基于q-高斯分布和零阶最小熵正则化的三维重力聚焦反演

3D focusing inversion of gravity data based on q-Gaussian distribution and zeroth-order minimum entropy regularization

观测的重力数据通常含有误差,传统的三维重力反演方法假设数据残差服从高斯分布,数据误差的大小和可靠估计对于三维重力反演的精度和可靠性是非常重要的.在模型正则化方面,传统的三维重力反演主要是基于Tikhonov正则化理论来获得稳定解,但是当地下密度异常体存在尖锐边界时,基于L_(2)范数正则化的三维重力反演得到的密度异常体边界比较平滑,这给后续的地质解释带来一定的困难.为此,本文提出了一种基于q-高斯分布和零阶最小熵正则化的三维重力聚焦反演方法,该方法不需要估计数据误差,且对较大数据误差的敏感性较弱,同时能够获得聚焦反演结果,且不需要确定合理的聚焦参数.理论模型测试表明,本文提出的三维重力聚焦反演方法得到的反演模型具有聚焦效果,能够较好地刻画异常体边界和密度值,且对含有较强干扰的重力数据具有一定的适用性.将本文方法应用于墨西哥圣尼古拉斯矿区的实测重力数据,反演得到的硫化物矿体与已知资料具有较好的一致性.本文在理论模型和实际资料测试中还进行了反演模型不确定性分析,分析结果表明q取值为1.5能够得到令人满意的反演结果.

Observed gravity data usually contain various errors,and conventional 3D gravity inversion assumes a Gaussian distribution of data residuals.So the size of measurement errors and the reliable estimation of measurement errors are vital for the accuracy and reliability of 3D gravity inversion.In the aspect of model regularization,traditional 3D gravity inversion methods are typically based on Tikhonov regularization.However,when sharp boundary exists between anomalous body and its surrounding rock,3D gravity inversion with L_(2)-norm based model regularization technique recovers a density model with smoothed boundary,which brings some difficulty in subsequent geological interpretation.This paper proposes a 3D gravity focusing inversion method based on q-Gaussian distribution and zeroth-order minimum entropy regularization.This approach has no need to estimate the errors present in the observed gravity data and is less than sensitive to the large data noise.Meanwhile,the method can obtain a more focused recovery of density bodies with no need of choosing a proper focusing parameter.The test of synthetic gravity data shows that this proposed method produces a more focused density model with clearer boundary and density value closer to the true value,and can be applied to the inversion of gravity data with large errors.This method is utilized to invert the real gravity data from the San Nicolas deposit in Mexico,and the recovered sulfide body is in good agreement with the known information.The uncertainty analysis of the inversion results is also performed in the test of synthetic and real gravity data,indicating that a satisfactory inversion model can be obtained when q=1.5.