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Fast Frechet derivative calculation using an auxiliary source array method; an application to array resistivity measurements

Tsili Wang and Alberto Mezzatesta
Fast Frechet derivative calculation using an auxiliary source array method; an application to array resistivity measurements
Geophysics (October 2001) 66 (5): 1364-1371

Abstract

Frechet derivatives provide the vital information for parametric resistivity inversion, but the calculation for a multidimensional problem is often computer intensive. This paper presents a new technique for fast calculation of the Frechet derivatives of resistivity measurements with respect to formation resistivity properties. The technique, referred to as the auxiliary source array method (ASAM), generalizes the reciprocity principle-based methods in that for closely spaced receivers it may not be necessary to place a fictitious source at each receiver location. Rather, an auxiliary source array comprised of sparsely spaced fictitious sources can be constructed from which the field for any fictitious source location can be reconstructed. The ASAM was tested with a deviated-well resistivity model for an array resistivity device that acquires 8 potential, 16 first potential difference, and 14 second potential difference data points at each depth level. The Frechet derivatives calculated by the ASAM agree well with those obtained through the parameter perturbation method. The tests showed that the calculation time of the ASAM has little dependence on the number of parameters for which the Frechet derivatives are to be calculated. The method can calculate the Frechet derivatives of 5 to 138 resistivity parameters with only 20% to 50% additional computer time. For the 138-parameter model, the ASAM is about two orders of magnitude faster than the parameter perturbation method.


ISSN: 0016-8033
EISSN: 1942-2156
Coden: GPYSA7
Serial Title: Geophysics
Serial Volume: 66
Serial Issue: 5
Title: Fast Frechet derivative calculation using an auxiliary source array method; an application to array resistivity measurements
Affiliation: Baker Atlas, Houston, TX, United States
Pages: 1364-1371
Published: 200110
Text Language: English
Publisher: Society of Exploration Geophysicists, Tulsa, OK, United States
References: 15
Accession Number: 2002-003694
Categories: Applied geophysics
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus.
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2017, American Geosciences Institute.
Update Code: 200202
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