Seismic imaging and inversion

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</parsererror> 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). 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. 2). 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—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 shows the seismograms that would be recorded from this scenario, ignoring the direct wave in the upper layer, multiples, and noise. Notice that the distance used to label the seismic gathers is the total sourcereceiver distance. (Synthetic seismic gather taken from Yilmaz.)

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  Fig. 2—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 reflected multiple times. The direct wave (straight-line arrivals seen at the upper edge of the arrivals on the seismic gather) are not considered in the analysis (after Yilmaz).

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. 3). 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. 3—Interval velocities. The stacking velocities are those obtained from the velocity analysis (see Fig. 2); 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. 4 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. 5). 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. 4-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. 5-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 imaged using 3D post-stack time migration. Note the improving quality of the data, particularly deeper in the section (after Yilmaz).

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. 6 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. 6—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.<html><parsererror style="display: block; white-space: pre; border: 2px solid #c77; padding: 0 1em 0 1em; margin: 1em; background-color: #fdd; color: black">