Inversion for microseismic focal mechanisms in attenuated strata and its resolution

Microseismic focal mechanism inversion is significant for the unconventional oil and gas development. Microseismic signal is characterized by high frequency and small energy, so it is easy to be influenced by formation attenuation effect, and to cause serious waveform distortion and unreliable inversion results. After analyzing the previous microseismic moment tensor inversion methods and some of their deficiency, this paper proposes a new method for microseismic focal mechanism inversion considering the stratum attenuation effect. On the other hand, the Q factor of actual strata is hard to estimate precisely and the microseismic events are very complex. So we design a simple observation model with three vertical wells and four basic moment tensors which are added 30% random perturbation to simulate the actual field situation. In the process of numerical computation, we assume the sediments' Q factor has different levels of error. Based on this assumption, we can calculate the inversion error of the new moment tensor inversion method and analyze the inversion resolution by using the SVD of Frechet derivative matrix due to Q factor error. According to the theoretical calculation, the application conditions of the various focal mechanism inversions can be summarized for different types of microseismic data. Furthermore, the theoretical calculation proves that only using direct P waves can obtain a better inversion result than using direct P and S waves simultaneously. After analyzing the inversion error and the inversion resolution, we conclude that the joint inversion by using direct P and S wave data can estimate a better T value and a better k value can be inversed by using direct P wave separately. Moreover the direct P wave has a less sensitivity about the sediment Q factor. Based on this conclusion we can effectively reduce the negative influence on the focal mechanism inversion result by utilizing different types of wave data to determine the different parts of microseismic focal mechanisms.