Algorithm for 2D Modeling of the Propagation of a Sound Wave in an N-layer Elastic Medium with Inclusions with Various Physical-Mechanical Properties of a Hierarchical Type Located in an Oil Reservoir

A new method has been developed for modeling acoustic monitoring of a layered-block elastic medium with several inclusions of various physical, mechanical and phase hierarchical structures. An iterative process is developed for solving the direct problem for the case of three hierarchical inclusions of l, m, s-th ranks based on the use of 2D integral-differential equations. The degree of hierarchy of inclusions is determined by the values ​​of their ranks, which can be different. Hierarchical inclusions are located in one layer: the first is anomalously dense, the second is anomalously plastic, and the third is anomalously elastic and fluid-saturated density. The degree of filling with inclusions of each rank for all three hierarchical inclusions is different. The simulation results can be used in monitoring studies of the control of fluid return from oil fields developed as part of horizontal drilling.