基于最小二乘的三维正交介质弹性波高精度正演模拟

Three-dimensional elastic wave forward modeling in orthorhombic media based on least squares

本文借助线性滑动理论,将裂隙密度、纵横比等不同物性参数等效为正交介质刚度矩阵,建立两组正交直立裂隙介质正演模型.利用基于最小二乘法优化的高精度交错网格高阶有限差分法模拟弹性波在正交介质中的传播过程.模拟结果表明介质各向异性强度与裂隙物性直接相关,正演波场和共炮点显示相比普通交错网格,最小二乘优化方法可以压制数值频散现象,明显提高模拟精度,子波主频较高和模型波速较低时改善效果更为突出.

In this paper, with the help of the linear slip theory, different physical parameters such as fracture density, aspect ratio are equivalent to stiffness matrix of orthorhombic medium, to establish forward model of two sets upright orthorhombic fractures. through high-precision staggered grid high-order finite difference, which is optimized by the least squares method, to simulate the propagation process of in this medium. The simulation results show that the anisotropy of the medium is directly related to the physical properties of fractures, forward wave field and common shot point gathers display that, compared to the original staggered grid, least squares method can be used to suppress the numerical dispersion phenomena, improve simulation accuracy significantly, the effect is more prominent when the wavelet frequency is high or the velocity of model is low.