Electromagnetic Imaging and Simulated Annealing
Electromagnetic Imaging and Simulated Annealing
复制标题
电磁成像和模拟退火
DOI：
10.1029/91jb00278
复制
发表时间：
1991
影响因子：
--
通讯作者：
J. Virieux
中科院分区：
文献类型：
--
作者：
D. Gibert;J. Virieux
与波场受传播效应支配的声学成像方法相比，导电介质的电磁成像受到电磁场的扩散行为的影响。当致力于实现电磁成像时要解决的一个重要问题涉及解决扩散阻尼的可能性。精确反演将着眼于与扩散场及其对偶波场相关的积分方程的可解性。这个方程是不适定的，因为它的类拉普拉斯核使得寻找对偶波场的逆问题是出了名的困难（数值和数学上）。随机反演是另一种基于最小二乘拟合的方法。在这种反问题方法中，提取波场仍然是一个相对不稳定的过程，尽管没有噪声的数据的L2失配函数呈现全局最小值。模拟退火克服了这个问题的参数化设计如下的不稳定性。未知波场被期望为脉冲函数序列。脉冲函数的个数可以通过使用一个叫做AIC的统计准则来确定，该准则来自Prony技术。对反射位置进行模拟退火，而不作为参数的振幅则通过线性拟合获得。模拟退火方法被证明是有效的，即使在存在噪声。此外，这种非线性数值反演简化了统计量，从而可以估计分辨率。简单的合成实例说明了反演的性能，而合成有限元实例显示了通过标准地震偏移技术处理的最终伪地震剖面。
In contrast with acoustical imaging methods, for which the wave field is dominated by propagation effects, electromagnetic imaging of conductive media suffers from the diffusive behavior of the electromagnetic field. An important question to address when working toward the achievement of electromagnetic imaging concerns the possibility of resolving the diffusion damping. Exact inversion will be looking at the solvability of the integral equation relating a diffusive field to its dual wavefield. This equation is ill posed because its Laplace-like kernel makes the inverse problem of finding the dual wave field a notoriously difficult (both numerically and mathematically) one. Stochastic inversion is another alternative based on least squares fitting. In this inverse problem approach, extracting the wave field is still a relatively instable process, although the L2 misfit function for data without noise presents a global minimum. The simulated annealing overcomes this instability for parameterization of this problem designed as follows. The unknown wave field is expected to be a sequence of impulsive functions. The number of impulsive functions can be determined by using a statistical criterion, called AIC, which comes from the Prony technique. The simulated annealing is applied to the positions of the reflections, while the amplitudes, which are not taken as parameters, are obtained by linear fitting. The simulated annealing method proves to be efficient even in the presence of noise. Furthermore, this nonlinear numerical inversion furnishes statistical quantities which allows an estimation of the resolution. Simple synthetic examples illustrate the performance of the inversion, while a synthetic finite element example shows the final pseudo-seismic section to be processed by standard seismic migration techniques.