Collaborative Research: Multiscale Aspects for Wave Propagation Inverse Problems

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Many natural materials exhibit structural heterogeneity across a wide range of scales. Examples of such media with microstructure include virtually every part of the Earth's crust, and manufactured composite materials such as concrete. These materials also support wave motion, and various technologies have evolved which use propagating waves for nondestructive interogation of material structure. In their present state, these technologies (reflection seismology, ultrasonic nondestructive evaluation, etc) are for the most part based on theoretical understanding and computational methods developed for waves in homogeneous (or near-homogeneous) materials. This divide between theoretical basis and application context is bridged to some extent by effective medium theories which attempt to express at macroscopic scales the effect of microscopic heterogeneities. However rigorous justification of the effective medium approach is largely limited to periodic material models, which do not resemble disordered materials such as sedimentary rock. This study will attempt to leverage recent advances in the simulation of acoustic and elastic waves in media with microstructure to assess the feasibility of explaining simulated experimental data by means of simpler models without microstructure. These models may exhibit physical characteristics not present on the microscopic scale, for instance viscous loss or anisotropic response. Our approach combines various numerial simulation methods, including numerical upscaling, for computing waves in highly heterogeneous models, with inversion or parameter estimation to determine macroscopic models. The proposed work will rely upon a previously developed computational framework for inversion.For scientists to be able to produce oil and gas, to predict earthquakes and other tectonic events such as tsunamis, to safely remediate contaminants, and to bury excess greenhouse gases underground, they must first be able to image the earth's subsurface. Rock layers, fluids, and faults need to be mapped and their depths and lateral extent understood. To create an image of the subsurface, energy is sent into the ground which generates a wave. The heterogeneous nature of the subsurface causes a portion of these waves to be sent back to the surface where seismometers (microphones) record the waves as they pass. From these signals scientists try to infer the structure of the subsurface. This inference is enormously complicated by the very complex mechanical nature of rock, which is composed of microscopic grain particles in a porous lattice. The physical characteristics of these tiny constituents and the fluids within the pores combine in a complex and poorly understood way to yield the observable response of the Earth. In our previous work, we havedevised methods to simulate propagation of waves through complex microscopically structured material, and also procedures to determine the macroscopic material descriptions from observable data. This proposal envisions the fusion of these two lines of work and could shed light on which aspects of subsurface structure can, or can't, be inferred from seismic recordings.