Optimal nonlinear design of marine borehole seismic surveys

Abstract

We explore [Formula: see text]-optimization, a recently introduced method in optimal experimental design theory, as a tool to minimize the forecasted postinversion model uncertainty in marine borehole seismic applications. The [Formula: see text]-criterion is a design objective function crafted specifically for nonlinear data-model relationships and, when used in conjunction with greedy, sequential optimization algorithms, is among the first of its kind to be computationally efficient enough for industrial-scale applications. The benefits and disadvantages of greedy algorithms are briefly discussed, and one of the most popular, the Construction algorithm, is confirmed to take (nearly) linear time, as predicted by theory. The [Formula: see text]-criterion is rederived here to show that restrictive assumptions in its original derivation were unnecessary. This new derivation is cast in terms of expected likelihood ratios, which quantify the discriminability of geomodels constrained by observed seismic data. A 3D vertical seismic profiling (VSP) survey and a walkaway VSP survey are [Formula: see text]-optimized for a site in the Gulf of Mexico, from which several potential applications are identified, including: (1) prescribing the maximum radius of 3D VSP spirals; (2) a novel annular-spiral 3D VSP geometry to reduce acquisition time and cost; (3) a novel azimuthal-walkaway geometry for presurvey acquisition; (4) identifying optimal data for rapid postacquisition quality control and quick-look inversion; (5) optimizing data decimation to facilitate the analysis of massive data sets which cannot be practically analyzed in toto; and (6) optimizing source vessel placement for offset/azimuth checkshots.