Robbert van Vossen

Finite-difference modeling of wave propagation in a fluid-solid configuration

Finite-difference (FD) techniques are widely used to model wave propagation through complex structures. Two main sources of error can be identified: (1) from numerical dispersion and numerical anisotropy and (2) by modeling the response of internal grid boundaries. Conventional discretization criteria to reduce the effects of numerical dispersion and numerical anisotropy have long been established (5-8 gridpoints per wavelength for a fourth-order accurate FD scheme). We analyze the second source of errors, comparing different staggered-grid FD solutions to the Cagniard-de Hoop solution in models with fluid-solid contacts. Our results confirm that it is sufficient to rely on conventional discretization criteria if the fluid-solid interface is aligned with the grid. If accurate modeling of the Scholte wave is required, then a new imaging method we propose should be used to allow for conventional sampling of the wavefield to minimize numerical dispersion. However, for an interface not aligned with the grid (irregular interfaces), a spatial sampling of at least 15 gridpoints per minimum wavelength is required to obtain acceptable results, particularly in seismic seabed applications where Scholte waves may need to be modeled more accurately.

Surface-consistent deconvolution using reciprocity and waveform inversion

Source and receiver responses must be equalized when their behavior or coupling changes with location within a given survey. Existing surface-consistent deconvolution techniques that account for these effects assume that common-midpoint (CMP) gathering is valid — the seismic trace is decomposed into a source function, a receiver response, a normal-incidence reflectivity term, and an offsetrelated component that is laterally shift invariant. As a result, the performance of existing surface-consistent deconvolution techniques is best when applied to primary reflection data only, since the offset dependency of ground roll and multiples varies laterally in media with lateral variations. We have developed an alternative method for surfaceconsistent deconvolution that is applicable to the entire seismic trace and is therefore essentially a raw-data preprocessing step. The method is based on reciprocity of the medium response. Assuming that conditions for applicability of reciprocity are met, we can attribute differences between normal and reciprocal recordings to the source and receiver perturbations. Contrary to existing surfaceconsistent deconvolution methods, this approach uses the full description of the wavefield and is therefore ideally suited for prestack processing. We have applied this technique to single-sensor data acquired in Manistee County, Michigan. At this site, nearsurface conditions vary, and this significantly affects data quality. The application of the new deconvolution procedure substantially improves S/N ratio on both prestack and poststack data, and these results compare favorably to those obtained using existing surface-consistent deconvolution techniques, since they require subjective data scaling to obtain acceptable results. The obtained source corrections are correlated to changes in near-surface conditions — in this case, to changes in water-saturation levels. We do not observe such a correlation for the receiver corrections, which vary rapidly along the spread. Finally, the receiver response does not agree with the generally accepted damped harmonic oscillator model. For frequencies below 100 Hz, the retrieved receiver variations are larger than predicted by this model, and we cannot explain the receiver response using a single resonant frequency for the geophone-ground coupling.

Full-waveform static corrections using blind channel identification

Near-surface wavefield perturbations can be very complex and completely mask the target reflections. Despite this complexity, conventional methods rely on parameterizations characterized by simple time and amplitude anomalies to compensate for these perturbations. Determining and compensating for time shifts is generally referred to as residual static corrections, whereas surface-consistent deconvolution techniques deal with amplitude anomalies. We present an approach that uses the full waveform to parameterize near-surface perturbations. Therefore, we refer to this method as waveform statics. Important differences from conventional static corrections are that this approachallowstimeshiftstovarywithfrequencyandtakesamplitudevariationsdirectlyintoaccount.Furthermore,theprocedure is fully automated and does not rely on near-surface velocity information. The waveform static corrections are obtained using blind channel identification and applied to the recordings using multichannel deconvolution. As a result, the method implicitly incorporates array forming. The developed method is validated onsyntheticdataandappliedtopartofafielddatasetacquiredin an area with significant near-surface heterogeneity. The source and receiver responses obtained are strongly correlated to the near-surfaceconditionsandshowchanges,bothinphaseandfrequency content, along the spread. The application of the waveform statics demonstrates that they not only correct for near-surface wavefield perturbations, but also strongly reduce coherent noise.This results in substantial improvements, both in trace-totrace coherency and in depth resolution. In addition, the procedure delineates reflection events that are difficult to detect prior to our proposed correction. Based on these results, we conclude that complex near-surface perturbations can be successfully dealt with using the multichannel, full-waveform, static-correctionprocedure.

Subsonic near-surface P-velocity and low S-velocity observations using propagator inversion

Detailed knowledge of near-surface P- and S-wave velocities is important for processing and interpreting multicomponent land seismic data because (1) the entire wavefield passes through and is influenced by the near-surface soil conditions, (2) both source repeatability and receiver coupling also depend on these conditions, and (3) nearsurface P- and S-wave velocities are required for wavefield decomposition and demultiple methods. However, it is often difficult to measure these velocities with conventional techniques because sensitivity to shallow-wave velocities is low and because of the presence of sharp velocity contrasts or gradients close to the earth’s free surface. We demonstrate that these near-surface P- and S-wave velocities can be obtained using a propagator inversion. This approach requires data recorded by at least one multicomponent geophone at the surface and an additional multicomponent geophone at depth. The propagator between them then contains all information on the medium parameters governing wave propagation between the geophones at the surface and at depth. Hence, inverting the propagator gives local estimates for these parameters. This technique has been applied to data acquired in Zeist, the Netherlands. The near-surface sediments at this site are unconsolidated sands with a thin vegetation soil on top, and the sediments considered are located above the groundwater table. A buried geophone was positioned 1.05 m beneath receivers on the surface. Propagator inversion yielded low near-surface velocities, namely, 270 ± 15 m/s for the compressional-wave velocity, which is well below the sound velocity in air, and 150 ± 9 m/s for the shear velocity. Existing methods designed for imaging deeper structures cannot resolve these shallow material properties. Furthermore, velocities usually increase rapidly with depth close to the earth’s surface because of increasing confining pressure. We suspect that for this reason, subsonic near-surface P-wave velocities are not commonly observed.

Source and receiver amplitude equalization using reciprocity — application to land seismic data

Source and receiver amplitude equalization is necessary when their behavior changes with location within a given survey. Preferably, these corrections are performed in the early stages of processing. However, existing techniques which account for these effects, such as surface-consistent deconvolution, are applicable to primary reflection data only. Therefore, these techniques require prior processing. We developed an alternative method to compensate for source and receiver perturbations which has the advantage of being purely a preprocessing step. It is applicable to the whole seismic trace, and no assumptions are imposed on the subsurface. The method is based on reciprocity of the medium response. As a result of reciprocity, differences between normal and reciprocal recordings can be attributed to the source and receiver perturbations. We applied this technique to single-sensor data acquired in Manistee County, Michigan. At this site, near-surface conditions vary, and this significantly affects the data quality. The application of the equalization procedure led to a significant improvement in signal-to-noise ratio, on both prestack and poststack data.

Propagator Inversion For Shallow Structure

Near-receiver material properties are required to separate the recorded wavefield into Pand S-, and upand downgoing components, and can enhance static corrections and improve depth estimates of refractors. We present an approach for estimating local material properties between two geophones, one buried and one positioned at the surface. We do so by inverting the vertical wavefield propagator in the time domain. Both its amplitude and phase are used to determine the local structure between the two geophones. Synthetic experiments and noise tests demonstrate that the propagator inversion provides accurate estimates for P and S velocities, and is robust with respect to near-surface reverberations.