Publications

In their recent paper, Djikpesse and Tarantola (Geophysics 65 (4) pp. 1023-1035, hereinafter D and T) raise a central question about geophysical inversion: how accurately must the physics of seismic waves in the Earth be modeled in order that inversion succeed? Two general criteria for successful inversion appear in D and T's discussion: fit of predicted to observed data, and prediction of Earth structure. The hypothesis underlying inversion is that these criteria are unextricably linked, so that data fit should lead to accurate inference of subsurface features. The authors have also worked on the data discussed in D and T, using different modeling choices and inversion algorithms but also achieving quite successful inversions, in both senses. They feel that a brief comparison of methods and results might highlight the subtle relation between accuracy in modeling and success in inversion as well as raising questions about the appropriateness of D and T's modeling and inversion choices.

Finite difference methods for solving the wave equation more accurately capture the physics of waves propagating through the earth than asymptotic solution methods. Unfortunately. finite difference simulations for 3D elastic wave propagation are expensive. We model waves in a 3D isotropic elastic earth. The wave equation solution consists of three velocity components and six stresses. The partial derivatives are discretized using 2nd-order in time and 4th-order in space staggered finite difference operators. Staggered schemes allow one to obtain additional accuracy (via centered finite differences) without requiring additional storage. The serial code is most unique in its ability to model a number of different types of seismic sources. The parallel implementation uses the MP1 library, thus allowing for portability between platforms. Spatial parallelism provides a highly efficient strategy for parallelizing finite difference simulations. In this implementation, one can decompose the global problem domain into one-, two-, and three-dimensional processor decompositions with 3D decompositions generally producing the best parallel speed up. Because i/o is handled largely outside of the time-step loop (the most expensive part of the simulation) we have opted for straight-forward broadcast and reduce operations to handle i/o. The majority of the communication in the code consists of passing subdomain face information to neighboring processors for use as ''ghost cells''. When this communication is balanced against computation by allocating subdomains of reasonable size, we observe excellent scaled speed up. Allocating subdomains of size 25 x 25 x 25 on each node, we achieve efficiencies of 94% on 128 processors. Numerical examples for both a layered earth model and a homogeneous medium with a high-velocity blocky inclusion illustrate the accuracy of the parallel code.