频率与空间相关噪声对大地电磁反演解释影响的量化研究

For 2D and/or 3D MT inversion, frequency and spatially correlated noise can substantially bias inversion results, or even worse, fail to recover the real structure. The research, motivated by solving this problem is to study on the effect of correlated noise on inversion, and to estimate the degree of correlation. This involves several related advanced techniques, necessary to develop for this purpose. Improving modeling and inversion efficiency is achieved via deploying multigrid method for both of them, minimizing the unknowns used to represent a physical model. In estimation of the correlation matrix, proper representation of the correlation relationship and attenuation between channels and/or frequencies is required to guarantee a meaningful posterior estimate of correlation. With a proper form for the correlation matrix, it can be described by statistical variables and included in the posterior probability density(PPD). Sampling the PPD, uncertainties caused by correlated noise can be evaluated in terms of 1D ,2D or even higher dimensional marginal distribution, visualizing the effect of correlated noise on inversion. Validity of inversion results, is examined by different statistical tests, e.g., KS test, Runs test. Finally the effect of noise correlation on inversion can be quantified and the estimation of correlation can be achieved. Quantification of the correlation effect on inversion can be used to improve the accuracy of MT data interpretation and facilitate the study on other factors, which also affects the inversion, e.g., physical heterogeneity.

在2D、3D的MT反演中，噪声的微弱相关性可能会导致反演解释结果的严重偏差，甚至错误。针对该问题，本项目拟采用基于贝叶斯框架的概率反演方法研究频率和空间相关噪声对MT反演解释结果的影响，探索相关噪声对反演解释的作用、影响规律，后验估计MT数据中噪声相关性大小。项目研究内容涉及基于多重网格的正、反演研究，采用合理的未知量表述模型，提高计算效率；选择符合实际的相关噪声表示形式和误差衰减形式，在反演中后验估计MT数据中相关噪声的大小；引入随机参数对噪声相关性进行描述，并包含在后验概率密度函数中，研究MT数据噪声相关性对反演结果的变化规律；采用KS、Runs验证等方法对反演假设和反演结果的有效性进行验证。实现量化相关噪声对反演解释结果的影响，得到MT数据噪声相关性大小。对提高2D、3D MT数据反演解释具有现实意义，为进一步研究影响反演结果的其它因素（模型参数的各向异性等）提供基础。

由于大地电磁数据存在相关噪声，它的存在对反演结果会产生影响，致使反演解释结果产生偏差或错误。该项目针对该问题开展了相关噪声对反演影响研究，采用贝叶斯反演理论，量化相关噪声对反演影响的大小。利用所提出的方法，通过合成模型考察了反演中频率和空间相关噪声对反演解释的影响。反演结果显示反演中如果忽略噪声的相关性，反演结果将产生严重的偏差，通常是低估反演结果的不确定度。因此在反演中，应考虑噪声的相关性带来的影响，否则反演结果将产生偏差，而且可能很严重。该结果将量化研究人员对相关噪声对反演影响的认识，改变在反演中可以忽略相关噪声影响的认识。