Positioning of seismic sources combined with forward and inversion of spherical wave in double-layer horizontal media

The positioning method of geometric average in double-layer horizontal media is unable to determine the horizontal coordinates of seismic sources directly. When it is extended to multilayer medium, the positioning parameters containing depth are difficult to be determined and corrected, and it is difficult to determine the layer where the sources are located. Using the travel time equation by which the depth and horizontal coordinates are separated and the square root is removed, the time when the earthquake happens is obtained through inversion and corrected reasonably. According to the forward modeling method for wave front of spherical wave in double-layer horizontal media, nonlinear equations containing space coordinates of the sources are got, and the depth and horizontal coordinates are yielded by solving the nonlinear equations. The calculated results of positioning under a variety of conditions show that the larger values of positioning error of depth and horizontal coordinates derived by the positioning model combined with forward and inversion are all not greater than those by the geometric average method, and the new positioning method is more suitable than the geometric average method for positioning of deep seismic sources. The sensitivity analysis of parameters shows that the origin time of earthquakes is not sensitive to the positioning parameters, and the sensitivity of the focal position error to wave velocity and wave velocity ratio is between the geometric average method and classical linear method. But the proposed model cannot improve the defect of the geometric average method. When the ratio of horizontal to vertical distance between stations and sources is large, the positioning accuracy is poor. There is also no advantages when the ratio of distances from the interface of sources and stations is too large or too small. So stations in the area where earthquakes are easily prone to happen are suggested to be arranged and the classic linear positioning methods are employed. There is no need to determine or correct the positioning parameters containing depth for the positioning model combined with forward and inversion. It is easy to eliminate or identify which layer the seismic sources are located in. Accordingly, the proposed model is more suitable than the geometric average method for positioning of seismic sources in multilayer horizontal media.