A linearized rock physics inversion method is proposed to deal with two important issues, rock physical model and inversion algorithm, which restrict the accuracy of rock physics inversion. In this method, first, the complex rock physics model is expanded into Taylor series to get the first-order approximate expression of the inverse problem of rock physics; then the damped least square method is used to solve the linearized rock physics inverse problem directly to get the analytical solution of the rock physics inverse problem. This method does not need global optimization or random sampling, but directly calculates the inverse operation, with high computational efficiency. The theoretical model analysis shows that the linearized rock physical model can be used to approximate the complex rock physics model. The application of actual logging data and seismic data shows that the linearized rock physics inversion method can obtain accurate physical parameters. This method is suitable for linear or slightly non-linear rock physics model, but may not be suitable for highly non-linear rock physics model.

针对岩石物理模型和反演算法这两个重要问题，提出了一种线性化岩石物理反演的方法，制约了岩石物理反演的精度。在这种方法中，首先，将复杂的岩石物理学模型扩展为泰勒级数，以获得岩石物理学反问题的一阶近似表达式。然后采用阻尼最小二乘法直接求解线性化的岩石物理反问题，得到岩石物理反问题的解析解。该方法不需要全局优化或随机抽样，而是直接计算逆运算，计算效率高。理论模型分析表明，线性岩石物理模型可用于近似复杂岩石物理模型。实际测井资料和地震资料的应用表明，线性岩石物理反演方法可以获得准确的物理参数。此方法适用于线性或稍微非线性的岩石物理模型，但可能不适用于高度非线性的岩石物理模型。