John E. Anderson

Fast full-wavefield seismic inversion using encoded sources

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.

Efficient seismic forward modeling using simultaneous random sources and sparsity

The high cost of simulating densely sampled seismic forward modeling data arises from activating sources one at a time in sequence.Toincreaseefficiency,onecouldleveragerecentinnovations in seismic field-data acquisition and activate several e.g., 2‐6 sources simultaneously during modeling. However, such approaches would suffer from degraded data quality because of the interference between the model’s responses to the simultaneoussources.Twonewefficientsimultaneous-sourcemodeling approachesareproposedthatrelyonthenoveltandemuseofrandomness and sparsity to construct almost noise-free model response to individual sources. In each approach, thefirst step is to measure the model’s cumulative response with all sources activated simultaneously using randomly scaled band-limited impulses or continuous band-limited random-noise waveforms. In the second step, the model response to each individual source is estimated from the cumulative receiver measurement by exploiting knowledge of the random source waveforms and the sparsity of the model response to individual sources in a known transformdomaine.g.,curveletdomain.Theefficiencyachievable by the approaches is primarily governed by the sparsity of the model response. By invoking results from the field of compressive sensing, theoretical bounds are provided that assert that the approaches would need less modeling time for sparser i.e., simpler or more structured model responses.Asimulated modelingexampleisillustratedthatshowsthatdatacollectedwithas manyas8192sourcesactivatedsimultaneouslycanbeseparated into the 8192 individual source gathers with data quality comparable to that obtained when the sources were activated sequentially.Theproposedapproachescouldalsodramaticallyimprove seismic field-data acquisition efficiency if the source signatures actuallyprobingtheearthcanbemeasuredaccurately.

Finite-difference frequency-domain modeling of viscoacoustic wave propagation in 2D tilted transversely isotropic (TTI) media

A 2D finite-difference, frequency-domain method was developed for modeling viscoacoustic seismic waves in transversely isotropic media with a tilted symmetry axis. The medium is parameterized by the P-wave velocity on the symmetry axis, the density, the attenuation factor, Thomsen’s anisotropic parameters δ and ϵ , and the tilt angle. The finite-difference discretization relies on a parsimonious mixed-grid approach that designs accurate yet spatially compact stencils. The system of linear equations resulting from discretizing the time-harmonic wave equation is solved with a parallel direct solver that computes monochromatic wavefields efficiently for many sources. Dispersion analysis shows that four grid points per P-wavelength provide sufficiently accurate solutions in homogeneous media. The absorbing boundary conditions are perfectly matched layers (PMLs). The kinematic and dynamic accuracy of the method wasassessed with several synthetic examples which illustrate the propagation of S-waves excited at t...

Elastic RTM: Anisotropic Wave-mode Separation And Converted-wave Polarization Correction

In this study, we investigate the impact of different wavemode separation approaches on TTI anisotropic elastic reverse time migration (RTM). We tested the cheap but less accurate Helmholtz decomposition method as well as the expensive but more accurate pseudo-derivative method on a simple 2D model. Our study shows that the stacking operator associated with the RTM algorithm can naturally remove most of the leaking-mode artifacts generated by the less accurate Helmholtz decomposition method in anisotropic media. Therefore, for the purposes of kinematic imaging, it is practically acceptable to use the Helmholtz decomposition for mode separation in elastic anisotropic RTM. Another issue in elastic RTM is that converted PS wavefields have mixed polarity depending on the P-wave incidence angle. As a result, a given event has opposite signs in different shot images, causing the event to be destroyed after stacking over all shots. We propose a correction approach in which the angle-domain commonimage gathers are computed at every imaging point and the polarity is corrected in the angle domain before stacking. The polarization correction allows the same event to be stacked constructively yielding a more consistent PS image.

Fast Full Wave Seismic Inversion Using Source Encoding

Full Wavefield Seismic Inversion (FWI) estimates a subsurface elastic model by iteratively minimizing the difference between observed and simulated data. This process is extremely compute intensive, with a cost on the order of at least hundreds of prestack reverse time migrations. For time-domain and Krylov-based frequency-domain FWI, the cost of FWI is proportional to the number of seismic sources inverted. We have found that the cost of FWI can be significantly reduced by applying it to data processed by encoding and summing individual source gathers, and by changing the encoding functions between iterations. 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. We demonstrate, using synthetic data, significant cost reduction by applying FWI to encoded simultaneous-source data.

Comparison of elastic and acoustic reverse-time migration on the synthetic elastic Marmousi-II OBC dataset

We use the synthetic elastic Marmousi-II ocean bottom cable (OBC) dataset to compare the results from elastic reverse-time migration (RTM) and acoustic RTM. We applied acoustic RTM to the pressure data and applied elastic RTM to the horizontal and vertical particle velocity data for simulated OBC data at the sea bottom. The results show clear improvement on the elastic P-wave RTM images compared to the acoustic RTM images.

Characterization of spatially varying surface waves in a land seismic survey

Summary We present several methods for analyzing surface waves in a highly sampled 3-C, 3D survey, and report the most important characteristics derived from those analyses. In particular, we demonstrate the spatial variability of surfacewave velocities and polarization properties. We also show that surface-wave velocities are correlated with other seismic and nonseismic properties of the near surface, such as shear-wave statics and surface texture derived from satellite imagery.