1-D Full-Region Inversion Of CASMT Of Bipolar Source

In this paper we carry out CSMAT 1D forward calculation and inversion. First ,we calculate the response on the ground excited by bipolar source ,then carry out 1D full-region inversion without near-field correction using damping least squares and OCCAM inversion method respectively .First, we divide bipolar into some current dipolar source according to the distance of sender and receiver, then, we calculate the response excited by current dipole source by Hankle transform, stack the responses to obtain the response of dipolar. Field excited by dipole is an integral expression of Bessel function. Bessel function Jv (mr)was oscillating decay with the increase of m , but is very slow, the feature of integral nuclear is rapid increase with increase of m , because of integral nuclear not convergence ,direct integral will lead to wrong result even if the filter length is long, so ,it is necessary to deal with integral nuclear to ensure convergence, this calculation can not only guarantee the correctness, but also save computing time. For the electric field, the original integral nuclear minus the integral nuclear when R ?and R equal 1, and integral with new nuclear, then coupled with the electric field results of the uniform land; for the magnetic field, the calculation of it is more complicated because of the Bessel function ,so the original integral nuclear minus the limit of nuclear , integral with new nuclear, and then plus the integral of the limit.We use damping least-squares method to achieve one-dimensional inversion of the full-region CSAMT , through the method of difference to calculate partial differential countdown matrix, iterative step is control through the damping factor , when iteration to the divergent direction, there is a need to increase damping factor to small Iteration step to ensure iterative convergence ;when the iterative convergence, small damping factor to reduce the increasing iterative step to accelerate convergence rate, this not only guarantee that Iterative convergence but also the speed of the inversion. When the initial model choose the right conditions, the damping of the least-squares of one-dimensional inversion can get the correct model of the ground floor, while avoiding the error of the near-field correction, and further verification of the full-region CSAMT inversion.In damping least squares inversion, from a model of speculation, the parameters of the model that gradually update, eventually to inversion results. However, linearization of nonlinear problems making the large dependence to initial model, when the original value choose suitable, inversion can obtain accurate model, but initial model speculation is difficult, in many cases, the results model hard to know. For dependence of the initial model for damping least squares, the paper then applied OCCAM inversion to CSAMT inversion, OCCAM inversion introduce the smooth restraint of model to inversion, fitting observational data, at the same time, the model as smooth as possible, This inversion method does not depend on the initial model, at the same time obtain smooth model at the cost of reduce the data fitting.The classic OCCAM algorithm is that in every iteration, using scanning method or one-dimensional search methods, obtain Lagrange multipliers in the direction of large value to small value , making the iterations result to fit a given area .If there are multiple values meet the requirements, only for the value large is choose at this time. Judge at this time whether the objective function to minimize, if so, then end then calculation, otherwise, into the next round of iteration until the conditions to achieve convergence. Scanning or one-dimensional search to are based on the model data fitting, requires a large amount of forward calculation.This paper sum up rule of influence of Lagrange multipliersβto data fitting , that the following laws: a fixedβ, after a certain step of iteration, the data fitting is no longer reduced, the greaterβ,the greater data fitting ;the smallerβ, the smaller data fitting. When the model is far from the true model, lagerβcan make iteration convergence, but too small will make iterative divergence, when the model is near from the true model smallerβcan make iterative convergence; when then number of the model is large ,smallerβmay lead to pseudo extremum. Through the above law, this paper simplify the inversion of conventional OCCAM, use damping factor and Lagrange multipliers to control iterative process, realize 1D OCCAM inversion without search of Lagrange multipliers and improve efficiency. Given large Lagrange multipliers, then inversion with the multipliers, when the data fitting in very small variance, reduce the value of multipliers, whenβless than the given value,βis no longer decreasing, until the data fitting to an acceptable value or achieve given iteration number. Damping factor is used to control iterative step size, when the iterative divergence ,increased damping factor, when convergence, reduced damping factor to ensure the stability and speed of iteration.As Cagniard apparent resistivity aberration occurred in the near-field, the value will be very large compare to that in the far-field, to balance the apparent resistivity value, I restraint apparent resistivity using countdown of 1 % the measured data to ensure the same rat between different frequency. Smoothness constraint matrix determined by the thickness of the layers, the initial Lagrange multipliers can choose great value, , when Lagrange multipliers is large, decrease by multiple, when small Lagrange multipliers decreases by a fixed step. Acceptable data fitting related to the measured data error, minimum Lagrange multipliers related to the model of smoothness expectations, if the given data fitting is large , it have reached an acceptable data fitting without reduced to the minimum Lagrange multipliers, if the given data fitting is smaller, choose to decrease Lagrange multipliers or choose to accept the current model after a certain number of iterative.The inversion of the theoretical models indicate that iterative can be stable even the initial model far from true model, at the same time the given smallest Lagrange multipliers avoid the pseudo discontinuity caused by data excessive fitting and artificial stratification. CSAMT 1D inversion of full-region is feasible without the near-field correction, although Cagniard apparent resistivity in the near and intermediate region can not correctly reflect the structure of the underground, but the inversion can still get the right result.