基于线性相关约束的地球物理联合反演研究

The method of constraints in model space is the key issue in geophysical joint inversion. Researchers studied constraints for geophysical joint inversion from the different points of view, such as: physical properties, structural similarities, linearly dependent of vectors. Literature analysis show that there are some problems in the typical constraints: (1) the applicability of petrophysical constraints is weak; (2) the operation of constraints using cross-product is complicated; (3) the priori information about the variation directions of physical properties is needed in constraints using dot product; (4) the expression of Gramian constraints is not intuitive;(5) the research on synchronous implementation of petrophysical and structural constraints is not enough...In view of these problems, we present linearly dependent constraints under which the implementation of petrophysical and structural constraints synchronously is feasible. We try to integrate the new constraints into the joint inversion of seismic, magnetotelluric(MT) and gravity, as well as, discuss the way of joint optimization for the implementation of petrophysical and structural constraints synchronously. Also, we will examine the suitability and practicability of the new constraints by a series of model tests and real data feedback. The development of this new constraints can provides the technique support for the study of geophysical joint inversion.

模型空间的约束方式是地球物理联合反演的核心问题。众多学者从不同角度对地球物理联合反演约束方式进行了研究，例如：岩石物性、构造、向量线性相关。文献分析显示目前典型的地球物理联合约束方式存在如下问题：（1）岩石物性约束适用性弱；（2）梯度叉乘运算复杂；（3）梯度点乘约束需根据先验信息确定物性变化方向；（4）Gramian约束表达形式不够直观；（5）对同时开展岩石物性和构造约束研究不足。.针对以上问题，本课题基于向量线性相关，提出了一种新型的可将岩石物性和构造约束统一在一起的约束方式。课题拟将新型约束方式融入地震、大地电磁测深（MT）和重力联合反演，并讨论利用新型约束同时开展岩石物性和构造约束的联合优化机制，并通过模型试验和实际资料反馈验证新型约束方式的适用性和实用性。该约束方式的研发，可为地球物理联合反演研究提供新的技术支撑。

在地球物理联合反演领域，基于线性相关的约束方式正发挥着越来越重要的作用。目前，虽然基于线性相关的约束方式表达形式各异，但普遍具有对先验信息依赖低、具有一定的广义性等优点。本项目围绕着地球物理联合反演的实现，将线性相关融入地球物理联合反演，并分别讨论了在联合反演中利用线性相关开展物性约束、构造约束以及物性和构造混合约束的可行性。研究表明：可利用线性相关开展物性约束，该约束适用于正、反比例物性关联的条件；可利用线性相关开展构造约束，该约束适用于完全或部分共界面的条件；可利用线性相关开展物性和构造混合约束，该约束可为解决约束项加权因子选择问题提供新思路；有必要分区域施加联合反演约束，以提高约束方式的灵活性。研究成果有望为今后的地球物理联合反演研究提供借鉴。