论文部分内容阅读
现代地电数据采集系统每天可记录10万多个数据。尽管当今计算机的计算能力有了很大提高,而且有许多有效的数值算法,但对这些资料的解释仍然是一件比较困难的工作。本文提出了一种可表述为多通道反褶积的二维一遍反演程序。它是基于波恩近似的线性化电势方程,并且利用了计算均匀半空间的二维形式的弗莱歇导数。反演是在波数域进行的,因此,二维的空间问题可划分为许多较小的一维问题。由此得出的多通道反褶积算法速度非常快,并且节约内存。由表征地电阻率和数据误差的统计特性的协方差矩阵使反演算法稳定。假设地电阻率的分布具有两个参数、自亲和分形的统计特性。地电阻率的区域视幅度和分数维是通过地电观测直接估计出来的。在传统的测量误差协方差矩阵上加上非线性误差协方差矩阵。非线性误差对电极结构和地电阻率幅度和分数维的依赖特性的统计模型是通过非线性模拟实验实际得出的。对综合实例和野外实例的测试都很好地证实了这一结论,即对于长的数据剖面来说,基于多通道反褶积的反演算法能自动产生线性化的电阻率估计值,这一估值能很好地反映模型的主要特性。
Modern geoelectric data acquisition system can record more than 100,000 data per day. Despite the tremendous increase in computational power of computers today and the many valid numerical algorithms, it is still a difficult task to interpret these data. In this paper, we present a two-dimensional inversion procedure that can be expressed as multi-channel deconvolution. It is based on the linearized potential equation of the Bonn approximation and takes advantage of the Fletcher’s derivative that calculates the two-dimensional form of the uniform half-space. Inversion is performed in the wavenumber domain, so two-dimensional spatial problems can be divided into many smaller one-dimensional problems. The resulting multi-channel deconvolution algorithm is very fast and saves memory. The inversion algorithm is stabilized by a covariance matrix that characterizes the statistical properties of earth resistivity and data error. It is assumed that the distribution of earth resistivity has two parameters, the statistical properties of self-affine fractal. The area resistivity of the region depending on the magnitude and fractional dimension is directly estimated by geoelectric observations. Add the nonlinear error covariance matrix to the traditional covariance matrix of measurement errors. The statistical model of the dependence of the nonlinearity on the electrode structure and the magnitude and fractional resistivity of the earth resistivity is obtained through the nonlinear simulation experiment. This conclusion is well validated both for the integrated and field examples, where a multi-channel deconvolution based inversion algorithm automatically generates a linearized resistivity estimate for long data profiles Valuation can well reflect the main features of the model.