Event locations: Speeding up grid searches using quadratic interpolation

These are the synthetic example data associated with \"Event locations: Speeding up grid searches using quadratic interpolation\" by Hanh Bui and Mirko van der Baan, submitted to Geophysical Journal International. Abstract: \"The grid search method is a common approach to estimate the three spatial coordinates of event hypocenters. However, locating events in large search spaces with small grid spacings is computationally prohibitive. This study accelerates the grid searches over large search spaces using a quadratic interpolation technique. We start with the coarse-grid-estimated location, where we have the minimum value of the difference in the traveltimes between S- and P-waves summed over all receivers. Then, we select the neighbouring grid points and build a 3D quadratic function. The unknown coefficients of the 3D quadratic function are computed by solving a system of linear equations. After that, we interpolate the location by solving partial derivatives of the quadratic function. The quadratic interpolation technique performs well on both synthetic and real microseismic data examples, typically leading to similar event locations as those obtained using 10 times smaller grid spacings in all three directions, at a minor additional computational expense, and without the need to generate traveltimes at new spatial positions.\"

本数据集为Han Bui与Mirko van der Baan提交至《国际地球物理杂志》（Geophysical Journal International）的论文《Event locations: Speeding up grid searches using quadratic interpolation》配套的合成示例数据集。摘要：网格搜索法是估算事件震源三维空间坐标的常用方法。然而，在网格间距极小的大型搜索空间内开展事件定位，计算成本高昂，难以实现。本研究采用二次插值技术，加速大型搜索空间内的网格搜索流程：首先以粗网格估算的震源位置作为初始点，该点对应所有接收点的S波（S-wave）与P波（P-wave）走时差之和的最小值；随后选取相邻网格点，构建三维二次函数；通过求解线性方程组，求得该三维二次函数的未知系数；最后通过求解该二次函数的偏导数，完成震源位置的插值估算。该二次插值技术在合成与实际微地震数据示例中均表现优异，通常可获得与在三个方向上将网格间距缩小至原1/10时一致的震源定位结果，仅需极少量额外计算开销，且无需在新空间位置重新生成走时数据。