologic interpretation, and thereby determine the need for seismic surveys at increased resolution. Additional information is usually available concerning the in-situ conditions of the reservoir, including the formation temperature, pressure, and the properties of the oil/gas and brine.

Rock Physics Control

Reservoir geophysics studies are directed at differentiating between competing reservoir models or at developing new ones. The ability of a given study to accomplish this lies not just in the geophysical model but in the rock physics, or "seismic petrophysics," of the reservoir rock and neighboring formations Logs, particularly sonic logs of compressional and shear velocities, when combined with density logs and with image logs, can be used (carefully) to provide basic seismic properties, which are in turn modeled for variations in lithologic character, fluid content, and in-situ conditions such as pore pressure. Core samples can be used to provide the basis for a theoretical framework or measurements on them can be used (again, carefully) to provide the same basic seismic properties. Reservoir geophysicists should always be on the alert for accidental misuse of the input data. They should also be concerned with upscaling of the properties, particularly with the possibility that physical effects occuring at one scale not be mistakenly applied at other scales (such as the increased incompressibility observed in laboratory ultrasonic experiments on saturated rocks). Rock properties of interest to reservoir geophysicists are described in the General Engineering volume of this Handbook. An excellent summary of rock physics aspects, appropriate for reservoir geophysics studies, is found in Mavko, Mukerji, and Dvorkin.

Survey Design

The design of a seismic survey for reservoir geophysics purposes can often be optimized for specific interpretation goals. Once a field has been discovered, developed, and under production for some time, information is available to the geophysicist, allowing a geophysical survey design that maximizes the likelihood that the data collected will significantly aid reservoir management. That is, if the goal of the survey is to define the structural limits of the field, a 3D seismic survey can be designed with that in mind. If, however, the goal of the survey is to define the extent of a gas zone, the geophysicist may be able to use log data, seismic petrophysical modeling, and pre-existing ("legacy") seismic data to determine which offset ranges are required, for example, to differentiate between the water and gas zones. If highly accurate well ties or wavelet phase control are needed, an appropriately placed vertical seismic profile (VSP) may be designed. Or, if an acquisition "footprint" (features that appear in seismic data but are acquisition-related artifacts) was observed in a previously acquired seismic data set and that footprint obscured the attributes needed to define the reservoir target, the geophysicist can design the new survey in a way that eliminates the troublesome artifacts. In short, the fact that the target is well known permits the reservoir geophysics survey to be designed in a more enlightened manner than a typical exploration survey. The expense of a properly conducted seismic survey for reservoir characterization purposes can often be justified (or at least properly evaluated) because the financial impact of the survey can be calculated with greater confidence than for typical exploration seismic surveys.

3D Seismic Data

Most reservoir geophysics is based on reflection seismic data, although a wide variety of other techniques are employed regularly on specific projects. Nearly all seismic data collected for reservoir studies is high-fold, three-dimensional, vertical-receiver data (see the petrophysics chapters in the Reservoir Engineering and Petrophysics volume of this Handbook), and many good case histories have been published. In order to overcome specific problems, however, the use of multicomponent receivers on land or on the seafloor and of multicomponent sources on land is increasing. Most seismic surveys are designed to exploit compressional (P) waves using hydrophones or vertical geophones, but some are designed to record shear (S) waves using horizontal and vertical geophones.

One increasingly common usage of multicomponent seismology involves imaging beneath gas clouds. Gas clouds encountered above reservoirs obscure the P-wave image by intense scattering of these waves because of the strong velocity dependence of P-waves on saturation. Seismic waves that are converted from P to S at the reflecting horizon (also called C-waves) are often used to image reservoirs beneath such gas clouds, by allowing a downgoing P-wave to pass underneath the gas cloud, while the upcoming converted S (or C) wave, which is much less sensitive to scattering by gas, passes through the cloud without significant distortion. Fig. 1.1 demonstrates the geometry that makes undershooting a gas cloud possible with converted waves.

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  Fig. 1.1—Geometry of undershooting a gas cloud over a reservoir of interest. The upper diagram shows the paths taken by a selected P-wave seismic ray; scattering, because of the velocity inhomogeneity caused by the pockets of gas, result in an inability to image through the gas cloud. The lower diagram shows the path taken by one selected converted (C) wave. This ray enters the sea floor (at the top edge of the figure) as a P-wave and converts on reflection at the top of reservoir to an S-wave (dashed); because fluid content has little effect on the velocity of S-waves, this ray is not scattered, and the reservoir can be imaged using multicomponent receivers on the seafloor.

The recognition that fractures play an important role in many reservoir development schemes has led to a number of experimental programs for multicomponent sources and receivers in an effort to identify shear-wave splitting (and other features) associated with high-fracture density. These studies make use of the fact that shear waves, polarized in directions parallel to the fractures, travel faster than those polarized perpendicular to fractures. In fact, an arbitrarily polarized shear wave will split into two polarized shear waves—one, polarized parallel to the fracture trend faster than the other, as shown in Fig. 1.2. Several case histories, demonstrating the use of shear-wave splitting, have been published, and the technology is gaining greater acceptance in the industry.

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  Fig. 1.2-Splitting of polarized S-waves. Shear wave splitting is because of propagation through vertically aligned fractures. An arbitrarily polarized shear wave will separate into two orthogonally polarized waves; the faster one will be polarized in a direction parallel to the fracture direction (after Hitchings and Potters)

Although some of these techniques are being used increasingly often, at the present, most surface seismic studies designed to characterize existing reservoirs are high-quality 3D surveys using vertical-component-receiver surveys on land or hydrophone streamers at sea.

Geostatistics

In contrast to exploration geophysics, in which fully deterministic models can be required for interpretation because of the lack of well data, reservoir geophysics studies are often faced with huge volumes of data, not all of it consistent, yet also not complete. Geostatistical techniques (see the chapter on Geologically Based, Geostatistical Reservoir Modeling in this section of the Handbook) have been developed to manage this data and its inconsistencies and incompleteness. For example, simple averaging between wells can easily lead to misleading results, so the technique of kriging was developed for use with features observed to correlate over certain distances (usually from other data). The technique has been refined to include data that provide additional "soft" evidence between the "hard" data locations at wells, and seismic data often provide the soft evidence. If a statistical (and physically meaningful) correlation is found to exist between formation parameters observed at wells and some seismic attribute observed throughout the study area, geostatistical techniques are available that honor the hard data at the wells, and interpolated between wells (generally using kriging and cokriging techniques), simultaneously honoring the seismic interpretation, to a greater or lesser degree. Various "realizations" of properties in the interwell regions can be generated using additional geostatistical techniques, with each realization being just as likely to occur as any other. The use of seismic data, with reliable predictive capabilities, can significantly reduce the range of such models. Many case histories, using these approaches, have been published.

Focused Approaches

A reservoir geophysics study generally focuses on a specific target, makes use of legacy seismic data calibrated to wells, and employs models of the seismic petrophysical responses of various scenarios anticipated in the reservoir. As a result, a reservoir geophysics study could collect that data, and only that data, which will be required to observe the features of interest. For example, one could acquire only far-offset seismic data, if one were convinced that the far offsets contained all the information that was essential to the study. It is not clear that such highly focused approaches are being used; which is true probably because the cost savings do not warrant the added risk of missing an important piece of data. There may also be a natural aversion to collecting, purposefully, data that are not as "good" or "complete" as conventionally-acquired seismic data.

Attributes

In most exploration and reservoir seismic surveys, the main objectives are, first, to correctly image the structure in time and depth and, second, to correctly characterize the amplitudes of the reflections. Assuming that the amplitudes are accurately rendered, a host of additional features can be derived and used in interpretation. Collectively, these features are referred to as seismic attributes. The simplest attribute, and the one most widely used, is seismic amplitude, and it is usually reported as the maximum (positive or negative) amplitude value at each sample along a horizon picked from a 3D volume. It is fortunate that, in many cases, the amplitude of reflection corresponds directly to the porosity or to the saturation of the underlying formation.

Attributes can be obtained from typical post-stack seismic data volumes, and these are the most common types. On the other hand, additional information can be obtained from attributes of the individual seismic traces prior to stacking, in a prestack analysis. The most common of these is the variation of amplitude with offset [or amplitude vs. offset (AVO)], which is often used as an indicator of fluid type. The interpretation of any attribute is nonunique, and calibration to well data is required to minimize the ambiguities present.

Well Calibration

Calibration of seismic attributes at wellbores, using all available log data, core data, and borehole seismic information, should be undertaken in order to test the correlation of observed attributes with rock properties. It is simple to correlate the attribute of interest with the well-log (or log-derived) data of interest; a strong correlation between seismic amplitude and porosity is often enough to convince many workers that the correlation is meaningful and that seismic amplitude can be used as a proxy for porosity in reservoir characterization. On the other hand, there are many potential pitfalls in this approach, so statistical tests should be performed on the correlations; geologic inference should be brought in to evaluate the reasonableness of the results; and, most importantly, the physical basis for the behavior of an observed attribute should be understood. Spurious correlations can readily be obtained, and, without a geologic or physical basis, simple statistical correlations should be suspect unless their statistical basis is very robust.

Post-stack Attributes

The stacked seismic data volume is commonly used for interpretation of geologic structure and seismic attributes. The most common attribute is simply amplitude, although its interpretation in thin-layered beds is not necessarily straightforward. Amplitude is often found to correlate strongly with porosity and/or liquid saturation (oil/water vs. gas) because those reservoir properties have a strong effect on both velocity and density, and seismic reflections are generated at boundaries where the acoustic impedance (the product of velocity and density) changes. The "bright-spot" identifiation of hydrocarbons, as demonstrated in Fig. 1.3, is a result of this property, although other nonhydrocarbon changes in lithology can also result in large-amplitude reflections.

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  Fig. 1.3-Amplitudes resulting from changes in seismic impedance. A perspective view of a single horizon containing several potential reservoirs is shown from the Teal South area of the Gulf of Mexico (from Pennington et al.). The coloring is based on the amplitude of the reflected arrival at this horizon, with the hotter colors indicating larger (negative) amplitudes, resulting (in this case) from high-GOR oil in both producing and unproduced reservoirs. The reservoirs have been highlighted for increased visibility on the black-and-white version of a typically color display. (Data provided by Diamond Geophysical, through the Energy Research Clearing House.)

The use of seismic attributes extends well beyond simple amplitudes. Most of the "original" seismic attributes were based on the Hilbert transform (see the section on reservoir characterization and evaluation) and consisted of the instantaneous amplitude (or amplitude of the wave envelope); the instantaneous phase (most useful for accurate time-picking); and the instantaneous frequency (probably most often relating to thin-bed reverberations) (see Fig. 1.4). Variations on these attributes have evolved, and other classes of attributes have come into use (see Fig. 1.5). There are now over two hundred attributes in use in some geophysical interpretation software packages; many of these attributes result from slightly differing approaches to determining a specific property, such as frequency or amplitude. Attributes based on stacked data (post-stack attributes) can be computed at each point on the seismic trace independently (such as amplitude); over a time window on each trace independently [such as root mean square (RMS) amplitude over 24 ms]; or by comparing neighboring traces within a time window (such as coherence, dip, and azimuth). Coherence is an attribute of similarity among neighboring traces and is often used to identify fractures or faults that tend to disrupt reflections locally (see Fig. 1.6). Dip and azimuth describe the direction of trace offset for maximum similarity and can yield finely detailed images of bed surfaces. Additional attributes may be created based on combinations of original attributes, with the intention of identifying specific features known to be of interest (see Fig. 1.7).

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  Fig. 1.4-Some trace-based attributes. The original seismic trace from one location in a seismic volume is shown on the left; the three common attributes of instantaneous amplitude (or envelope), instantaneous phase (wrapped), and instantaneous frequency follow to the right. Additional attributes of average energy and peak-to-trough ratio are also shown. The values of these attributes are usually not important, and often not cited, because it is the relative value of an attribute along a given horizon or interval that is important. Exceptions would be the phase (which varies from –180 degrees to +180 degrees in the plot shown) and frequency (which varies from 0 to 110 Hz). (This figure was modeled after one in Radovich

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  Fig. 1.5-Classification of attribute types. Attributes can be point-based along a given time slice or horizon, or they can be based on a window that is constant in time, time associated with a given horizon, or times associated with two horizons (after Brown).

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  Fig. 1.6-Coherence and faults or other discontinuities. The upper portion of the figure shows a time-slice through the coherence volume of a deformed area in the Gulf of Mexico; the faults are clearly visible and easy to track laterally. The lower portion shows a conventional amplitude display of the same time-slice in which the doming, because of salt movement (at depth), is evident, but the faulting is less easily identified (after DeAngelo and Wood).

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  Fig. 1.7-Use of combined attributes. This map shows a specific attribute, made up of a combination of two other attributes (instantaneous frequency and amplitude), designed to indicate specific features. The black arrow points to the red regions of low frequency and high amplitude, which likely correlate (in this instance) with high-productivity regions within the overall sand body that is outlined in white (after Radovich and Oliveros).

Prestack Attributes (AVO)

The volume of seismic data available to the interpreter is usually the stacked-data volume, resulting from the stacking of all of the moveout-corrected traces, each with a different offset between the source and receiver but with reflection points at a common location. In post-stack analysis, it is assumed that the composite (stacked) trace exhibits the seismic reflection character as that which would result from single source-receiver pairs with no separation. Under these conditions, the reflection coefficient, R₀, at each interface between two layers is determined by the ratio of the difference in acoustic impedance between these two layers, ΔI, to twice the average acoustic impedance and is written as

....................(1.1)

V_p and ρ are the P-wave velocity and density of the medium; subscript 2 indicates the medium that is causing the reflection and containing the refracted or transmitted rays, and subscript 1 indicates the medium that is containing the incident and reflected seismic rays. (See additional discussion, particularly concerning sign conventions, in the Fundamentals of Geophysics chapter in the Reservoir Engineering and Petrophysics volume of this Handbook, where R₀ is called R.)

This "zero-offset" approximation is often satisfactory for interpretation of the seismic data, but it neglects a potentially important component: the amplitude variation with offset (or AVO), as shown in Fig. 1.8. As a result of boundary conditions (such as conservation of energy and continuity of displacement) across a reflecting interface between two layers, any P-wave arriving at non-normal incidence is likely to produce not only a transmitted P-wave and a reflected P-wave but also a transmitted S-wave and a reflected S-wave, with angles determined by Snell's law (Fig. 1.9) and amplitudes determined by a set of equations known as Zoeppritz equations.

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  Fig. 1.8-Seismic gather showing an AVO effect. This seismic gather demonstrates an amplitude increase with offset (toward the left) for the reflection at about 2.85 seconds. This figure shows the basic components of seismic data. Each “trace” is the recording of ground velocity at a specific location, with varying distance from the source, ranging from “near” (perhaps a few meters) to “far” (up to a kilometer or two). The positive values have been filled in with black to aid the eye in correlating reflection events from trace to trace (from Dey-Sarkar and Svatek).

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  Fig. 1.9-Snell’s law illustrated in diagram form. In this example (and in general for reflection seismology), the wave incident on an interface between two layers is a downgoing P-wave. At the interface, it separates into reflected upcoming P- and S-waves and transmitted or refracted P- and S-waves, each with the appropriate angle. In this diagram, the length of the rays roughly indicates the relative velocities; that is, V_p2 > V_p1 > V_s2 > V_s1.

Snell's law governs the angles of reflection and transmission for a given angle of incidence (i) and is determined by the velocities on either side of the reflection/transmission boundary. It can be derived by applying the boundary condition that the apparent velocity V_app along the boundary is required to be identical on either side of the boundary.

....................(1.2)

The ray parameter, p, is also termed the slowness and is constant for any given incident ray and all of the reflected and transmitted rays that result from striking that boundary. This expression is usually implemented for an incident P-wave by recognizing the relationships shown in Eq. 1.3. The subscripts are identified in Fig. 1.9.

....................(1.3)

In AVO studies, the dependence of the reflected P-wave amplitude on the contrast between the P and S velocities in both layers is exploited. In particular, a simple approximation can often be applied to predict the amplitude as a function of angle of incidence (determined by Snell's Law), as shown in the example in Fig. 1.10. The interpretation is generally made in terms of the slope or gradient (B) of the amplitude as plotted against the square of the sine of the angle of incidence and the intercept or zero-offset reflection amplitude (R₀).

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  Fig. 1.10-Dependence of amplitude on offset. The upper diagram shows the (exact) amplitude-vs.-offset behavior for a specific shale-over-sand example typical in parts of the Gulf of Mexico. Squares indicate 5-degree increments in angle of incidence (i) for the P-wave at the interface, with a larger square at 30 degrees. The lower diagram shows the same data plotted against the square of the sine of the angle of incidence, and compares the exact solution with Shuey’s approximation.

....................(1.4)

B is primarily a function of the change in Poisson's ratio across the interface. This is only one of many approximations to the complete solution, but it is the one most commonly used. For offsets corresponding to angles of incidence greater than about 30 degrees, a more complete relationship must be substituted.

The advantage to using prestack attributes is that they can provide some distinction between lithologic changes and changes in reflection character because of fluid content along an interface. The ratio of P-wave velocity (V_p) to S-wave velocity (V_s) is often very sensitive to the compressibility of the fluid within the pore spaces of the rock and not very sensitive to the porosity of the rock; that is, within a given formation, the changes in V_p / V_s, because of anticipated changes in saturation, are generally much greater than those anticipated from changes in porosity or lithology. Variation in rock types and pore structures is great, and local calibration is essential, but the empirical results summarized in Fig. 1.11 can be useful. Poisson's ratio, ν, and the V_p / V_s ratio can be related through Eqs. 1.5 and 1.6 and the graph shown in Fig. 1.12.

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  Fig. 1.11-Empirical relationships of V_p and Poisson’s ratio. The model of Greenberg and Castagna can be used to generate curves of the relationship between Poisson’s ratio and P-wave velocity for pure rock types, as shown here. This sort of guide is useful when little or no local calibration is available.

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  Fig. 1.12-Comparison of V_p/V_s and Poisson’s ratio, obtained from Eqs. 1.5 and 1.6.

....................(1.5)

and

....................(1.6)

The results of many studies are expressed in terms of Poisson', ν, although V_p / V_s may be more physically meaningful. A variety of AVO attributes has been developed using different combinations of the AVO slope and intercept, generally with the intention of maximizing the distinctions between fluid types. Some formulations break the AVO trend into three components to isolate density contrasts, as shown by example in Fig. 1.13. As more offset ranges are used (and as each range gets narrower), the results tend to be noisier, and the robustness of the process suffers as additional parameters are sought.

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  Fig. 1.13-An example of using three-parameter amplitude-vs.-offset attributes applied to a field that has been produced. The map on the left shows the amplitude along the horizon, indicating hydrocarbon regions; the map in the center shows an AVO map indicating the same regions. The map on the right indicates differences in density, as derived from a three-component AVO model and indicates that large portions of the reservoirs in blocks 1 and 2 have been reduced to residual hydrocarbon saturation, but those in blocks 3 and 4 remain at high hydrocarbon saturation (after Skidmore et al.).

Ultra-Thin Beds

Methods to extract meaningful interpretations from seismic data in the presence of thin beds (less than one seismic wavelength in thickness) are discussed in the chapter on Fundamentals of Geophysics in the Reservoir Engineering and Petrophysics section of this Handbook. Additional techniques have recently been developed, which help the interpreter identify properties of extremely thin beds well below what has traditionally been considered the quarter-wavelength resolution of seismic data. These techniques make use of the various frequency components within a band-limited seismic wavelet; one operates in the frequency domain, and the other in the time domain.

The frequency-domain approach, called spectral decomposition, looks for notches in the frequency band representing an interference between the reflections from the top and bottom of the thin bed. The frequency at which constructive and destructive interference occurs is related to the (two-way) time-thickness of the bed; because the seismic wavelet contains a range of frequencies, spectral notches or peak frequencies can be used to indicate extremely thin beds. Additional attributes can be derived from the spectral character of the reflections, further refining an interpretation. The thinning-out of a channel or shoreline, for example, can be observed by mapping the locations of various frequency components, as shown in Fig. 1.14.

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  Fig. 1.14-Ultra-thin bed example. This map shows an attribute calculated over a 100-ms window centered on a mapped horizon within which distributary channels were known to exist. This attribute represents the peak frequency within that window, and clearly indicates the thickest parts of the channels (white) and the thinner, and less productive parts ranging from gray to black. (From Marfurt and Kirlin, where the figure is in color.)

The time-domain approach involves classifying the character of the reflected wavelet, often using a neural-network technique. The wavelet along a given horizon can be classified into several different characteristic wavelets, perhaps differing from each other only in subtle ways. The resulting map of classified wavelets can resemble a map of the geologic feature being sought (see Fig. 1.15), and the classification is often referred to a "seismic facies" classification. Because this method tends to compare relative amplitudes of features within a wavelet packet (side lobes vs. main lobes, for example) or slight changes in period, it often responds to interference from very thin features that were previously considered to be below seismic resolution.

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  Fig. 1.15-Seismic facies classification map and wavelets. The classification of this reservoir has been accomplished by recognizing similarity (using a neural network approach) of waveforms in four classes, based on representative waveforms at four wells, as shown.

Both of these techniques run the risk of leading to incorrect interpretations if seismic petrophysical modeling is not performed to direct the analysis and interpretation or to confirm the results. The processing involved can produce signals that appear realistic but are geologically meaningless, unless care is taken to ensure that the interpretation is physically sound.

Imaging and Inversion

The ability of seismic reflection technology to image subsurface targets is possible largely through the geometry of sources and receivers. A method similar to triangulation is used to place reflections in their correct locations with (more-or-less) correct amplitudes, which can then be interpreted. The amplitudes are indicative of relative changes in impedance, and the seismic volume can be processed to yield impedances between the reflecting boundaries.

Stacking and Interval Velocities

The geometry of sources and receivers in a typical reflection seismic survey yields a number of seismic traces with common midpoints or central bins for stacking. These traces were recorded at different offset distances, and the travel times for seismic waves traveling to and from a given reflecting horizon varies with that distance (Fig. 1.16). If the overburden through which the seismic waves pass is of constant velocity, then the time-variation with distance is a simple application of Pythagorean geometry, and the shape of the reflector on a seismic "gather" of traces is hyperbolic. As the overburden velocity structure becomes more complex, the shape is less perfectly hyperbolic, but most standard processing routines still assume a hyperbolic "moveout" of each reflector. An analysis is then made of selected seismic gathers to establish the ideal moveout required to "flatten" each reflection in the gather. This moveout is expressed in terms of a velocity and represents the seismic velocity that the entire overburden, down to the point of each particular reflection, would have to result in the idealized hyperbolic shape observed. This velocity analysis is usually conducted by examining the semblance (or some other measure of similarity) across all the traces, within a moving time window, and for all reasonable stacking velocities (Fig. 1.17). The seismic processor then selects the best set of velocities to use at a variety of reflectors and constructs a velocity function of two-way travel time. These velocity functions are interpolated, both spatially and in two-way travel time, and all seismic gathers are then "corrected for normal moveout" using them. Each moveout-corrected gather is then summed or "stacked" after eliminating ("muting") those portions of the traces that have been highly distorted by the moveout process.

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  Fig. 1.16-Ray diagram for normal moveout and a synthetic seismic gather. At the top of the figure is a schematic ray diagram, showing an earth model with four reflecting interfaces; rays are drawn from three source locations to three receiver locations, as they are reflected from two of the interfaces (the other source-receiver rays and reflections from other interfaces are not shown). The lower part of the figure

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  Fig. 1.17-Velocity analysis (on the right) of a single common midpoint gather (on the left). The gather is analyzed over narrow time windows for the values of semblance (or some other measure of similarity) according to a range of stacking velocities. The contours indicate the level of semblance, and the processing geophysicist selects the values deemed to be because of primary reflections and not events

The final stacked traces exhibit a considerably better signal-to-noise ratio than the individual seismic traces recorded at zero-offset, but the improvement is better than just the square root of the number of traces that might be expected because of the systematic removal of coherent noise. Much of the noise present in individual seismic traces is not random but represents unwanted events, including surface waves or ground roll and multiply-reflected arrivals from shallow horizons; both of these can usually be identified in the velocity analysis and selected against. The stacking process then removes most of the unaligned energy associated with these types of coherent noise.

The velocities obtained in the analysis previously described are not true seismic velocities—they are simply those velocities which provided the best stack of the data and may or may not truly reflect the actual root mean square (RMS) velocities that approximate the accumulated effect of the stack of layers above the reflector (the name RMS is derived from the arithmetic used to define this overall velocity). If we assume, however, that the stacking velocities do in fact provide a reasonable approximation to the aggregate effect of the layers overlying each reflector, the actual velocities of each layer can be obtained through a set of equations because of Dix (see Fig. 1.18). These "interval" or "Dix" velocities can sometimes be used to characterize the rocks in each layer and may be sufficiently precise to enable differentiation of gross rock types, although the errors associated with interval velocities can be fairly large.

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  Fig. 1.18-Interval velocities. The stacking velocities are those obtained from the velocity analysis (see Fig. 1.15); from these, the velocities of various intervals can be estimated (after Connolly).

Time and Depth Migration

Even after accounting for normal moveout and stacking the gathered traces to a common zero-offset equivalent set of traces, the locations of the reflected events are not usually correct because of lateral variations in velocity and dipping interfaces. Fig. 1.19 shows a simple 2D example of a dipping interface from which we observe a reflection. Each seismic trace is plotted directly beneath the respective midpoint or bin location used for stacking, but the reflection from any given interface may not have come from that location. The events have been shifted downdip to deeper locations, and the dip of the interface is less steep. To correct for this shift, the seismic processor "migrates" each sample to its appropriate position. In the simple case shown in the figure, we need only know the velocity of the one overlying layer, but in more realistic cases, the velocity function may be quite complex and is derived through a trial-and-error approach guided by statistical tests of lateral coherence, knowledge of expected geologic structure, and other constraints such as interval velocities and well log data. The problem can become quite difficult in complicated 3D data sets, and software has been developed to manage and visualize the velocity volume. The result of this model-driven 3D migration can be somewhat subjective, and, although it is possible to create structures where none really exist through this process, migration should be performed on all seismic data sets for appropriate imaging of structures. 3D migration can drastically improve the imaging of virtually any target by improving the accuracy of the spatial location of various features and by sharpening the image itself, allowing finer resolution than either migrated 2D data or unmigrated 3D data (see Fig. 1.20). The results can occasionally be quite dramatic for interpretation; for example, a locally high feature on an unmigrated data set may move to a significantly different map location after migration. In general, the more dramatic the structure, or the larger the velocity contrasts between layers, the more important 3D migration is for proper imaging.

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  Fig. 1.19-Migration of one dipping interface. The true Earth model (in two-way travel time) for a simple dipping interface is shown at the top, with normal-incidence (zero-offset) seismic rays drawn to two surface source-and-receiver locations. Because the seismograms are plotted directly beneath the surface locations, a seismic section will display the dipping interface at the incorrect location, as shown at the bottom. Notice that the seismic images the event downdip of its true location and with a less-steep dip. The processing step of migration attempts to correct for this, displacing the events back to their true locations.

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  Fig. 1.20-Example of improvement using 3D migration. These three panels show the same cross section of the Earth. The panel on the left was imaged as a 2D stack, extracted from a 3D data volume without migration. The panel in the center was imaged using 2D migration techniques. The panel on the right was

The process of imaging through modeling the velocity structure is a form of inversion of seismic data, and the term inversion is often used to imply building a velocity model which is iteratively improved until it and the seismic data are optimally in agreement. Improvements in imaging are continually being made, and research in this area is one of the most fruitful in reservoir and exploration geophysics. The current methods of migration involve operating in two-way travel time (as previously described), or in depth (using the model velocities to convert from travel time to depth), and either method can be performed prestack or post-stack. In addition, there have been a number of shortcuts developed over the years to provide reasonable results in a short time; all of the methods are quite computation-intensive, and the technology has benefited greatly from improved computing capacity. The finest results can usually be obtained from prestack depth migration, in which each sample of each trace, prior to gather, is migrated using the velocity function to a new location then stacked and compared with various tests for model improvement; the model is changed, and the process is repeated.

In areas where it is important to image beneath layers of high velocity contrasts, such as beneath salt bodies, prestack depth migration is required. The example shown in Fig. 1.21 shows the possible improvements that can be obtained using prestack depth migration. The process required to create the final stack is as follows: a velocity model is first constructed through the water and sediment layers to the top of salt, and prestack depth migration is used to optimize that model. Then, the salt velocity (which is fairly constant and typically much higher than the surrounding sediments, resulting in severe bending of seismic ray paths) is used for the half-space beneath the top of salt. The reflections from the base of the salt body then appear, although the underlying sediments are very poorly imaged. Finally, the velocity model within these sediments is modified until an acceptable image is obtained.

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  Fig. 1.21-Improvements in imaging using different migration techniques. The upper part shows a result of imaging beneath salt using prestack time migration; the middle part uses post-stack depth migration; and the bottom uses prestack depth migration. Note the increasing ability to image sediments below the salt body (after Liro et al.).

Trace Inversion for Impedance

Seismic reflections at zero offset result from contrasts in acoustic impedance, involving just the P-wave velocity and density of the layers at the interface. If we can identify the seismic wavelet that propagated through the earth and reflected from the layer contrasts, we can then remove the effect of that wavelet and obtain a series of reflection coefficients at the interfaces. Then, we can simply integrate these reflection coefficients and determine the acoustic impedance in the layers between the interfaces. This "inversion" procedure leads us to a seismic volume that portrays layer properties (in terms of impedance), rather than interface characteristics, and assumes that the reflecting horizons have already been properly migrated to their appropriate positions. (Note that in the strict sense, the inversion described for migration or imaging and the inversion described in this section have equivalent goals: they both attempt to model the velocity and/or density structure of the earth that best fits and images the seismic data set. However, the approaches used are quite different, and the two processes should not be confused. Future research developments may tend to blur this distinction, by integrating appropriate aspects of both techniques into one method.)

Acoustic Impedance. If the seismic data were noise-free and contained all frequencies, from zero frequency (infinite wavelength) to very high frequencies (short wavelengths), the solution should be unique, but seismic data are noisy and band-limited and do not contain the very lowest frequencies nor the higher frequencies that are often of interest. A number of methods have been developed to overcome these shortcomings, including a "sparse-spike" inversion, in which the trade-off between the number of reflecting horizons and "noise" is chosen by the investigator (a technique that simultaneously solves for the "background" velocity trend and the impedance contrasts) and statistical or neural-network techniques that relate seismic features to properties inferred from borehole data. To a greater or lesser degree, these techniques rely on borehole sonic logs or on other velocity information or assumptions to incorporate long-wavelength velocity models (the background velocity trend). In general, a calibrated and competently processed inversion volume can be of considerable use to the interpreter or the engineer, providing insight to layer properties and continuity, which may not be apparent from the traditional reflection-seismic display; in particular, the thinner beds are usually more distinctly identified through removal of wavelet tuning (interference of reflections from the top and bottom of the bed) and subtle changes in impedance that are not easily recognized in the reflection image that can be seen in the inverted volume. Because the inversion process results in volume properties, rather than interface properties, it is possible to isolate and image individual bodies within certain impedance ranges. An example of the results of body-capture after a sparse-spike inversion, intended to identify hydrocarbon reservoirs, is shown in Fig. 1.22.

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  Fig. 1.22-An example of sparse-spike inversion results. The results of trace inversion can be used to identify spatially distinct bodies with specific impedance ranges. This example is of the same area of the Gulf of Mexico as shown in Fig. 1.3, but after a sparse-spike inversion routine has been performed and the lowest-impedance areas selected as individual bodies. In this area, virtually all these bodies are hydrocarbon reservoirs, although not all are large enough to be economically produced. The two reservoirs identified by A and B in Fig. 1.3 are also identified here. (Data provided by Diamond Geophysical through the Energy Research Clearing House; figure prepared by J.I. Haataja.)

In general, it is appropriate to invert only true zero-offset seismic data for acoustic impedance because the nonzero offsets are influenced by other parameters, notably the ratio between the P-wave velocity and the S-wave velocity (or, alternatively, Poisson's ratio; see previous discussion under Sec. 1.2.3, "Prestack Attributes."). Yet typical seismic data has been processed by stacking all appropriate offsets after correcting for normal moveout and muting, and the amplitude of each reflection represents a sort of average amplitude over all of the offsets used. In many cases, this distinction is not important because the amplitude normally decays slightly with offset (after routine correction for geometric spreading) and affects all stacked samples similarly, but for many cases, and especially those of most interest, the amplitudes vary with offset. Inverting a seismic section containing stacked data does not always yield a true acoustic impedance volume. (Note: the term "acoustic" refers to compressional-wave effects only, and acoustic models assume that the material does not propagate shear waves or that shear waves are not of any significance in wave transmission.) In practice, this is true for seismic compressional waves at normal incidence but is not valid for compressional waves at nonnormal incidence in a solid material because of partial conversion to reflected and refracted shear waves. The term "elastic" is used to describe models incorporating compressional and shear effects.) Thus, if we interpret a stacked seismic volume that has been inverted for acoustic impedance, we have implicitly assumed that the offsets used in stacking were small and/or that the offset-dependence of amplitudes is negligible. In the cases where these assumptions are not true, we must recognize that the values of acoustic impedance resulting from the inversion process are not precise; in fact, the disagreement of the acoustic inversion results, with a model based on well logs, is often an indication of AVO effects and can be used as an exploration tool.

Elastic Impedance. In order to separate the acoustic model (compressional-wave only) from the elastic model (including shear effects), the inversion process can be conducted on two or three different stacked seismic volumes, each composed of traces that resulted from stacking a different range of offsets. The volume created from traces in the near-offset range (or a volume made by extrapolating the AVO behavior to zero offset at each sample) is inverted to obtain the acoustic impedance volume. A volume created from traces in the far-offset range is inverted to obtain a new impedance volume called the "elastic impedance." The elastic impedance volume includes the effects of the compressional impedance and the AVO behavior resulting from the V_p  / V_s ratio; the two volumes can be interpreted jointly to obtain the desired fluid or lithology indicator sought. Just as in AVO studies, one can also try to obtain a three-parameter inversion, using three different offset ranges and, for example, solve for compressional/shear velocities and density. Converted-wave data can also be inverted for shear impedance.

Borehole Seismic and Sonic Methods

Reservoir geophysics should aggressively take advantage of data from boreholes that are very close to the target itself, not just for correlating seismic data to the well but also using those wells for the collection of novel geophysical data from below the noisy surface or weathered zone. New techniques for acquisition of seismic data from wellbores are available, and should become routine tools in the arsenal of the reservoir geophysicist. The principles of borehole geophysics, including vertical seismic profiling (VSP), reverse VSP, and crosswell seismic profiling (CSP) and sonic logging, are described in various chapters in the Reservoir Engineering and Petrophysics volume of this Handbook. In this chapter, we demonstrate some applications of these techniques to reservoir characterization and monitoring.

Single-Well Techniques

Single-well techniques involve placing seismic sources and receivers in the same well and include sonic logging and single-well imaging. Sonic logging has become routine, and the collection of compressional and shear velocities in fast and slow formations is more-or-less straightforward, particularly with the use of dipole sonic tools and waveform processing. The application of modified sonic-logging tools for imaging near the wellbore is not routine but has been demonstrated in several cases; research and development continues in this area.

Modern sonic logging tools can provide a good measure of compressional and shear velocities, values that are required for calibrating seismic data at wells and for the investigation of lithology and fluid content from seismic data. Of course, the interpreter must be careful to know if the data represent invaded or uninvaded conditions and make appropriate corrections if necessary. Modern sonic logging tools can often provide reliable values for velocities through casing; often, the most-reliable sonic logs in soft shales can only be found behind casing because of the inability to log openhole the depth intervals in which shales are flowing or collapsing.

Compressional sonic log values are used in reservoir geophysics to tie well depths to seismic two-way travel time. First, the sonic transit time is integrated to obtain a depth-calibrated time scale, and then synthetic seismograms are created through determination of reflection coefficients (including the density log) and convolution with a known or assumed wavelet. This synthetic seismogram is often adjusted to account for borehole effects, absence of data in the shallowest section, and other unspecified effects, including velocity dispersion caused by thin-bed layering below seismic resolution. The shear sonic log values are then added to create synthetic seismograms that demonstrate AVO behavior for comparison with the prestack data near the well. Often, additional work is conducted to model the changes in seismic response when rocks of slightly different lithology or fluid saturation are encountered away from the well. Both the compressional and shear sonic data are required to accomplish fluid-substitution modeling, although some empirical models and other short-cuts are available. The most common fluid substitution models employ Gassmann in clastic rocks; a number of models also exists for fractured rocks.

Single-well imaging, although not yet widespread, may provide a useful tool for detailed close-up structural studies, such as salt-proximity studies designed to assist in the planning of a development sidetrack from an exploration well, or in determining the location of interfaces with respect to a horizontal well. In general, a sonic-logging tool or a string of VSP receivers (geophones and/or hydrophones), coupled with a downhole seismic source, is lowered into the well, often using tubing-conveyed methods in highly deviated wells. The experiment then becomes similar to a surface reflection-seismic experiment, except that reflections may come from any direction around the well, not just from beneath it. The technique has been shown to be useful to image fractures and to determine proximity to upper and lower interfaces in horizontal wells as demonstrated in Fig. 1.23.

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  Fig. 1.23-Single-well imaging. The use of a string of receivers and a seismic source in a highly deviated well is shown in this example to provide an image showing the proximity of the well to layers of interest above and below it.

Well-to-Surface Techniques

Methods of calibrating seismic data and imaging that involve sources and/or receivers in one well and others at the surface include checkshot surveys, VSP, reverse VSP, and seismic-while-drilling. Checkshots and VSPs were developed primarily to assist in the tie between surface seismic data and well observations, but they have been extended beyond that in many cases. VSPs provide the best data for detailed event identification and wavelet determination, but they can also be used to image the near-wellbore environment, and the image can be improved if a number of offsets and azimuths (for a 3D VSP) are used for the source location. The ability to create a 3D image from borehole methods is greatly enhanced by placing a seismic source in one well and deploying surface receivers, which are already around the well, in a reverse VSP configuration. Images from such experiments can be highly detailed (see Fig. 1.24), and the time required for 3D reverse VSP acquisition is significantly reduced over the 3D VSP case in which the source is moved around the surface.

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  Fig. 1.24-VSP and reverse VSP reflection images of different portions of the same reef in Michigan. The left image was obtained using surface sources in a VSP configuration, and the right image was obtained using a downhole source in a reverse VSP configuration. The Earth model is also shown (after Turpening

The drill bit can also be used as a seismic source much like an uncontrolled, but monitored, vibrator; it is capable of providing, in at least some instances, information useful for selecting casing or coring points and for estimating proximity to overpressure zones. Through the use of receivers in a logging-while-drilling unit near the bit, a surface VSP source can be recorded during pauses in the drilling operation, which occur as a new joint of pipe is being added.

Multiple-Well Techniques

By placing a seismic source in one well and receivers in another well, a seismic velocity model between the two wells can be constructed using tomographic techniques, and a reflection image can be obtained by processing the reflected arrivals. Although the images are constrained to lie in a plane connecting the two wells, the additional fine-scale information, available from such surveys, can be of significant value to the reservoir engineer (Fig. 1.25).

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  Fig. 1.25-An example of crosswell imaging and the associated surface seismic and log data, showing the relative scales involved (after Harris et al.).

Seismic Time-Lapse Reservoir Monitoring

Traditional methods of monitoring reservoir behavior, including reservoir simulation and history-matching with production rates and pressure, can produce nonunique solutions for reservoir behavior in the interwell regions. In some instances, the uncertainty can be significant, and additional information is needed to optimize production and improve estimates of ultimate recovery. In many cases, the effect of the changing reservoir pressure and/or saturation on seismic data can be used to map the changing pattern of these reservoir properties, by obtaining seismic data repeatedly during production of the reservoir. With care, seismic data, obtained for other purposes (such as regional exploration), can sometimes be used for time-lapse seismic monitoring, but new data are often obtained from seismic experiments designed particularly to monitor the reservoir. The desire to minimize differences in acquisition parameters between surveys has led, in some cases, to permanent installation of sensors in the oilfield. Because most sensors deployed in this manner are deeply buried and/or cemented, this also has the effect of removing many of the sources of random seismic noise.

Many seismic time-lapse monitoring experiments have been conducted offshore, where the wells are few and very far apart, and interwell information is especially important. Other experiments have taken place in unusual or expensive production scenarios, such as steamflooding operations in heavy oil, CO₂ flooding, or thermal recovery. Because of the need for careful calibration, seismic time-lapse experiments usually include some detailed borehole work, although meaningful results can sometimes be obtained and interpreted even in the absence of good borehole data.

Three-dimensional (3D) seismic time-lapse studies [occasionally, although ambiguously, referred to as four-dimensional (4D) seismic] use two or more migrated 3D seismic images obtained months or years apart. These can consist of straightforward stacked data volumes or stacks created from partial offsets if AVO aspects are considered. They may also consist of inverted volumes obtained from stacked full-offset or partial-offset data. The comparison can be made in any number of ways, including simple visual inspection. But, it is important to recognize that differences can occur in seismic data even without changes in reservoir properties because of variations in acquisition or processing of the data sets. For example, 3D seismic data acquired from a towed-streamer marine experiment will contain an imprint that results from the direction traveled by the ship. If the experiment is repeated with the ship traveling along a different direction, even though the map grid covered is identical, the seismic rays that are gathered and stacked in each bin will have traveled through different overburden bodies in the two experiments (Fig. 1.26), resulting in some subtle but noticeable differences. In addition, there are many other small and sometimes uncontrollable differences between most pairs of experiments that must be removed. The process of matching seismic data from multiple experiments is called "cross equalization" and must be carried out, taking care not to remove the differences being sought. Usually, seismic data from areas where changes are not anticipated, such as the shallow section, are used to control the cross-equalization process.

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  Fig. 1.26-Rays with different overburden in 3D azimuths. When seismic lines are shot in different directions, the seismic traces may not be identical, even for common reflection points, because of the different overburden encountered. This figure shows two different source-receiver lines with a common reflection point. The reflection characteristics of the horizon observed from a survey shot in one direction may be different from those observed from a survey oriented in a different direction.

The observations made on seismic time-lapse studies frequently include changes in amplitude and changes in time, although any attribute, including inversion results, can be used. Changes in amplitude can often be used to directly monitor fluid migration because the reflection character changes as a result of replacing oil/water with gas, as shown in the example in Fig. 1.27. Other changes in reservoir properties must always be considered, such as effective pressure acting on the rock frame, and it is not always possible to separate these effects using stacked data alone. The use of offset stacks or elastic impedance volumes helps reduce this ambiguity, separating the changes that seem to be caused by fluid substitution from those caused by pressure change, and a seismic petrophysical model is required in the interpretation.

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  Fig. 1.27-Example of time-lapse seismic monitoring of a reservoir from the Gulf of Mexico. Where the amplitude difference is colored in red, gas is expected to have been released or injected into the reservoir. The wells bear this out, with a well colored in red indicating a gas injector or producer with high GOR; a well in blue has watered out, and a well in green produces oil (after Johnston et al.).

The change in seismic velocity between separate monitoring experiments will also result in a change of two-way travel time to reflectors that lie beneath the producing reservoir. This velocity-induced "sag" or "pull-up" may be monitored and provides an indication of the spatial location of reservoir changes, even in reservoirs too thin to image directly (Fig. 1.28). Because of this effect, interpreters should take great care in the use of direct difference volumes (obtained by simple subtraction of seismic volumes obtained at different times) in the analysis of changes below the uppermost-affected area on the seismic section.

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  Fig. 1.28-Example of seismic time-lapse velocity sag effects. The presence of steam (or other fluid and pressure changes) can change the seismic velocity of the fluid-filled rock enough to result in differences in arrival time for rays passing through the steamed zone. This map shows the change in travel time between two layers encompassing the steamed interval, indicating the movement of steam between two

Fluid or pressure changes may occur outside of the reservoir being produced, and these can sometimes be observed on seismic time-lapse studies, even if they were not anticipated. Such changes can include variation in the fluid and rock velocities because of changes in pore pressure (therefore, also in effective or differential pressure); changes in rock stress because of deformation of the overburden and sideburden surrounding the reservoir; and changes in fluid saturation in nearby, unproduced, hydrocarbon reservoirs because of changes in pore pressure (dropping below bubble point) that have been communicated through the aquifer.

Originally, seismic time-lapse monitoring was strictly a qualitative subject, and changes observed visually were related in a heuristic way to the reservoir production. As the seismic technology matured, and greater accuracy was assigned to the differences observed, there was an increasing effort to incorporate the results into more quantitative studies. Initially, output from reservoir simulators was used to provide input to Gassmann fluid-substitution schemes to compare with seismic observations; then, some pressure effects on the rock frame were included. The comparison between predicted seismic changes and those observed was sometimes used to update the original reservoir model, just as history-matching is used to improve the initial model. Currently, there is an effort to fully link the reservoir simulation and its history-matching capability with the data provided by seismic time-lapse monitoring, guiding the simulator (or the engineer) in the interwell regions and further constraining the initial model. These efforts are in some cases related to work on geomechanical modeling of reservoirs for the inclusion of deformation in simulation (covered later in this chapter).

Passive Seismic Monitoring

In recent years, deformation of the reservoir host rocks has become a subject of great interest, prompted in part by the dramatic subsidence observed at Ekofisk platforms in the North Sea. Previous studies have been published in the scientific and earthquake literature relating earthquakes to oil/gas production and to injection practices; these studies clearly demonstrate that deformation is an important aspect of reservoir production, even without a significant compaction drive in many cases. Earthquake monitoring (called "passive" monitoring because the geophysicist does not activate a seismic source) has now become one standard way of monitoring reservoir and host-rock deformation. The technology has gradually become more precise and accurate, even at low levels of seismicity, largely because of the placement of geophones downhole, which is away from surface noise and closer to the sources of seismic energy, and processing and analysis techniques developed for this purpose. The production or injection of fluids induces change in fluid pressure, stress on reservoir host rocks, and the occurance of small (occasionally large) earthquake-like events, representing sudden shear failure along planes of weakness. These changes can occur at injection pressures well below the reservoir engineer's "parting" pressure for tensile failure or during production at pressures below original reservoir pressure. In some detailed studies, very small events indicate locations of fracture systems responsible for fluid migration (Fig. 1.29). In some other studies, the events identify faults that may be significant for reservoir management (Fig. 1.30), and seismicity may reveal reservoir behavior that aids in reservoir management. The migration of microseismic events, away from an injecting well, may also be used to determine permeability of the bulk rock, including fractures that serve as conduits of fluid flow.

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  Fig. 1.29-Passive seismic monitoring results showing fracture locations in a cross-sectional view of seismicity and intervals of gas production from Clinton County, Kentucky (after Phillips et al.).

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  Fig. 1.30-Passive monitoring for faults in Ekofisk: (a) Microearthquake locations at Ekofisk and (b) location of survey in the Ekofisk field, showing location of obscured reflection-seismic observations because of the gas cloud (after Maxwell and Urbancic).

There are multiple reasons to consider passive seismic monitoring, which include: earthquake hazard evaluation (and subsequent mitigation); deformation monitoring for reservoir management and optimization; monitoring of fluid leakage for environmental and economic considerations; and providing additional time-lapse constraints for reservoir simulation. The link between injection or production practices and seismicity, however, is complicated and not yet well-understood. The location and timing of microseismic events, or even large earthquakes, cannot easily be linked to a simple failure criterion in an otherwise static and nondeforming crust. The overall deformation of the rock surrounding the producing reservoir (or zone of injection), as well as spatial variation in pore pressure, can alter the state of stress in the host rock; subsequent changes in either pore pressure or deformation-induced stresses can then cause seismic events, even though these may occur at conditions that would not have originally induced seismicity. Conversely, the history of production and injection may inhibit seismicity that would have occurred under similar conditions but with a different history. Thus, the evolution of stresses in and near a reservoir seems to be almost as important as the absolute values of those stresses, in determining whether or not seismicity will occur. Of course, not all rocks will fail suddenly, producing a seismic event, but may creep or flow, and this form of failure will not be detected by passive seismic monitoring. Because of these complicating aspects and perhaps other reasons not necessarily related to reservoir engineering, passive seismic monitoring is not currently used widely as a tool for reservoir management. Improved geomechanical reservoir modeling is likely to aid in interpretation of microseismic event observations for reservoir management purposes, and environmental monitoring considerations are likely to increase; given these enhanced applications for the technology, it is probable that microseismic passive monitoring will become more widespread in the near future.

Hydraulic Fracture Monitoring

The creation of a fracture by injection of fluids (see the Hydraulic Fracturing chapter in the Production Operations Engineering section of this Handbook) is always accompanied by deformation of the earth's surface and radiation of seismic energy from microseismic events. Both features are often exploited in the monitoring of hydraulic fracture operations by using arrays of tiltmeters or seismic receivers. Knowing the orientation, height, and length of hydraulic fractures is often important in the design of closely-spaced pairs of injectors and producers, in designing optimal fracture treatments for other wells, and for optimizing reservoir management in fields with fracture-treated wells. In general, geophysical techniques are not currently capable of determining the width (aperture) of a single fracture nor the composite width of a multiple fractures.

Seismic receivers are used in a manner similar to that employed for passive seismic monitoring. Typically, they are deployed in one or more nearby wells, perhaps shallow wells drilled for this purpose, but they provide better observations the closer they are to the fracture depth. The receivers are usually multiple-component geophones that are clamped to the wellbore wall and deployed at multiple depths in the monitor well(s). The arrival times of the P-waves and S-waves are used to locate the events in space and time. Because the use of just one or two monitor wells does not permit traditional triangulation, it is usually necessary to supplement the arrival time information with the azimuth of the arriving P-waves, as determined from particle-motion analysis (or polarization), to help constrain the location of the events. In modern applications, the growth of the fracture can be monitored in real time, and information can be provided to the completions engineer on site. The events monitored consist primarily of shear events in the immediately surrounding rock, after the fracture tip has passed; by accumulating the locations of these events, an image of the fracture as it grows can be obtained in three dimensions (see Fig. 1.31).

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  Fig. 1.31-Hydrofrac microseismic example. Microearthquake location in map view (upper left diagram) and cross-section view (lower left diagram); and tracer results and microearthquake density with depth (right diagram) showing good correlation. The results suggest that these fractures have been confined to narrow vertical zones over significant lateral distances (after Rutledge and Phillips).

Tiltmeters can be deployed at the earth's surface or in wellbores (see Fig. 1.32). Noise from wind and other ambient conditions can largely be eliminated by placing the "surface" tiltmeters in shallow holes (20 to 40 ft; 6 to 12 m), and most modern studies use these shallow wells rather than placing tiltmeters directly on the surface. Tiltmeters can also be deployed in a deeper monitor well to provide better estimates of the fracture parameters. Deformation is monitored with an array of several tiltmeters; predictable tilt features caused by the solid-earth tidal loading are removed, and the resultant signal is inverted in near-real time to provide an interpretation of the fracture as it grows. As a reservoir is produced from a hydraulically fractured well, the stresses may change over time, and a new refracture treatment may result in a new set of fractures or extensions of the original fracture at different azimuths. Tiltmeter studies have demonstrated that complicated refracture reorientations can sometimes be significant for reservoir management.

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  Fig. 1.32-Schematic view of a vertical hydraulic fracture and its associated deformation field. Example locations of tiltmeters are shown.

Pore Pressure Prediction

Drilling engineers require estimates of the fluid pressures that they are likely to encounter in any given well, to anticipate mud weights required to maintain optimal drilling rates and safety (see the chapter on Geomechanics Applied to Drilling Engineering in the Drilling Engineering section of this Handbook ). In addition, the locations of anomalous pore-pressure regions are of interest in exploration because they often correlate with highly productive "sweet" spots in otherwise tight gas sands; provide constraints on basin evolution; and may correspond to density of open fractures, including bedding-plane fractures. Because seismic velocities correlate with effective pressure in the formation, sufficiently precise estimates of velocity obtained from seismic observations can be used to determine pore pressure. In the absence of dense well control, interval velocities derived from stacking velocities are used to estimate pore pressure. These interval velocities are compared with a general trend of velocities in the region (Fig. 1.33), and a pore pressure volume is developed for use by drilling engineers, as shown in Fig. 1.34. Acoustic impedance volumes obtained from seismic trace inversion can also be used to identify and detect anomalous pore pressure regions. In any case, calibration to local velocity-pressure profiles is required. Without this calibration, the pore-pressure indicator is relative rather than absolute, although some empirical relationships exist. The resolution of pore-pressure volumes obtained from seismic interval velocities is fairly coarse, compared to velocities used in detailed migration or tomography, which are somewhat more detailed, as shown by the example in Fig. 1.35. To meet the need for fine-scale predictions of pore-pressure ahead of the bit, new or improved methods for obtaining reverse VSP data, using the drill bit as a seismic source, and VSP data that uses logging-while-drilling techniques are being developed.

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  Fig. 1.33-Geopressure trend curve schematic examples. The left side shows a plot of the seismic interval velocity, determined from stacking velocities, as a function of depth and a smooth monotonically increasing trend line; the right side shows the pore-pressure interpretation from these data. Notice the overpressured zone where the velocity departs from the trend.

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  Fig. 1.34-Seismic data and pore pressure predictions. The top diagram shows an interpreted seismic line with faults and specific horizons indicated. The same faults and horizons are also shown on the bottom diagram with predicted pore pressure displayed in color. Notice that the major faults seem to act as pressure barriers in this case.

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  Fig. 1.35-Anomalous pore pressure regions resolved using tomography. The upper figure is a porepressure volume determined from interval velocities that had been calculated from stacking velocities.

Mechanical Properties and Seismic Properties

The relationship between seismic velocities and mechanical properties is a strong one. Moduli, such as bulk modulus (and its inverse, compressibility), rigidity (or shear modulus), and Young's modulus, can be determined either from static (very slow) experiments or dynamic experiments, involving the passage of a seismic wave through the sample. The relationship between seismic velocities and the dynamic bulk modulus (K), the dynamic shear modulus (G), and the density (ρ) are given by

....................(1.7)

and

....................(1.8)

Eqs. 1.7 and 1.8 are correct only for isotropic media and are strictly appropriate only for moduli measured at the same frequency and amplitude as the seismic wave. Investigators often ignore these distinctions and use the seismically determined moduli to approximate the static moduli sought by reservoir or completions engineers for compaction drive estimates or hydraulic-fracture design. When properly calibrated, the spatial or temporal variations in velocity-derived moduli can often be used to indicate changes in static moduli.

The static or dynamic moduli are often related to other mechanical properties, such as strength, mostly because the features of the rock fabric that determine elastic moduli are also the features that determine strength. Thus, variations of moduli within a given rock type can often be correlated to variations in strength and other mechanical properties (Fig. 1.36). (A simple analogy is worth describing: the integrity of railroad-carriage wheels can crudely be tested by a hammer strike; the intact wheel responds with a clear and distinct sound, while a cracked wheel sounds different and can be identified by this sound, providing a "seismic" evaluation of mechanical properties.) Again, with local calibration, these correlations can be quantitatively useful but otherwise should be considered to be qualitative and subjective estimates of relative differences.

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  Fig. 1.36-Modulus vs. strength diagram. The relationship of dynamic and static shear modulus to shear strength is shown for some selected weak sandstones (after Fjaer et al.).

The monitoring of reservoir production in some instances includes monitoring of compaction, partly for environmental or facility-design considerations (e.g., subsidence) or as a part of prudent reservoir management and efficient production strategies. Laboratory studies on core samples can be conducted to provide a relationship between pore pressure and porosity, bulk volume, compressibility (as a static measure), and seismic wave velocities (dynamically measured). With such correlations, and accounting for the frequency/size scaling effects between ultrasonic laboratory measurements and low-frequency field seismic observations, the velocities observed in seismic time-lapse monitoring experiments can be interpreted in terms of pore compressibility and/or collapse.

Nonseismic Techniques

In general, the dominance of seismic technology in reservoir geophysics is because of three factors: seismic waves respond fairly well to reservoir and host-rock properties of interest; they provide high-resolution images; and there is a wide and deep base of knowledge of seismic techniques in the petroleum industry. However, other technologies can often be shown to investigate properties of the earth that correlate better with the properties of interest. If the images from these technologies can be provided at appropriate resolution, and the knowledge required for interpretation and wise application of these technologies is available within the industry, they should be used. For example, electrical methods are extremely sensitive to variations in saturation, yet surface-based methods provide very poor resolution. Reservoir compaction can be directly observed from surface deformation, and pore-volume or gas-saturation changes can be detected from changes in the gravitational field.

Surface-Based Methods

Surface-based methods of reservoir geophysics include: reservoir characterization by gravity and electromagnetic techniques; monitoring of deformation (by releveling surveys, satellite interferometry, gravimetry, or tiltmeters); and monitoring of fluid migration by gravimetry, electrical, and electromagnetic techniques.

Dramatic examples of surface deformation induced by reservoir compaction have been provided by releveling studies (involving repeated high-accuracy surveying) and satellite-based interferometry. These technologies are directly applicable only to onshore fields, although extensions to bathymetric observations are possible. As pressure in a reservoir decreases during primary production, the overburden load causes a compaction in the reservoir rock. In some instances, encroachment of water can also cause weakening of the matrix and subsequent pore collapse, particularly in some chalk reservoirs. Virtually any reservoir compaction will ultimately be reflected in subsidence at the surface, although in many cases the elastic properties of the overburden rock will delay this for years, perhaps millennia, and may distribute the stresses and strains over such a large area that the actual amount of subsidence in any one location is miniscule. In some cases, however, the subsidence is nearly immediate and profound and should be monitored for a number of reasons. Direct measurements of surface deformation can be obtained by detailed bathymetric surveys, relevelling surveys, or satellite-interferometry surveys. Fig. 1.37 shows an example of satellite-based observations of ground deformation.

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  Fig. 1.37-Examples of satellite-observed deformation. This subsidence map was obtained using satellite interferometry over the Lost Hills and Belridge oil fields for a period covering 105 days (after Xu and Nur).

The gravitational field at the surface of the earth responds to the masses of the objects near it. The distribution of density beneath the surface gravimeter determines the gravitational attraction it senses. If that density distribution changes, for example through subsidence or the displacement of gas by water, a time-lapse high-resolution gravity survey may be able to determine the geographical distribution of that deformation or fluid migration. Surface-based gravity measurements have found some application in exploration geophysics, particularly in aiding the recognition of gas zones. Time-lapse gravity surveys show promise for monitoring gas-cap changes and reservoir deformation. Gravity gradiometry measurements (in which two or more gravimeters or accelerometers are deployed a fixed distance apart) can increase the resolving power.

Surface-based electrical or electromagnetic methods have application to reservoir geophysics through their strong response to saturation and ability to penetrate salt and igneous rocks. In general, their resolution is poor in comparison with seismic methods (see Fig. 1.38), although there may be instances in which they are appropriate for reservoir management. In some applications, an electrical source is used, and in others, the naturally varying electromagnetic field of the earth is used.

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  Fig. 1.38-Example of results of a 2D electromagnetic survey over a known salt body in the Gulf of Mexico. The white line represents the outline of the salt as determined from seismic data; various symbols indicate different aspects of the inversion constraints, while the color indicates the resistivity (after Hoversten et al.).

Borehole-Based Methods

Because of the proximity of tools located in a borehole, the resolution problem associated with some of the nonseismic geophysical techniques is reduced. In particular, electrical, electromagnetic, and gravity studies find application in borehole-based reservoir geophysics projects, but currently not all of them are in common use.

Electrical and electromagnetic borehole-based methods are extensions of comparable logging technologies (see the Reservoir Engineering and Petrophysics section of this Handbook) but with significant differences that involve imaging at greater distances and through casing. The presence of steel casing in most producing environments seriously limits the capabilities of current methods, but techniques have been developed that can operate in one or more steel-cased wells (see Fig. 1.39 for an example). These methods have their greatest application in monitoring changes in fluid saturation, for determining proximity to bed boundaries while drilling, or for observing the "streaming potential" created by fluid flow.

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  Fig. 1.39-Crosshole electromagnetic (EM) profiling for waterflood monitoring. The upper diagram shows, schematically, the different conductivity paths crossing the reservoir target when a borehole EM source is used in one well, and a set of receivers in another. The lower diagram shows a three-dimensional representation of the change in resistivity as a result of waterflooding operations over eight years for a reservoir in California (from Wilt and Morea).

Borehole gravity measurements can be used to characterize reservoir density (and therefore porosity); monitor fluid movements (particularly gas vs. liquid); and, to a lesser degree, monitor changes in porosity because of compaction. Fig. 1.40 shows the application of borehole gravity.

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  Fig. 1.40-Principles of borehole gravity as used to determine density in an area surrounding the wellbore (after Ander and Chapin).

Summary

As geophysical techniques have matured over the years, they have provided an increasingly fine level of detail, and many are now used routinely for purposes related to reservoir production. The most widely used technique, just as in exploration, is reflection seismic, where it is almost exclusively 3D. Emerging techniques, having successfully proven their capabilities but in various stages of commercial availability, include: crosswell, forward and reverse VSP, single-well imaging, and passive seismic monitoring (gravity, electromagnetic, and other techniques). The distinct advantage provided to reservoir geophysics over exploration geophysics lies in the quantity and quality of existing data on the reservoir target, enabling surveys to be focused on specific targets and allowing calibration (necessary to have confidence in the results, as well as to improve imaging) of the geophysical observations to the formation. As geophysical techniques become more familiar to the engineer and as engineering practices become more familiar to the geophysicist, continuing and increased use of reservoir geophysical techniques can be expected.

Nomenclature

B	=	gradient of reflection amplitudes with changing angle of incidence
C	=	converted (wave)
g	=	acceleration due to gravity
G	=	dynamic shear modulus
i	=	angle of incidence
K	=	dynamic bulk modulus
p	=	ray parameter
P	=	compressional (wave)
R0	=	zero offset reflection amplitude
R(i)	=	reflection amplitude as a function of angle i
S	=	shear (wave)
v	=	Poisson's ratio
Vapp	=	apparent velocity
Vp	=	P-wave velocity
Vs	=	S-wave velocity
ΔI	=	change in impedance
Δz	=	change in depth
ρ	=	density
γ	=	universal constant of gravity

Subscripts

p	=	compressional
s	=	shear

Acknowledgements

This chapter was prepared with support provided by a contract from the U.S. Dept. of Energy through its Natl. Petroleum Technology office in Tulsa, DE-AC26-98BC15135, "Calibration of Seismic Attributes for Reservoir Characterization." Much of the writing was completed while the author was on sabbatical at Schlumberger Cambridge Research. The author gratefully acknowledges the assistance provided by Schlumberger and Michigan Technological U. during this sabbatical.

References

SI Metric Conversion Factors

ft	×	3.048*	E – 01	=	m
in.	×	2.54*	E + 00	=	cm
mile	×	1.609 344*	E + 00	=	km

*

Conversion factor is exact.