Parallel Direct Search Methods Applied to Seismic Inverse Problems

Abstract

The ultimate goal of this work is to improve the data processing techniques used to prospect for petroleum. The improvements will come from extracting detailed estimates of local parameter fluctuations in a model of the earth which may indicate lithological features associated with oil and gas deposits. Our hope is to further the evaluation of the widely-believed economic potential for finding and producing petroleum through more precise use of seismic data. A key component of this research lies in robust estimation of wave velocity models directly from waveform data. Interesting instances of this problem can be formulated via differential semblance optimization as a low (e.g., two- to four-) dimensional minimization problem [2], [3]. The catch is that while the number of control variables is small, the number of state variables is quite large. Thus an implementation of the objective function on a Stardent Titan, running at 20 Mflops, currently takes up to eight hours to return a function value. Noise in the data means that more than two digits in the value of the objective function is irrelevant. An analytic expression for the gradient is not yet available and a finite-difference approximation to the gradient appears fraught with numerical difficulties.