Fast 2D inversion of large borehole EM induction data sets with an efficient Fréchet-derivative approximation

Abstract

In addition to reliability and stability, the efficiency and expediency of inversion methods have long been a strong concern for their routine applications by well-log interpreters. We have developed and successfully validated a new inversion method to estimate 2D parametric spatial distributions of electrical resistivity from array-induction measurements acquired in a vertical well. The central component of the method is an efficient approximation to Fréchet derivatives where both the incident and adjoint fields are precomputed and kept unchanged during inversion. To further enhance the overall efficiency of the inversion, we combined the new approximation with both the improved numerical mode-matching method and domain decomposition. Examples of application with synthetic data sets show that the new methodis computer efficient and capable of retrieving original model re-sistivities even in the presence of noise, performing equally well in both high and low contrasts of formation resistivity. In thin resistive beds, the new inversion method estimates more accurate resistivities than standard commercial deconvolution software. We also considered examples of application with field data sets that confirm the new method can successfully process a large data set that includes 200 beds in approximately [Formula: see text] of CPU time on a desktop computer. In addition to 2D parametric spatial distributions of electrical resistivity, the new inversion method provides a qualitative indicator of the uncertainty of estimated parameters based on the estimator’s covariance matrix. The uncertainty estimator provides a qualitative measure of the nonuniqueness of estimated resistivity parameters when the data misfit lies within the measurement error (noise).

Improved estimation of mineral and fluid volumetric concentrations from well logs in thinly bedded and invaded formations

“…Thus, the Jacobian matrix can be calculated locally to avoid unnecessary calculations. On a related subject, Wang et al (2009) introduced a domain decomposition method for fast 2D resistivity inversion. They divided the entire depth interval into overlapping depth subdomains, assuming that variations of formation resistivity in each subdomain did not affect resistivity measurements acquired in other depth subdomains.…”

Rock quality assessment using the effect of mud-filtrate invasion on conflicting borehole resistivity measurements

“…Resistivity modeling and inversion starts with a horizontal multilayer formation with three cylindrical zones; borehole, invaded formation, and undisturbed formation (Wang et al, 2009). Figure 7 depicts a general earth model indicating the various cylindrical zones and layers.…”

“…We used the University of Texas at Austin Petrophysical and Well-Log Simulator (UTAPWeLS) software to perform inversion of resistivity measurements. The resistivity inversion module of UTAPWeLS applies a numerical-mode matching method (Chew et al, 1984;Zhang et al, 1999) for the forward model of conductivity measurements and a domain decomposition method (Wang et al, 2009) to minimize equation 1. This method can perform rapid inversion of large induction data sets acquired across very long depth intervals.…”

“…This assessment will determine whether resistivity logs in the appraisal wells accurately defined a lower rock quality reservoir than well 1, or alternatively, if the induction measurements were in error. We used piston-like invasion for resistivity inversion Wang et al, 2009) and fluid-flow forward modeling by accounting for the interplay between mud and formation properties that occurs during synthetic oil-based mud-filtrate invasion ) to assess such a discrepancy. We selected one depth interval in well 1 and one depth interval in well 2 to perform inversion of raw AIT measurements and to simulate the process of mud-filtrate invasion and study its effect on those induction measurements.…”

Unmagnetized plasma media parameters reconstruction using FDTD and gradient‐based minimization method

“…In the past few decades, electromagnetic scattering and inverse scattering have been widely used in civilian and military fields, such as nondestructive testing and evaluation, material characterization, biomedical imaging, applied geophysics, and radar imaging . Electromagnetic inverse scattering is the process of inferring the geometrical and/or electrical properties of unknown objects in a region of interest from the measured electromagnetic field outside the region .…”