基于ASSA方法的等值性电测深数据反演及数据误差相关性分析

Electrical sounding data equivalence inversion based on ASSA and correlation analysis of errors

针对直流电测深数据等值性反演的病态性(等值性层参数及层参数间的狭长平坦的强相关性),尝试采用自适应单纯形模拟退火(ASSA)方法反演具等值性电测深模型,通过与Lamarckian-marked-constraint(LMC)算法对比,发现ASSA方法能较好地解决电测深等值性反演问题,且反演精度较高。目前地球物理反演多基于数据误差为高斯分布和空间不相关(非对角元素为零)的假设,对贝叶斯反演而言,后一假设如果运用不当往往会低估反演结果的不确定性,从而导致对反演结果可靠性的误判。为了合理评价反演结果的不确定性,文中采用Runs-test非参数化判别方法,通过对等值性模型的归一化数据残差的判别,确定数据误差是空间相关的。由此得出的协方差矩阵应用于贝叶斯反演,进而对反演结果的不确定性、相关性等进行更合理、准确的评价。

Aiming at the ill-posed electrical sounding data equivalence inversion,an adaptive simplex simulated annealing(ASSA)approach is applied to invert electrical sounding data with equivalence.Compared with Lamarckian-marked-constraint(LMC),the inversion result proves that ASSA can better perform electrical sounding equivalence inversion and the inversion precision is higher.Presently,many geophysical inversions are performed based on the assumption that data errors are Gaussian-distributed and spatially uncorrelated(off-diagonal elements are zero for covariance matrix).For Bayesian inversion,the latter assumption is not valid,and it may lead to the less-estimation of uncertainty to inversion data and a wrong decision about the reliability of inversion result.In order to reasonably evaluate the uncertainty of inversion result,nonparametric Runs-test method is used to estimate the full covariance matrix from data residuals of equivalence model,and determine if data errors are spatially correlated.The covariance matrix obtained is applied to Bayesian inversion,thus the uncertainty,correlation of inversion data is more correctly and reasonably evaluated.