Optimal Experiment Design for Timelapse Tomography: Customizing Crosswell Micro-Arrays for Monitoring Applications

Abstract

Geophysical monitoring techniques offer the only approach capable of assessing both the spatial and temporal dynamics of subsurface fluid processes. Historically, monitoring datasets have consisted of surveys sequentially collected using acquisition geometries and sensor platforms similar to static measurements. Unfortunately, a host of logistical constraints hamper the repeatability of such surveys, particularly difficulties replicating the source/receiver geometry. 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 re-configure once installed, a premium is placed on selecting a geometry capable of imaging the desired target at minimum cost. We present a simple approach to optimizing downhole sensor arrays for monitoring experiments making use of differential seismic traveltimes. In our case, we use a design quality metric based on the accuracy of tomographic reconstructions for a suite of imaging targets. By not requiring an explicit SVD of the forward operator, evaluation of this objective function scales to problems with a large number of unknowns. We also restrict the design problem by recasting the array geometry into a low dimensional form more suitable for optimization. A side effect of using these restrictive parameterizations for experiment geometry is a well-behaved objective function more amenable to local search techniques. To demonstrate the efficacy of our algorithm, we consider a series of possible designs optimization problems for a next-generation permanent tomographic monitoring system. We test two search algorithms on the design problem, the Nelder-Mead downhill simplex method and the Multilevel Coordinate Search algorithm. The complete design algorithm is tested for three crosswell acquisition scenarios relevant to continuous seismic monitoring, a 2 parameter array length optimization, a 4 parameter length/offset optimization, and a comparison of optimal multi-source designs. In the last case, we also examine trade-offs between source sparsity and the quality of tomographic reconstructions. Preliminary results suggest that high-quality differential images can be generated using only a small number of optimally positioned sources, an observation with immediate relevance to several field projects still in the development phase.