A field expansions method for scattering by periodic multilayered media

The interaction of acoustic and electromagnetic waves with periodic structures plays an important role in a wide range of problems of scientific and technological interest. This contribution focuses upon the robust and high-order numerical simulation of a model for the interaction of pressure waves generated within the earth incident upon layers of sediment near the surface. Herein is described a Boundary Perturbation Method for the numerical simulation of scattering returns from irregularly shaped periodic layered media. The method requires only the discretization of the layer interfaces (so that the number of unknowns is an order of magnitude smaller than Finite Difference and Finite Element simulations), while it avoids not only the need for specialized quadrature rules but also the dense linear systems characteristic of Boundary Integral/Element Methods. The approach is a generalization to multiple layers of Bruno & Reitich's "Method of Field Expansions" for dielectric structures with two layers. By simply considering the entire structure simultaneously, rather than solving in individual layers separately, the full field can be recovered in time proportional to the number of interfaces. As with the original Field Expansions method, this approach is extremely efficient and spectrally accurate.National Science Foundation (U.S.) (grant No. DMS–0810958)United States. Dept. of Energy (Award No. DE–SC0001549)Massachusetts Institute of Technology. Earth Resources Laborator

Rapid 4D FWI using a local wave solver

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

Operator expansions and constrained quadratic optimization for interface reconstruction: Impenetrable periodic acoustic media

Grating scattering is a fundamental model in remote sensing, electromagnetics, ocean acoustics, nondestructive testing, and image reconstruction. In this work, we examine the problem of detecting the geometric properties of gratings in a two-dimensional acoustic medium where the fields are governed by the Helmholtz equation. Building upon our previous Boundary Perturbation approach (implemented with the Operator Expansions formalism) we derive a new approach which augments this with a new “smoothing” mechanism. With numerical simulations we demonstrate the enhanced stability and accuracy of our new approach which further suggests not only a rigorous proof of convergence, but also a path to generalizing the algorithm to multiple layers, three dimensions, and the full equations of linear elasticity and Maxwell’s equations

SVD enhanced seismic interferometry for traveltime estimates between microquakes

In general, Green's functions obtained with seismic interferometry are only estimates of the true Green's function, introducing uncertainties to the information recovered from them. However, there are still many cases in which the source‐receiver geometries are suitable for seismic interferometry, usually allowing the recovery of kinematic information. Here we show how to use the singular value decomposition to reenforce the accuracy of traveltimes obtained from interferometric Green's functions. We apply the combination of seismic interferometry and the singular value decomposition to obtain physically accurate inter‐event traveltimes for microquake pairs at a geothermal reservoir. With a synthetic example, we show that the P‐wave phase and coda‐wave energy information are closer to correct with the singular value decomposition than without. These traveltimes could be used for velocity tomography and event location algorithms to obtain more accurate event locations and locally accurate velocity models

Separating a wavefield by propagation direction

Determining the propagation direction of waves in a wavefield is important in several seismic imaging techniques and applications. This can be achieved using the Poynting vector method, but it performs poorly when waves overlap, returning incorrect wave amplitude and direction. An alternative, the local slowness method, is capable of separating overlapping waves, but suffers from low angular resolution. We describe modifications of these two approaches that improve the ability to extract the wave amplitude propagating in different directions. The primary modification is the addition of a wavefront orientation separation step. We evaluate the original and modified methods' ability to separate six overlapping waves in a constant velocity model and find that the modifications significantly improve the results

Coupling a Local Elastic Solver to a Background Acoustic Model to Estimate Phase Variation

In characterizing reservoirs, we are often interested in detailed elastic parameters about only a very limited part of the subsur-face. To that end, we introduce a local solver which uses an acoustic solver to propagate the wavefield to a sub-domain on which we use a local elastic solver. This avoids the use of an expensive full domain elastic solver while still incorporating elastic physics in the region where it is most important. We apply the local solver to modeling phase variation with angle

On the topological sensitivity of transient acoustic fields

The concept of topological sensitivity has been successfully employed as an imaging tool to obtain the correct initial topology and preliminary geometry of hidden obstacles for a variety of inverse scattering problems. In this paper, we extend these ideas to acoustic scattering involving transient waveforms and penetrable obstacles. Through a boundary integral equation framework, we present a derivation of the topological sensitivity for the featured class of problems and illustrate numerically the utility of the proposed method for preliminary geometric reconstruction of penetrable obstacles. For generality, we also cast the topological sensitivity in the so-called adjoint field setting that is amenable to a generic computational treatment using, for example, finite element or finite difference methods

An efficient coupled acoustic-elastic local solver applied to phase inversion

In characterizing reservoirs, we are often interested in retrieving detailed elastic parameters for only a very limited part of the subsurface. One way of doing so involves studying the seismic reflection response within the region of interest. To that end, we introduce a local solver that uses an acoustic solver to propagate the wavefield to a subdomain on which we use a local elastic solver. This avoids the use of an expensive full-domain elastic solver while still incorporating elastic physics in the region where it is most important. We then study whether this modeled phase is sufficiently accurate for recovering important subsurface reservoir properties in an inversion procedure

Laser characterization of ultrasonic wave propagation in random media

Lasers can be used to excite and detect ultrasonic waves in a wide variety of materials. This allows the measurement of absolute particle motion without the mechanical disturbances of contacting transducers. In an ultrasound transmission experiment, the wave field is usually accessible only on the boundaries of a sample. Using optical methods, one can measure the surface wave field, in effect, within the scattering region. Here, we describe noncontacting (laser source and detector) measurements of ultrasonic wave propagation in randomly heterogeneous rock samples. By scanning the surface of the sample, we can directly visualize the complex dynamics of diffraction, multiple scattering, mode conversion, and whispering gallery modes. We will show measurements on rock samples that have similar elastic moduli and intrinsic attenuation, but different grain sizes, and hence, different scattering strengths. The intensity data are well fit by a radiative transfer model, and we use this fact to infer the scattering mean free path