Full-waveform inversion FWI is a challenging data-fitting procedure based on full-wavefield modeling to extract quantitative information from seismograms. High-resolution imaging at half the propagated wavelength is expected. Recent advances in high-performance computing and multifold/multicomponent wide-aperture and wide-azimuth acquisitions make 3D acoustic FWI feasible today. Key ingredients of FWI are an efficient forward-modeling engine and a local differential approach, in which the gradient and the Hessian operators are efficiently estimated. Local optimization does not, however, prevent convergence of the misfit function toward local minima because of the limited accuracy of the starting model, the lack of low frequencies, the presence of noise, and the approximate modeling of the wave-physics complexity. Different hierarchical multiscale strategiesaredesignedtomitigatethenonlinearityandill-posedness of FWI by incorporating progressively shorter wavelengths in the parameter space. Synthetic and real-data case studies address reconstructing various parameters, from VP and VS velocities to density, anisotropy, and attenuation. This review attempts to illuminate the state of the art of FWI. Crucial jumps, however, remain necessary to make it as popular as migration techniques. The challenges can be categorized as 1 building accurate starting models with automatic procedures and/or recording low frequencies, 2 defining new minimization criteria to mitigate the sensitivity of FWI to amplitude errors and increasing the robustness of FWI when multiple parameter classes are estimated, and 3 improving computational efficiency by data-compression techniquestomake3DelasticFWIfeasible.

/pdf/an-overview-of-full-waveform-inversion-in-exploration-59sei7fzvh.pdf

An overview of full-waveform inversion in exploration geophysics

Full-wavefield seismic inversion (FWI) estimates a subsurface elastic model by iteratively minimizing the difference between observed and simulated data. This process is extremely computationally intensive, with a cost comparable to at least hundreds of prestack reverse-time depth migrations. When FWI is applied using explicit time-domain or frequency-domain iterative-solver-based methods, the seismic simulations are performed for each seismic-source configuration individually. Therefore, the cost of FWI is proportional to the number of sources. We have found that the cost of FWI for fixed-spread data can be significantly reduced by applying it to data formed by encoding and summing data from individual sources. The encoding step forms a single gather from many input source gathers. This gather represents data that would have been acquired from a spatially distributed set of sources operating simultaneously with different source signatures. The computational cost of FWI using encoded simultaneous-source gathers is reduced by a factor roughly equal to the number of sources. Further, this efficiency is gained without significantly reducing the accuracy of the final inverted model. The efficiency gain depends on subsurface complexity and seismic-acquisition parameters. There is potential for even larger improvements of processing speed.

Fast full-wavefield seismic inversion using encoded sources

Frequency‐domain shot‐record migration can produce higher quality images than Kirchhoff migration but typically at a greater cost. The computing cost of shot‐record migration is the product of the number of shots in the survey and the expense of each individual migration. Many attempts to reduce this cost have focused on the speed of the individual migrations, trying to achieve a better trade‐off between accuracy and speed. Another approach is to reduce the number of migrations. We investigate the simultaneous migration of shot records using frequency‐domain shot‐record migration algorithms. The difficulty with this approach is the production of so‐called crossterms between unrelated shot and receiver wavefields, which generate unwanted artifacts or noise in the final image. To reduce these artifacts and obtain an image comparable in quality to the single‐shot‐per‐migration result, we have introduced a process called phase encoding, which shifts or disperses these crossterms. The process of phase encoding...

Phase encoding of shot records in prestack migration

Prestack depth migration of shot profiles by downward continuation is a practical imaging algorithm that is especially cost-effective for sparse-shot wide-azimuth geometries. The interpretation of offset as the displacement between the downward-propagating (shot) wavefield and upward-propagating (receiver) wavefield enables us to extract offset-domain common image-point (CIP) gathers during shot-profile migration. The offset-domain gathers can then be transformed to the angle domain with a radial-trace mapping originally introduced for shot-geophone migration. The computational implications of this procedure include both the additional cost of multioffset imaging and an implicit transformation from shot-geophone to midpoint-offset coordinates. Although this algorithm provides a mechanism for imaging angle-dependent reflectivity via shot-profile migration, for sparse-shot geometries the fundamental problem of shot-aliasing may severely impact the quality of CIP gathers.

Offset and angle-domain common image-point gathers for shot-profile migration

Reverse-time migration (RTM) exhibits great superiority over other imaging algorithms in handling steeply dipping structures and complicated velocity models. However, low-frequency, high-amplitude noises commonly seen in a typical RTM image have been one of the major concerns because they can seriously contaminate the signals in the image if they are not handled properly. We propose a new imaging condition to effectively and efficiently eliminate these specific noises from the image. The method works by first decomposing the source and receiver wavefields to their one-way propagation components, followed by applying a correlation-based imaging condition to the appropriate combinations of the decomposed wavefields. We first give the physical explanation of the principle of such noises in the conventional RTM image. Then we provide the detailed mathematical theory for the new imaging condition. Finally, we propose an efficient scheme for its numerical implementation. It replaces the computationally intensiv...

An effective imaging condition for reverse-time migration using wavefield decomposition

Reverse-time migration has the capability to image all dips including overturned structures. However, the conventional imaging condition produces high-amplitude noises in the image, which often seriously mask the shallow structures. In this paper, we propose a new imaging condition to eliminate these noises which works by decomposing the full wavefields to their one-way components, and applying the imaging condition to the appropriate combinations of the wavefield components. Numerical tests verify that this new imaging condition successfully removes the undesired noises.

Reverse-time Migration Using One-way Wavefield Imaging Condition

Phase encoding of shot records provides a means of imaging a number of shots within a single migration. This results in a reduction in the required computation for a complete image, a reduction by the number of shots used in each individual migration, trading this increase in speed for additional noise in the resulting image. Some methods for phase encoding have been shown to limit this noise to a tolerable range when combining several shots, enabling speed ups of a factor of a few. In this paper, the authors present a use of phase encoding which allows faster imaging by an order of magnitude or more, with the additional benefit that the individual migrations can be stopped whenever the answer is good enough. This approach may ultimately render 3-D frequency-domain prestack depth migration cost effective.

/pdf/faster-shot-record-depth-migrations-using-phase-encoding-59vafdhynw.pdf

Faster shot-record depth migrations using phase encoding

In this paper, we decouple the P and SV wave components in an acoustic transversely isotropic media with vertical symmetric axis (VTI), and construct an independent pseudo-differential equation for each wave mode. The resulted wave equation for P-wave is unconditionally stable. A scheme based on the optimized separable approximation is proposed for their numerical implementation. We demonstrate the theory with some simple experiments.

Scott A. Morton

Papers

Phase encoding of shot records in prestack migration

An effective imaging condition for reverse-time migration using wavefield decomposition

Reverse-time Migration Using One-way Wavefield Imaging Condition

Faster shot-record depth migrations using phase encoding

Decoupled Wave Equations For P And SV Waves In an Acoustic VTI Media