The Order‐Depression Solution for Large‐Scale Integral Equation and Its Application in the Reduction of Gravity Data to a Horizontal Plane

Abstract

AbstractIn the equivalent source method used for continuation of potential field from an arbitrary surface, the kernel function of Fredholm equation shows self‐similarity and redundancy. According to these characteristics, we adopted the wavelet compression algorithm with non‐linear cosine threshold value to accomplish the order depression of the Fredholm equation, thus making the equivalent source method, put forward by Bhattacharyya in 1977, can deal with data from large area and with mass volume, which is hard to achieve before. Theoretical modeling indicates that, the hard threshold method obtains great accuracy when the compression ratio is 40.5%, while its accuracy decreases when the compression ratio is 81.1%. At this time, the nonlinear cosine threshold can improve the continuation accuracy obviously. At last, the hard threshold, soft threshold, and nonlinear threshold are used in the compression of line MT‐1 data of northeast Sichuan gas field. Results indicate that, when the compression ratio is 79%, all the three methods can acquire good results. But the nonlinear threshold has the highest fidelity, which can provide important evidence in searching for local structures related with petroleum reservoir.