T
he statics problem, whether short wavelength, long wave-length, residual, or trim, has always been one of the more time-consuming and problematic steps in seismic data pro-cessing. We routinely struggle with issues such as poor sig-nal-to-noise (S/N) ratio, cycle skipping, truncated refractors, wavelets with ambiguous first arrival times, etc. Elevation variations create their own problems and impact the choice of datum—floating, phantom or recourse to a zero-velocity layer. Even if we can overcome some of these problems, we still have a “catch 22” situation in which accurate velocity estimation requires good statics, while good statics estima-tion requires accurate velocities. To characterize these ambi-guities, we have come up the oxymoron “time-varying statics.”Here we construct a more effective model of the statics phenomenon by introducing the concept of a near-surface propagation operator. We argue that statics, as a physical phenomenon, does not really exist; the problem lies in our inability to define the velocity field with the necessary pre-cision. The downgoing source wavefront illuminates the subsurface, but suffers little distortion from the presence of near-surface heterogeneities (the far-field effect). On the other hand, the reflected upward traveling wavefield is sub-ject to distortion by these near-surface heterogeneities, and therefore the reflected wavefield reaches the geophone arrays
before it has had a chance to heal (the near-field effect).
We show that shot and receiver statics can be deter-mined directly from arrival time differences, without veloc-ity information. Shot and receiver statics share many similar characteristics but also differ in some of their far-field as well as near-field effects. We show that receiver statics represent a major portion of the short wavelength time perturbation in the recorded wavefield. The near surface is not simulated with a velocity model but rather with a distribution of Green’s functions that so often better represent the observed traveltimes. Such a change in perspective implies the need for a different class of time corrections, namely those result-ing from recourse to Berkhout’s double focusresult-ing method (Berkhout, 1995). Double focusing technology formulates the migration process as a cascade of two focusing steps: focus-ing in emission and focusfocus-ing in detection. It requires no explicit knowledge of the velocity field. Instead, wavefield operators, directly estimated from the seismic data, are used to perform the focusing. We remark that images can be gen-erated from the surface data without need to apply either long-wavelength or elevation statics corrections. We provide a new data processing sequence that produces more accu-rate and higher-resolution seismic images. Our proposed technique is equally applicable to 2D, crooked line, or 3D recording geometries.
There is a vast literature on the subject of statics. A few of the significant contributions are listed in “suggested read-ing” at the end of this article. Cox’s excellent monograph,
Static Corrections for Seismic Reflection Surveys, does a fine job
of summarizing our present knowledge and experience. It sometimes seems as if all there is to know about statics has already been published. However, we feel that this means that the end of this one particular road has now been reached, and that the time is right to look at this problem from a fresh vantage point.
Near-surface problem.Our underlying model is based on the detail-hiding matrix operator notation of Berkhout (1982). One can express the influence of a complex near sur-face on the seismic reflection data in the form of vectors and matrices
(1) where the vector ∆Piis the ithshot record containing the
reflec-tions from depth levels below the near surface (zኑ z1), while
the vector δPiis the ithshot record containing the diffractions generated by upward-traveling reflections at the irregular boundary of the near surface, respectively. In more detail,
(2) Here the vector Pi-(z1, z0) represents reflections
travel-ing upward, betravel-ing incident to the irregular lower bound-ary of the near surface, described by the diagonal matrix δ(z1, z1). Further, the matrices W(z0, z1) and W(z1, z0) are the
wavefield operators respectively carrying out up- and down-going propagation in the complex near surface. According to the theory of wave propagation, we have
The dynamics of statics
M. TURHANTANER, Rock Solid Images, Houston, USA A. J. BERKHOUT, Technical University of Delft, The Netherlands SVENTREITEL, TriDekon, Tulsa, Oklahoma, USAPANOSG. KELAMIS, Saudi Aramco, Dhahran, Saudi Arabia
ACQUISITION/PROCESSING
Coordinated by Jeff DeereW(z0, z1) = WT(z1, z0)
where the superscript T denotes the matrix transpose. This implies that traveltimes for up- and downgoing waves must be surface-consistent for any propagation angle. Finally, the matrix X(z1, z1) represents the multichannel spatial impulse
response from below the near surface (zኑ z1), the vector Si(z0)
is the ith source (array) located on the acquisition surface
z0, and the matrix Di(z0, z0) represents the distribution of
detectors at depth z0for the ith source. The spatial sampling
of W(z0, z1) is determined from the known detector
geome-try in the field, namely Di(z0, z0). Note that we generally have
the situation z=z(x,y).
Our concept and solution.We do not estimate the detailed near-surface velocity model, rather we estimate the near-sur-face propagation operator, W(z0, z1). This implies that the
com-plex near-surface behavior can be described in terms of the properties of this operator, which is determined by the near-surface velocity distribution as well as by the shape of the near-surface layering. In other words, W(z0, z1) is
deter-mined from the near-surface velocity distribution and from the shape of the near-surface layers. Further, δi(z1) represents
the irregular base of the near-surface layer z1. It results in
diffractions due to the short-wavelength variations. We estimate W(z0, z1) from the field data, followed by
removing the effects of W and WTfrom the data and replac-ing them by homogeneous propagators. This operator-dri-ven process will be called near-surface inversion.
At the present time we identify all effects acting in a time-constant manner as statics. We divide such statics into two fuzzy classes, namely short- and long-wavelength statics. We adopt such a fuzzy classification scheme because we do not have an absolute metric to differentiate between the two. We also use this term only as it refers to time delays. It is well known that the near surface is the most weathered and het-erogeneous part of the subsurface and that, therefore, waves propagating through it will be affected by time delays as well as amplitude and phase distortions. For the sake of sim-plicity, this article will restrict itself to time delay aspects only. A more general formulation can be developed with the “WRW” matrix notation introduced by Berkhout (1995).
In conventional processing we compute long-wavelength statics from the reflection geometry, which follows from the first-arrival times of refracted events. These static corrections serve to replace up to several hundred meters of lower-velocity, heterogeneous layering by a set of higher-lower-velocity, homogeneous layers. Unfortunately, these arrival times are not sufficient to determine overburden velocities directly. In most instances, we have to guess at these velocities. The static correction values and the long-wavelength refractor geometries we obtain in this way are the result of this guess-work. It is often possible to compute the refractor depth more accurately from reflected data. In most cases the near-offset traces that could contain reflected arrivals from near-sur-face refractors are not recorded.
Applied static corrections are computed from differ-ences between vertical traveltimes through the layers as obtained from estimated velocities of consolidated layers below the refractors, rather than from the actual travel path differences. This naturally creates traveltime errors. If we include large elevation variations, the situation becomes even worse. A number of approximations are available to handle the problem. We can use a floating datum and cor-rect the data so that each trace of a CDP gather is reduced to the same elevation. In this way elevations change from one CDP gather to the next. If the elevation change is severe,
the corrections within one CDP gather become very large and vary significantly with time. Truncated refractors also create problems. For example, refraction statics will have to be computed with different velocities on either side of a trun-cated refractor. Problems arise when the first refractor is shal-low, while the second is deep, so that it may not even be recorded. In other instances there could be many thin high-and low-velocity layers, which can give rise to a series of refracted arrivals and make it hard to construct a simple near-surface model. Often refractor signatures are weak or buried in noise. The determination of actual traveltimes, which are required for the refraction computations, may sometimes be a serious challenge.
In conventional processing we need to determine both short- and long-wavelength statics. In practice, shorter-wavelength statics are computed from differences in NMO-corrected reflection arrival times. Here we face cycle-skip problems due to uncertainties in trace-to-trace traveltime dif-ferences, inaccurate NMO velocity estimates, and poor S/N ratios. Some of these inconsistencies are mitigated by the computation of surface-consistent statics. The resulting sur-face-consistency equations yield solutions valid up to a cable length. Because computed statics are influenced by inaccu-racies of the applied NMO corrections, a new set of NMO velocities must be determined after the application of a sta-tics correction step. The procedure can be repeated until an acceptable solution has been achieved.
Thus far, we have reviewed problems encountered while trying to find and correct for time anomalies generated by the near surface. Now we take yet another look at the prob-lem, and sketch some simpler, more general solutions. The rest of this article consists of two parts. In the first we review near-surface effects and derive some general conclusions. The second part then allows us to describe processing sequences based either on more conventional approaches or on the more recent double focusing methods.
A simple surface statics model.It is generally accepted that four data samples per cycle are needed to define the ampli-tude and the phase of a wavefield frequency component. This holds for both temporal and spatial sampling. The lim-itations inherent in temporal sampling are better under-stood than those in spatial sampling. We can determine wave numbers properly for wavelengths greater than four times the receiver interval. All wavelengths shorter than this will be recorded, but not properly recognized. This also means that we need at least four recorded samples for each Fresnel zone. Diffracted waves arriving from shallower interfaces will be sharper and have shorter Fresnel zones. Thus they will tend to be undersampled. On the other hand, events arriving from deeper reflectors are associated with an expanding wavefront along with wider Fresnel zones. Thus, except for near-surface effects, the reflected wave-field will be adequately sampled.
seis-mic wavefront. We assume that the initial wavefront geom-etry is hemispherical as it originates in a near-surface layer. It is then perturbed by the near-surface heterogeneities, and will break down into many, smaller radius diffraction pat-terns containing short-wavelength delay patpat-terns. However, as propagation occurs over longer distances, the radii of the diffraction patterns increase and the perturbation wave-lengths become longer (with an increase of the size of the Fresnel zone). This is the well-known wavefront healing process, one which cannot be modeled by any ray-tracing method. Thus only reflections arriving from shallow depths will experience the influence of near-surface effects. The reflections from deeper layers will not display this effect, so that we see only an average delay for the arriving wave-front. Ironically, the so-called shot statics and their effective wavelengths are both time and space varying. This variation is most often observed in the shallow parts of the seismic data, and manifests itself as receiver-dependent delays, because each receiver records arrivals from a different prop-agation direction. Because we are generally imaging deeper targets, we need consider only the average time delays resulting from the combined effect of all near-source sur-face inhomogeneities. These are the source statics.
Figure 2 sketches the near-surface effects on upward-traveling waves before they arrive at the receivers. Here again a number of diffraction patterns are generated by inhomogeneities in the near surface. These patterns arrive at the receivers with various wavelengths, which tend to be proportional to the distance between a subsurface inhomo-geneity and a receiver. Thus, most short-wavelength time disturbances are generated by the near surface around and below the receiver positions. Because all upward-traveling wavefronts must pass through the near surface, their effect will be nearly constant with time, so that we can also treat this effect as “static.” Figure 2 shows that the upward-trav-eling short-wavelength time disturbances existing on com-mon source records result mostly from the influence of near-surface inhomogeneities on the upward-traveling wavefront. This effect is most pronounced immediately before it is recorded by the receivers. These phenomena, then, give rise to receiver statics.
A synthetic data example.For a more realistic example, we constructed the simple near-surface model shown in Figure 3. We generated synthetic seismograms for two different recording conditions. The surface of the model is horizontal, as are the deeper reflectors. Only the base of the near-surface, low-velocity layer is corrugated. In the first experiment we placed receivers at the surface and a source on the deep reflector. Figure 4 shows the wavefield recorded by the receivers at the surface. The data contain a large number of diffraction patterns with small Fresnel zones, as has already been remarked. The entire wavefield can be viewed as the envelope of all these small diffraction patterns. Nevertheless, its general shape indicates that it is an arrival from a deeper source. The statics problem is confined to the short wave-lengths.
Figure 2.A smoothed reflected wavefront impinging from below, scat-tered by the weathered layer.
Figure 3.The near-surface model. Vertical and horizontal distances are in meters.
Figure 4.Surface recording of near-surface location 2500 from a shot at the bottom of the model. Horizontal coordinate is distance (m) and vertical coordinate is time (s).
In the next test, we exchanged the positions of shot and receiver. The source was placed at the surface, and the waves were recorded at a deeper reflector level. This resulted in the seismogram shown in Figure 5. Again we see a number of diffraction patterns, but the Fresnel zones are now much wider than the ones of Figure 4. The first arrivals are much smoother and do not contain the short wavelength distur-bances arising from near-surface effects. While the shapes of the upward- and downward-traveling waves are differ-ent, the reciprocity principle is not violated. Figure 6 shows an overlay of two reciprocal traces, recorded by exchang-ing their source and receiver positions. To appreciate the sim-ilarities, we have shifted one trace by one pixel. It is clear from Figure 6 that both traces are identical.
Next, we generated several records with sources at var-ious positions along the deep reflector, while the receivers remained at their same surface positions. Figures 7–10, syn-thetic data recorded at the surface, clearly show the surface consistency of the short-wavelength perturbations. By sur-face consistency in this context we mean that the salient fea-tures of the delay patterns are similar, although there are small differences caused by the different travel paths at or near the surface. To render these similarities more visible,
we have applied approximate NMO to the first arrival times, and display them with their receiver positions in vertical alignment. We now observe that the similarities between the short wavelength delays are much more apparent in the cor-rected NMO display (Figure 11). It is interesting that, even though the amplitudes are now lower, the refracted events also exhibit similar short-wavelength perturbations.
To summarize, we account for the long-wavelength por-tion of the traveltime-distance relapor-tionships by parameter-izing in terms of average or rms velocity. This implies that for CDP processing, statics must be removed up to the wave-length equivalent of the maximum offset (i.e., one cable length). Therefore, the boundary between short- and long-wavelength statics is “one cable length.” This is not the case for the double focusing method. In this approach each path between an image position and the surface must be deter-mined and used separately, thus associating all delay effects Figure 6.Overlay of two reciprocal traces recorded by exchange of their
source and receiver positions (one trace has been shifted by one time sample for better visibility). Horizontal coordinate is time (s).
Figure 7.Synthetic data recorded at the surface from a shot near sur-face location 1000. In Figures 7–10, vertical coordinate is time (s), and horizontal coordinate is distance (m).
Figure 8.Synthetic data recorded at the surface from a shot near sur-face location 2000.
with the near surface and with the deeper layers. We there-fore will not have to contend with two separate statics prob-lems (Kelamis et al., 2002).
Short-wavelength statics can be computed from differential arrival times. Because the long-wavelength portion of the
traveltimes can be handled with the familiar time-distance approximations, the statics problem is not confined to the short-wavelength portion of the spectrum. A short wave-length implies that we can utilize differential arrival times rather than actual arrival times. This overcomes many prob-lems associated with refraction statics computations. Picking differential delay times, especially when considering sur-face consistency, is much simpler than first break picking. Figure 11 shows the degree of similarity of the delay pat-terns between several common source records. The picked differential times are integrated to obtain the actual statics correction times. Due to picking errors and inaccuracies, inte-gration may produce long-wavelength undulations. These can be removed by appropriate long-wavelength cut filter-ing. For CDP processing, such filtering must remove all undulations up to and including one cable length. In the dou-ble focusing method, these results are used as initial approx-imations of the required focusing operators. Such initial
estimates are then improved by an iterative process des-cribed by Berkhout (1997) and by Kelamis et al. (2002).
The longer wavelength “traveltime versus distance” relations are parameterized in terms of conventionally obtained stacking, or migration velocities. Most procedures used in conventional
processing, like CDP stacking and time or depth migration, are based on far-field imaging principles and on parame-terization of traveltime/depth relations. In practice, each portion of the wavefront propagates with a different speed. This speed depends on the dip and azimuth of a local por-tion of the wavefront, as well as on local geologic condipor-tions. We obtain theoretical traveltimes by basing them on assumed simple Earth models, parameterized in the form of “veloc-ities.” Such models, no matter how complicated they may be (homogenous, isotropic, anisotropic) are much simplified by our choice of the velocity fields. Therefore, structural con-figurations and individual bedding geometries are gener-ally modeled as longer wavelength approximations of the actual formations.
The short-wavelength time differences are the ones most damaging to our image construction procedure. We must therefore determine these differences, and adjust the appro-priate arrival times. If the near-surface variations are han-dled adequately, we can then obtain reasonably good images of the deeper structures. These shorter-wavelength portions thus become the basis for our statics correction method.
Large surface elevation differences can cause additional prob-lems. Another issue concerns how to handle surface
topog-raphy. A number of methods are known, but most tend to be oversimplified. Seismic data are usually generated and recorded at the surface. In order to visualize a section that approximately resembles an equivalent section recorded at given subsurface positions, we use an imaginary datum plane and adjust traveltimes from the surface to the datum. This datum could be a planar surface or it could be a smoothly varying surface that follows the surface topogra-phy. In any case, appropriate corrections can be determined for vertical traveltimes in a homogeneous medium. Conventional methods introduce errors which become more serious with increasing elevation variations. It is a fact that
the thing we know best about the subsurface is the surface. Thus,
after the proper handling of short-wavelength near-surface effects, imaging can then begin at the surface. For the dou-ble focusing method, such short-wavelength statics correc-tions are incorporated into the source or receiver focusing operators. As a result, images can be formed directly from the surface. Following time migration, adjustments to a datum plane can be made in the form of simple time shifts. This is both simpler and more accurate.
Examples.We computed short wavelength statics from the picks obtained with a commercially available first-break picking program. We produced statics with two maximum wavelengths, namely 750 and 1500 m. The center panel in Figure 12 shows the original common source gathers; the left and right panels show statics-corrected data for the 1500- and 750-m wavelength cases, respectively. Longer-wavelength statics give smoother arrival times and are more suitable for the more conventional hyperbolic velocity scans as well as for NMO correction. Because in this case the actual cable length was 3000 m, a statics correction solution designed for a 3000-m wavelength would have been more appropriate. Figures 13 and 14 show one of the benefits of stacking from the surface. Figure 13 is a conventional stack section generated with a smooth floating datum, as indicated on the section. Figure 14 shows the stack section generated with reference to the actual surface topography. Better over-Figure 11.A surface-consistent composite display of linear
moveout-corrected data shown in Figures 7–10.
all reflector resolution is now apparent. Because the surface is at zero time, the section reflects delays due to surface topography. This section can now be used directly as input for a given migration procedure.
To summarize: Traveltime perturbations on common source records are usually identifiable with short-wave-length near-surface (receiver) statics. These statics are nearly time invariant and should account for most observed short-wavelength time delays. The remaining delays are due to geometrical inaccuracies in the CDP gathers. These should be taken into consideration if the goal is improved stack-ing resolution. Shot statics can be viewed as averaged delays introduced by the near surface. These may be determined from traveltime differences obtained from common receiver trace gathers. Conversely, common source records provide data for the measurement of differential receiver statics. In conventional processing for statics corrections, the input is in the form of picked differential arrivals of reflected data. For noisy data, such differential arrivals can be checked for surface consistency, picking accuracy, and bad pick detec-tion. Differential arrival times can be integrated to determine a first statics estimate. This estimate will contain some slowly varying trends due to picking inaccuracies or some form of bias. Such trends can be removed with a long-wavelength suppressing filter. Its length must be selected to correspond with the spatial resolution capability of the recording geom-etry. Such a process is similar for both source and receiver statics.
The method we have outlined here completely decom-poses shot and receiver statics without the need to deter-mine velocities. The resulting statics-corrected data will exhibit improved spatial resolution and provides an ade-quate input for both NMO velocity determination or for prestack migration.
Long-wavelength trend removal filtering produces “zero mean” statics over the design wavelength. By this term we imply that some statics are positive (advances) and some are negative (delays). Because actual statics are time delays (they cannot be time advances), we will have to add a bias so that most of the computed statics become time delays. Such a step will remove most of the delay bias, leaving some residual time shifts on the final section.
We compute all velocities by taking the surface topog-raphy into account explicitly. This will eliminate the need for elevation corrections. Double focusing operators will con-tain all near-surface effects as a natural part of the travel-times between the focal point and the surface.
In the double focusing method, all traveltimes are defined between the surface and the subsurface focusing points. These traveltimes incorporate both the short- and Figure 12.A real shot record (center), statics-corrected up to
wave-length = 750 m (right), and up to wavewave-length 1500 m (left).
Figure 13.Conventional stack generated with a smooth floating datum.
long-wavelength portions of the time-distance relations, as well as elevation effects. The images are directly formed from the surface. However, short wavelengths will still be a prob-lem if not handled properly. Here, again, the probprob-lem can be solved by picking the differential arrival times in a sur-face-consistent manner. Integration and suppression of long wavelengths of the integrated results provides first-order estimates of short-wavelength perturbations. These can in turn be incorporated into an initial estimate of the times between the surface and the focal points. The travel-times are optimized with use of focusing analysis. Once the short-wavelength delay patterns to a first major boundary have been established, we will be free of near-surface dis-turbances. From then on we can compute partial focusing operators to the first major boundary, which can be specif-ically chosen to have an uncomplicated geometry.
Conclusions.We have presented a simple model of the near surface. Based on this model we have shown that short-wavelength undulations in the statics correction curves are due to near-surface effects on the upward-traveling reflected waves. These short-wavelength undulations cannot be explained by a computed velocity field, nor by the coarse-ness of the receiver spacing. We have shown that in con-ventional processing all statics up to the cable length must be eliminated. Based on these observations, we have pre-sented a statics correction method compatible with the pro-duction of sections from surface topography. This procedure eliminates the need to pick actual first breaks, the uncer-tainty associated with precursors of vibratory signals. It also handles difficulties arising from echeloning and from trun-cated refractor problems, from large elevation corrections, and from cycle skips of the residual static corrections. It also mitigates the effects of uncertainties in the near-surface velocities and in the corresponding long-wavelength stat-ics. In the case of other (longer wavelength) arrival time ver-sus distance relationships, these too are specifiable in terms of computed (parametric) velocities. Stacked and migrated sections are easily and more accurately generated by start-ing from the surface topography downward. Because stat-ics are computed independently of velocities, both can be determined separately, thus eliminating the need for clas-sic iterative velocity/statics computations. This approach is more economical and at the same time more accurate.
We have shown that the sampling interval in the time and space direction gives rise to the wavelength limitation for proper measurement and reconstruction of the reflected wavefield. On the other hand, short-wavelength distur-bances are generated in the near-surface layers. Thus, they are nearly time invariant and can be computed from dif-ferential arrival times with the desired wavelength. We have shown that the dividing line between statics and dynamics is controlled by the parameterization of the velocity/trav-eltime relationship. Conventional velocity analysis requires this separation to occur around a cable length. The double focusing method reduces this separation down to a geo-phone group interval. Therefore, wavelengths for the required corrections can be established deterministically and can be based on an imaging method. This can be done even before the statics corrections are determined.
In summary:
• When the subsurface is illuminated by a wavefront, it is healed from near surface irregularities by an expand-ing Fresnel zone.
• The reflected wavefield is recorded in the presence of near-surface irregularities before any appreciable
expan-sion of the Fresnel zone occurs.
• Events reflected from shallow zones exhibit shorter Fresnel zones, hence require shorter receiver intervals for proper sampling and imaging.
• Deeper reflectors will be recorded with wider Fresnel zones, which are more than adequately sampled. • Our recording intervals and our inability to construct
more detailed velocity fields for CDP type methods cre-ate the need for additional time correction terms under the general rubric of “statics.”
• Our difficulties stem from both wide shot and wide receiver distances. Thus, we cannot adequately represent the short-wavelength portion of a propagating wavefield. • Because we are dealing with a short-wavelength prob-lem, it is sufficient to observe and pick differential arrival times to determine the necessary corrections.
• Statics correction wavelengths will depend on the type of imaging process used. Conventional hyperbolic scans for velocity analyses require statics corrections up to a cable length. The double focusing method does not need a separate static correction, because each focusing oper-ator includes statics shifts as segments of the actual trav-eltimes.
• Static corrections should be applied only as time delays. • We propose to form images starting from the surface, where we know elevations from actual measurement. Apparently, what we know most about the subsurface is the surface.
• The remaining imaging steps can be implemented with respect to the surface elevations. Depth migration will require no further modification. Time migration will require time correction with respect to a well established datum plane. This correction is applied after migration. Imaging from the surface eliminates the elevation cor-rection problem.
• Our method aims to minimize the confusion introduced by various statics solutions namely, short and long wave-length, reflection or residual, elevation or datum cor-rection, etc. It also eliminates the need for first-break picking and the need for statics/velocity iteration. • There are no statics problems associated with the
dou-ble focusing method. A given traveltime represents the traveltime between a surface point and a subsurface focus point, without parametric approximation. The results are similar to those achieved with time migra-tion, but with better resolution. Depth images can also be obtained via tomographic inversion (Zhu et al., 1992).
Suggested reading.Seismic Migration by Berkhout (Handbook
of Geophysical Exploration, Volume 14a, Elsevier, 1982). “Prestack migration in terms of double focusing” by Berkhout (Journal of Seismic Exploration, 1995). “Imaging and characteri-zation with CFP technology, an overview” by Berkhout (SEG
1997 Expanded Abstracts). Static Corrections for Seismic Reflection Surveys by Cox (SEG, 1999). “Velocity-independent
redatum-ing: A new approach to the near-surface problem in land seis-mic data processing” by Kelamis et al. (TLE, 2002). “Tomostatics: Turning-ray tomography + static corrections” by Zhu et al.
(SEG 1992 Expanded Abstracts).TLE
