大型积分方程降阶解法与重力资料曲面延拓

The order-depression solution for large-scale integral equation and its application in the reduction of gravity data to a horizontal plane

分析了等效源曲面延拓方法积分方程核函数的自相似性、冗余性,根据Fredholm积分方程核函数特征,提出了一种小波余弦非线性阈值压缩算法,实现了大型Fredholm积分方程的降阶,使得Bhattacharyya等(1977年)提出的等效源曲面延拓方法能够处理大面积、大数据量的资料.理论模型结果表明,当压缩比为40.5%时硬阈值压缩方法的曲面延拓可以达到很高的精度,当压缩比为81.1%时,硬阈值压缩方法精度降低,而采用我们提出的余弦非线性阈值可以明显提高曲面延拓的精度.将硬阈值、软阈值和非线性阈值压缩三种不同方法用于川东北气田MT-1线资料的处理,当压缩比达79%时,三种不同方法曲化平结果都可以达到很好的效果,但非线性阈值压缩的曲化平结果失真最小,它能够客观地反映杨家河局部隆起,为在该区寻找与油气有关的局部构造提供重要依据.

In 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 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 proxide important evidence in searching for local structures related with petroleum reservoir.