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The separation of P- and S-wavefields is considered to be an effective approach for eliminating wave-mode crosstalk in elastic reverse time migration (RTM). At present, the Helmholtz decomposition method is widely used for isotropic media. However, it tends to change the amplitudes and phases of the separated wavefields compared with the original wavefields. Other methods used to obtain pure P- and S-wavefields include the application of the elastic wave equations of the decoupled wavefields. To achieve high computational accuracy, staggered-grid finite-difference (FD) schemes are usually used to numerically solve the equations by introducing an additional stress variable. However, the computational cost of this method is high because a conventional hybrid wavefield (the P- and S-wavefields are mixed together) simulation must be created before the P- and S-wavefields can be calculated. We have developed the first-order particle velocity equations to reduce the computational cost. The equations can describe four types of particle-velocity wavefields: the vector P-wavefield, the scalar P-wavefield, the vector S-wavefield, and the vector S-wavefield rotated in the direction of the curl factor. Without introducing the stress variable, only the four types of particle velocity variables are used to construct the staggered-grid FD schemes; therefore, the computational cost is reduced. We also develop an algorithm to calculate the P and S propagation vectors using the four particle velocities, which is simpler than the Poynting vector. Finally, we apply the velocity equations and propagation vectors to elastic RTM and angle-domain common-image gather computations. These numerical examples illustrate the efficiency of our methods. more...

Polarity reversal is a well-known problem in elastic reverse time migration, and it is closely related to the imaging conditions. The dot product of source and receiver wavefields is a stable and efficient way to construct scalar imaging conditions for decomposed elastic vector wavefields. However, for PP images, the dot product introduces an angle-dependent factor that will change the polarity of image amplitudes at large opening angles, and it is also contaminated by low-wavenumber artifacts when sharp contrasts exist in the velocity model. Those two problems can be suppressed by muting the reflections with large opening angles at the expense of losing useful information. We have developed an elastic inverse-scattering imaging condition that can retain the initial polarity of the image amplitude and significantly reduce the low-wavenumber noise. For PS images, much attention is paid to the polarity-reversal problem at the normal incidence, and the dot-product-based imaging condition successfully avoids this kind of polarity reversal. There is another polarity-reversal problem arising from the sign change of the PS reflection coefficient at the Brewster angle. However, this sign change is often neglected in the construction of a stacked PS image, which will lead to reversed or distorted phases after stacking. We suggested using the S-wave impedance kernel used in elastic full-waveform inversion but only in the PS mode as an alternative to the dot-product imaging condition to alleviate this kind of polarity-reversal problem. In addition to dot-product-based imaging conditions, we analytically compare divergence- and curl-based imaging conditions and the elastic energy norm-based imaging condition with the presented imaging conditions to identify their advantages and weaknesses. Two numerical examples on a two-layer model and the SEAM 2D model are used to illustrate the effectiveness and advantages of the presented imaging conditions in suppressing low-wavenumber noise and correcting the polarity-reversal problem. more...

Deprimary reverse time migration (RTM) is a newly proposed technology aiming at removing false structures in images computed by RTM. However, a side effect of this new technology is an inability to image steeply dipping structures. We first introduce how to obtain a composite wavefield, including a complete downgoing wavefield and a partial upgoing wavefield, using the combination of an f-k filter and a spatial-wavenumber filter. We next thoroughly analyze the root cause leading to this side effect in the deprimary RTM technology. By using a modified imaging condition accommodating a composite wavefield, we propose a novel flank-preserving deprimary RTM method to maintain the capability of removing false structures and preserve steeply dipping subsurface structures in the final image. We demonstrate the success of this new technology via several examples. Furthermore, we study different perspectives in depth to show that flank-preserving deprimary RTM is a trade-off solution between RTM and deprimary RTM. more...

The safety and efficiency of tunnel construction depend on the knowledge of complex geologic conditions. Hence, an accurate forward-prospecting technique is required to detect unexpected inhomogeneous geologic structures ahead of tunnel construction. As an accurate method to image geologic heterogeneities, elastic reverse time migration (ERTM) is introduced to the field of tunnel forward prospecting. However, in the tunnel environment, ERTM images may suffer from the interference of crosstalk artifacts, which are caused by converted waves on tunnel surfaces. Therefore, considering the actual influence of the tunnel body, the decoupled nonconversion elastic equation was incorporated into traditional ERTM. This method prevents the generation of converted waves but ensures independent P- and S-wave propagation. In addition, wave-mode separation for raw seismic data is required in our approach. Synthetic examples based on the real geologic environment of tunnels show that our method produces satisfactory results for P-wave and S-wave imaging and the S-wave can produce a better imaging effect in tunnels. Finally, we apply our method to the seismic data obtained from a real highway tunnel construction site to demonstrate its performance in real-world applications. The results indicate that the migrated images can help to accurately constrain the geologic formations ahead of the tunnel face. more...

Anisotropic reverse time migrations (RTMs) using pseudoacoustic or elastic wave equations are tested, and the migrated PP images, obtained using the same data set as input, are compared. In anisotropic elastic RTMs, both divergence operators, and localized low-rank approximations (LLA), are tested and compared for P/S separation. Tests with synthetic data indicate that elastic RTMs have better illumination apertures than pseudoacoustic RTMs in subsalt areas because of the involvement of converted S-waves in the former. Pseudoacoustic RTMs have diamond-shaped S-wave artifacts, which do not exist in elastic RTM images, provided that the P- and S-waves are separated in the elastic wavefields. LLAs provide affordable, accurate P/S separations in anisotropic media, and the separation results are better than those obtained using divergence operators. Anisotropic elastic RTMs with LLA give the best quality images. more...

A challenging outstanding problem in reverse time extrapolation is recovering accurate amplitudes at reflectors from the receiver wavefield. Various migrations have been developed to produce accurate image locations rather than correct amplitude information because of inadequate compensation of attenuation, dispersion, and transmission losses. We have evaluated the requirements, and determined the theoretical feasibility, of true amplitude recovery of 2D acoustic and elastic seismic data by using the analytic Zoeppritz equations for plane-wave reflection and transmission coefficients. Then, we used synthetic acoustic and elastic wavefield data generated by elastodynamic finite differences to verify the recovery, in the reverse time propagation, of spherical waves and illustrated the salient differences between the incident wavefields reconstructed from reflection data only and from the combination of reflection and transmission data. These examples quantitatively verify that recovering an incident plane or a spherical wave requires the reverse time propagation of all reflections and transmissions in a model with the correct velocity and density. Accurate reconstruction of an incident wave is not possible by backward propagation of only reflections. As an application, we removed downgoing internal multiple reflections generated by upgoing waves incident at reflectors shallower than a horizontal well, in which geophones are deployed. The subtraction of the downgoing reflection involves wavefield reconstruction at depths shallower than the horizontal well and separation of upgoing and downgoing wavefields. This approach assumes that the correct acoustic (or elastic) velocity and density models are available in, and shallower than, the layer where the horizontal well is located. Incident-wave reconstruction works equally well for smooth models, as for models with sharp boundaries. Uncertainties in the model used for reconstruction, and incompleteness of the data aperture are propagated into the equivalent uncertainties, and incompleteness of the reconstruction. more...

The simultaneous-source shooting technique can accelerate field acquisition and improve spatial sampling but it will cause strong interferences in the recorded data and artifacts in the final image. The previously proposed structural smoothing operator can effectively attenuate artifacts for relatively simple reflection structures during least-squares inversion, but it will cause damage to complicated reflection events such as discontinuities. To preserve discontinuities in a seismic image, we apply the singular spectrum analysis (SSA) operator to attenuate artifacts during least-squares inversion. Considering that global SSA cannot deal with overcomplicated data very well, we use local SSA to remove noise and to better preserve the steeply dipping components. The local SSA operator corresponds to a local low-rank constraint applied in the inversion process. The migration operator used in the study is the reverse time migration (RTM) operator. Tests using the Marmousi model showed the superior performance of the proposed algorithm in preserving the discontinuities of seismic images. more...

In reverse time migration (RTM) or full-waveform inversion (FWI), forward and reverse time propagating wavefields are crosscorrelated in time to form either the image condition in RTM or the misfit gradient in FWI. The crosscorrelation condition requires both fields to be available at the same time instants. For large-scale 3D problems, it is not possible, in practice, to store snapshots of the wavefields during forward modeling due to extreme storage requirements. We have developed an approximate wavefield reconstruction method that uses particle velocity field recordings on the boundaries to reconstruct the forward wavefields during the computation of the reverse time wavefields. The method is computationally effective and requires less storage than similar methods. We have compared the reconstruction method to a boundary reconstruction method that uses particle velocity and stress fields at the boundaries and to the optimal checkpointing method. We have tested the methods on a 2D vertical transversely isotropic model and a large-scale 3D elastic FWI problem. Our results revealed that there are small differences in the results for the three methods. more...