Optimal experiment design for time-lapse traveltime tomography

Abstract

Geophysical monitoring techniques offer the only noninvasive approach capable of assessing the spatial and temporal dynamics of subsurface fluid processes. Increasingly, permanent sensor arrays in boreholes and on the ocean floor are being deployed to improve the repeatability and increase the temporal sampling of monitoring surveys. Because permanent arrays require a large up-front capital investment and are difficult (or impossible) to reconfigure once installed, a premium is placed on selecting a geometry capable of imaging the desired target at minimum cost. We have taken a simple approach to optimizing downhole sensor configurations for monitoring experiments making use of differential seismic traveltimes. We used a design quality metric based on the accuracy of tomographic reconstructions for a suite of imaging targets. By not requiring an explicit singular value decomposition of the forward operator, evaluation of this objective function scaled to problems with a large numberof unknowns. We restricted the design problem by recasting the array geometry into a low-dimensional form more suitable for optimization at a reasonable computational cost. We tested two search algorithms on the design problem: the Nelder-Mead downhill simplex method and the multilevel coordinate search algorithm. The algorithm was tested for four crosswell acquisition scenarios relevant to continuous seismic monitoring, a two-parameter array optimization, several scenarios involving four-parameter length/offset optimizations, and a comparison of optimal multisource designs. In the last case, we also examined trade-offs between source sparsity and the quality of tomographic reconstructions. Asymmetrical array lengths improved localized image quality in crosswell experiments with a small number of sources and a large number of receivers. Preliminary results also suggested that high-quality differential images could be generated using only a small number of optimally positioned sources in tandem with a more extensive receiver array.