Study Of Three-dimensional Conjugate Gradients Inversion Of DC Resistivity Data

The subsurface' geoelectrical methods has increasingly become shallow hydrology,engineering, environment, archaeology and human social life, that is closely related toan important means of detecting areas. And shallow geological targets for theperformance of a limited number of three-dimensional(3-D) bodies of structuralgeology, if only 1-D or 2-D data invertion interpretation inevitably uneven nature ofelectricity will be 3D effect. Therefore, the need for 3D observation data and thecorresponding 3-D invertion interpretation.This article briefly described the use of a conjugate gradient iterative methodology3-D invertion DC resistivity methods are aimed at the 3-D measurements invertioninterpretation. Finite differential equations used to solving point sources 3-D electricfield is effective. Using incomplete Cholesky conjugate gradient (ICCG) 3-D iterativemethods seek limited differential linear system Ax=b formed, that avoid directinterpretation problems, making resistivity 3-D invertion is performed within thedemand drastically reduced, and greatly improving the speed of processing forresistivity 3-D invertion laid the foundation.For resistivity 3-D invertion, made the smallest tectonic invertion conjugategradient algorithm to solve the Jacobian matrix G and the reverse matrix GTG , butalso to avoid the storage G and the reverse matrix GTG. Using conjugate gradientiterative algorithm to solve the smallest tectonic invertion algorithms of linearequations, and only need calculate G-1 Vectors X product results Gx and the transposevectors GTy results. This is only required once for each invertion iterative calculation,accelerated the speed.Also we have improved the traditional minimum structure inversion algorithmsuccessfully. That is, althought only one forward calculation is required in eachinversion iteration, however, it requires tens of inersion iterations and each iterationcrquries much hours, so the inversion is much more time-consuming. Anew iterativetechnique is developed, by which a relative proper value of Lagrange multiplier X isgiven using a trivial method and keeps it unchangeable until convergence.Thusgreatly accelerates the xonvergence rate of the inversion.3-D models of synthetic data invertion tested, from many aspects, such as analysis ofthe sensitivity matrix invertion broadly effective from the region. Finally, adifferent model of the initial data invertion and bring errors to test invertion reliabilityand stability. The results showed : the resistivity 3-D invertion, the initial models anddata errors are smaller dependence, the result is stable and reliable invertion.