Simulation of borehole electromagnetic measurements in dipping and anisotropic rock formations and inversion of array induction data
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Borehole electromagnetic (EM) measurements play a crucial role in petroleum exploration. This dissertation develops advanced algorithms for the numerical simulation of borehole EM measurements acquired in dipping and anisotropic rock formations. The first technique is a full-wave modeling technique: the BiCGSTAB(L)-FFT (Bi-Conjugate Gradient STABilized(L)-Fast Fourier Transform). This technique is efficient both in terms of computational speed [~ ( ) 2 ON N log ] and computer memory storage [~O N( )], where N is the number of spatial discretization cells. The second technique, referred to as a “Smooth Approximation (SA),” substantially increases the accuracy of the viii simulated EM fields in electrically anisotropic media compared to the Born approximation and the Extended Born Approximation (EBA). The third technique, referred to as a “High-order Generalized Extended Born Approximation (Ho-GEBA),” is developed for further improvement of the efficiency and accuracy of EM simulation in electrically anisotropic media. These techniques have been used to simulate tri-axial borehole induction measurements acquired in dipping and anisotropic rock formations. Efficient algorithms are also developed for EM modeling in axisymmetric media. The three full-wave numerical simulation techniques investigated in this dissertation include the BiCGSTAB(L)-FFT algorithm, the BiCGSTAB(L)-FFHT (Fast Fourier Hankel Transform) technique, and the finite-difference method. In addition, two approximation techniques are developed to approach the same problem: a Preconditioned Extended Born Approximation (PEBA), and the HoGEBA, which includes the PEBA as its first-order term in a series expansion. These approximations are not only computationally efficient, but easily lend themselves to developing efficient inversion algorithms. In addition to forward modeling, inversion algorithms are developed to estimate spatial distributions of electrical resistivity from array induction measurements. This dissertation develops two types of inversion algorithms: Resistivity Imaging (RIM) and Resistivity Inversion (RIN). An inner-loop and outer-loop optimization technique is developed and used in the RIM. In both strategies, the Jacobian (or sensitivity) matrix is computed via the PEBA, which simulates the measurements and computes the Jacobian matrix simultaneously ix with only one forward simulation. The RIM assumes a continuous conductivity distribution, while the RIN assumes a discrete (blocky) conductivity distribution. Inversion exercises indicate that the RIN is superior to the RIM for the quantitative evaluation of in-situ hydrocarbon saturation.