Inversion of direct current borehole measurements requires a large number of forward simulations of the potential fields over different resistivity models. During the inversion, known parts of these models do not change, e.g., the borehole. This paper presents fast finite-different (FD) simulations using a Schur complement by leveraging this property. The approach geometrically divides the computational domain into two blocks: a background block having fixed resistivities and an anomalous block where resistivities can change. In the first modeling run, the method removes the unknown fields associated with the backgroundblock and computes the corresponding Schur complement. The Schur complement system is subsequently solved to compute the fields in the anomalous block, followed by inexpensive local substitutions to obtain fields in the background block. For each successive modeling with new anomalous block resistivities, only the relatively small Schur complement system needs to be solved. This method results in significant savings in computational times as compared to the standard FD method. We present forward simulations and hypothetical inversion for a simple cased borehole resistivity model to illustrate the efficiency of the developed Schur FD method relative to the standard FD method.

Presentation Date: Tuesday, October 16, 2018

Start Time: 1:50:00 PM

Location: 212A (Anaheim Convention Center)

Presentation Type: Oral

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