Micro-seismic event estimation and velocity analysis based on a source-focusing function

Attaining information corresponding to the micro-seismic source location helps in understanding the reservoir fracturing process. Time-reversal-based migration methods are widely used to get a source image directly. Such source-locating methods share a fundamental weakness: the accuracy of source image depends highly on the accuracy of the velocity model. Full waveform inversion (FWI) has been employed in micro-seismic data to include an optimization of the source image and velocity model, simultaneously. However, such inversions are vulnerable to cycle-skipping problems, more so when the source location and source origin time are unknown. They, also, cost a lot. In order to solve these problems, we introduce a source-focusing function as an additional objective to optimize the velocity model and source image with a much higher quality. This objective function used to measure the source-image focusing property is defined by the estimated source-location coordinate and the source image. The source image is poorly focused if the velocity is inaccurate, and the objective function reaches minimum when the velocity is accurate. We use the geometric-mean imaging condition to get the high-resolution source image at each iteration. Then, we use it to calculate the estimated source-location coordinate and the gradient of objective functional with respect to the velocity. The optimized velocity can improve the source-image quality. In the end, the final output velocity and source image will allow us to fit the objective for all these attributes of the model and source image. Using synthetic data generated from the 2D Marmousi and the 3D Overthrust models, we highlight the cycle-skipping immune and high-resolution features of the proposed method. The application to field data also shows that the proposed method can improve the velocity model and source-image quality.