Optimal experiment design for time-lapse traveltime tomography

Abstract

Geophysical monitoring techniques offer the only noninvasive approach capable of assessing both 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 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 configurations for monitoring experiments making 1 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 singular value decomposition 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 at a reasonable computational cost. We test two search algorithms on the design problem: the Nelder-Mead downhill simplex method and the Multilevel Coordinate Search algorithm. The algorithm is 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 multi-source designs. In the last case, we also examine trade-offs between source sparsity and the quality of tomographic reconstructions. One general observation is that asymmetric array lengths improve localized image quality in crosswell experiments with a small number of sources and a large number of receivers. Preliminary results also suggest that highquality differential images can be generated using only a small number of optimally positioned sources.2

Efficient nonlinear Bayesian survey design usingDNoptimization

“…When combined with a linearized sequential design algorithm (LSDA), the D N criterion renders nonlinear Bayesian design computationally feasible for large-scale industrial applications, a feature shared by no other geoscientific nonlinear design technique without recourse to cluster computing or reparameterization of the design space (e.g., Ajo-Franklin, 2009;Guest andCurtis, 2009, 2010). We expand upon this point in the Discussion.…”

Recent advances in optimized geophysical survey design

“…Representative published work Seismic tomography Ajo-Franklin, 2009Brenders and Pratt, 2007Curtis and Snieder, 1997Curtis, 1999a, 1999bMaurer et al, 2009Sirgue and Pratt, 2004 Seismic reflection surveys Liner et al, 1999 AVO/AVA/AVAz surveys or processing strategies Coles and Curtis, 2010Guest and Curtis, 2009, 2010van den Berg et al, 2003 Earthquake or microseismic location surveys Hardt and Scherbaum, 1994Lomax et al, 2009Rabinowitz and Steinberg, 1990Steinberg et al, 1995Winterfors and Curtis, 2008, 2010 Electric or electromagnetic surveys Coles and Morgan, 2009Coscia et al, 2008Furman et al, 2007Hennig et al, 2008Loke and Wilkinson, 2009Maurer and Boerner, 1998aMaurer et al, 2000Oldenborger and Routh, 2009Stummer et al, 2002Wilkinson et al, 2006 …”

Assessing the monitorability of CO2 saturation in subsurface saline aquifers

“…Optimal experimental and data processing designs may be used to improve these uncertainties. Optimal design theory is applied to both linear and nonlinear geophysical problems (Curtis, 2004a,b) such as seismic tomography (Curtis, 1999a,b;Maurer et al, 2009;Ajo-Franklin, 2009), amplitude variation with offset/angle survey and processing (van den Berg et al, 2003;Coles and Curtis, 2010;Guest and Curtis, 2009, 2011) earthquake or microcosmic location surveys (Curtis et al, 2004;Winterfors and Curtis, 2008) and electric and electromagnetic surveys (Maurer and Boerner, 1998;Maurer et al, 2000;Stummer et al, 2002aStummer et al, ,b, 2004Oldenborger et al, 2007). A review of the recent advances in survey design is given in Maurer et al (2010).…”