Study On Some Inverse Problems In Oil Geophysical Prospecting

In this Ph.D.thesis,the author considers some inverse problems including identification of resistance in SP log,multi-exponential inversion of T₂ spectrum in Nuclear Magnetic Resonance(NMR),conductivity imaging using dual-frequency EM Data,identification of boundary water fluxes of oil reservoir and so on,which arise in oil geophysical prospecting.The thesis is organized as follows:In Chapter 1,a new partial differential equation model for Spontaneous Potential (SP) log in heterogeneous formations is introduced.At the same time,the existence and uniqueness of weak solution to the problem are proved,and the problem of resistance identification in SP log is studied.Furthermore,a jump condition capturing finite difference scheme is proposed and applied to solve such elliptic interface problems.The effects of various factors on SP response,which include objective layers resistivity,bed thickness,bore-hole diameter,invasion and water-flooded zones and so on,are investigated quantitatively by the proposed method, and satisfactory results are obtained.In Chapter 2,we improve the Differential Evolution(DE) algorithm developed rapidly in recent years,and apply it to study the multi-exponential inversion problem in nuclear magnetic resonance.Satisfactory results are obtained,and the new algorithm has more advantages in speed,accuracy and anti-noise capability than conventional ones.In Chapter 3,we study the conductivity imaging using dual-frequency EM Data by some existing algorithms for ill-conditioned linear systems,such as Truncated Singular Value Decomposition(TSVD),Tikhonov regularization,Least Squares QR(LSQR) decomposition and Simultaneous Algebraic Reconstruction Technique (SART).Then a new Hybrid Differential Evolution(HDE) algorithm based on LSQR is proposed to solve linear inverse problems in geophysics.In Chapter 4,follow the approach to solve inverse heat conduction problem of estimating the unknown boundary heat fluxes,we propose an inversion algorithm based on Conjugate Gradient(CG) method to automatically identify boundary water fluxes in fixed oil reservoir with arbitrary geometry.