Rapid inversion of 2-D geoelectrical data by multichannel deconvolution
Rapid inversion of 2-D geoelectrical data by multichannel deconvolution
复制标题
通过多通道反褶积快速反演二维地电数据
DOI：
10.1190/1.1444969
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发表时间：
2001
期刊：
影响因子：
--
通讯作者：
N. B. Christensen
中科院分区：
文献类型：
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作者：
I. Møller;B. Jacobsen;N. B. Christensen
现代地电数据采集系统每个野外日可记录超过10万个数据值。尽管计算机能力的增长和更高效的数值算法的发展，解释这样的数据量仍然是一项不平凡的计算任务。我们提出了一种多道反褶积的二维单通道反褶积方法。它基于Born近似下线性化的电势方程，并利用均匀半空间中Fr‘echet导数的二维形式。该方法是在波数域中进行的，从而将二维空间问题分解为许多小的一维问题。由此得到的多通道去卷积算法非常快速且存储效率高。通过表示地电阻率和数据误差的随机特性的协方差矩阵来稳定反演方案。假设地电阻率分布具有双参数、自相关的统计特征。地电观测直接估算了地电阻率的局部视振幅和分维值。将非线性误差协方差矩阵添加到常规测量误差协方差矩阵中。通过非线性模拟实验，确定了非线性误差与电极结构、电阻率幅值和分维的关系的随机模型。对合成实例和包括井控在内的现场实例的检验表明，对于较长的数据剖面，该方法能自动产生能真实反映主要模型特征的线性化电阻率估计值。
Modern geoelectrical data acquisition systems can record more than 100 000 data values per field day. Despite the growth in computer power and the development of more efficient numerical algorithms, interpreting such data volumes remains a nontrivial computational task. We present a 2-D one-pass inversion procedure formulated as a multichannel deconvolution. It is based on the equation for the electrical potential linearized under the Born approximation, and it makes use of the 2-D form of the Fr ´ echet derivatives evaluated for the homogeneous half-space. The inversion is formulated in the wavenumber domain so that the 2-D spatial problem decouples into many small 1-D problems. The resulting multichannel deconvolution algorithm is very fast and memory efficient. The inversion scheme is stabilized through covariance matrices representing the stochastic properties of the earth resistivity and data errors. The earth resistivity distribution is assumed to have the statistical characteristics of a two-parameter, selfaffine fractal. The local apparent amplitude and fractal dimension of the earth resistivity are estimated directly from geoelectrical observations. A nonlinearity error covariance matrix is added to the conventional measurement error covariance matrix. The stochastic model for the dependence of nonlinearity error on electrode configuration as well as resistivity amplitude and fractal dimension is determined pragmatically through nonlinear simulation experiments. Tests on synthetic examples and field cases including well control support the conclusion that for long data profiles this method automatically produces linearized resistivity estimates which faithfully resolve the main model features.