S U M M A R YIn a set of problems ranging from 4-D seismic to salt boundary estimation, updates to the velocity model often have a highly localized nature. Numerical techniques for these applications such as full-waveform inversion (FWI) require an estimate of the wavefield to compute the model updates. When dealing with localized problems, it is wasteful to compute these updates in the global domain, when we only need them in our region of interest. This paper introduces a local solver that generates forward and adjoint wavefields which are, to machine precision, identical to those generated by a full-domain solver evaluated within the region of interest. This means that the local solver computes all interactions between model updates within the region of interest and the inhomogeneities in the background model outside. Because no approximations are made in the calculation of the forward and adjoint wavefields, the local solver can compute the identical gradient in the region of interest as would be computed by the more expensive full-domain solver. In this paper, the local solver is used to efficiently generate the FWI gradient at the boundary of a salt body. This gradient is then used in a level set method to automatically update the salt boundary.
Rapid 4D FWI using a local wave solver Abstract Much of the computational cost involved in full-waveform inversion comes from the solution of the wave equation in a large domain. These computations must be done for the entire domain through which we expect waves to pass for a particular survey, despite the fact that our region of interest is often significantly smaller. In addition to the wasted time spent propagating waves through less important parts of the model, computing updates on the entire domain may result in slower convergence of the inversion algorithm due to the larger model space. This can be especially important in 4D seismic monitoring, where we often see the majority of changes within a small subregion of the total domain, such as the reservoir. We present a local wave solver that accurately computes the solution of the wave equation within only a subdomain of the region covered by the survey, representing a significant cost saving in the computation of full-waveform inversion. We also show how this solver can improve the resulting velocity estimates in full-waveform inversion for time-lapse applications and observe that the local solver requires fewer iterations to converge than does the full-domain solver. IntroductionFull-waveform inversion (FWI) typically involves solving the forward problem of propagating waves from the source to the receiver multiple times per iteration (see, e.g., Virieux and Operto, 2009, and references therein). The calculation of these wavefields is the primary computational cost of an FWI algorithm. However, when waves from the same sources are propagated through a model that has changed little between iterations, much of this computation is repeated from one iteration to the next. For 4D seismic applications, the impact of this repetition on computational cost is greater because we are typically interested in only a small region of the model (e.g., the reservoir), and we may have several data sets to invert. If we are able to perform FWI on only a small subset of the subsurface model, while still taking all of the data into account, we can improve the speed of the inversion process while still preserving the accuracy of the recovered results. To do this, we require an algorithm that solves the wave equation on a subdomain, giving exactly the same wavefield (on that subdomain) as would be obtained when solving the full wave equation in the full domain. We presented such an algorithm in , building upon the work of van Manen et al. (2007). Here, we show how this algorithm can be used to increase the efficiency of FWI for the particular case of 4D velocity change estimation. If there are significant changes outside the reservoir region, as can occur due to compaction for example, then our method may not result in significant cost savings as the number and size of the relevant subdomains grow.Full-waveform inversion for 4D is challenging because of the nonuniqueness of the problem (there are multiple models that fit (Yang et al., 2014a), and model-space regularization me...
colm, Enabling numerically exact local solver for waveform-inversion-a low-rank approach, Computational Geosciences
We demonstrate that a workflow combining emergent time-lapse full-waveform inversion (FWI) and machine learning technologies can address the demand for faster time-lapse processing and analysis. During the first stage of our proposed workflow, we invert long-wavelength velocity changes using a tomographically enhanced version of multiparameter simultaneous reflection FWI with model-difference regularization. Short-wavelength changes are inverted during the second stage of the workflow by a specialized high-resolution image-difference tomography algorithm using a neural network. We discuss application areas for each component of the workflow and show the results of a West Africa case study.
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