Retrieving the Seismic Moment Release Rate of Small Seismic Events Using the Adjoint Method - Theory and Numerical Validation
Abstract
Abstract Classical seismic data analysis for source characterization includes hypocenter determination, moment tensor inversion, and spectral analysis, which provide estimates of key source parameters such as seismic moment, source radius, static stress drop, and apparent stress. Additional parameters, including source duration, rupture directivity, rupture velocity, and dynamic stress drop, can also be inferred from seismic recordings, provided that the source time function (\stf), which describes the temporal evolution of seismic moment release at the source, is known. However, accurate estimation of the \stf\ remains a challenging task. Currently, \stf\ estimation is performed primarily using either full-waveform inversion (\fwi) or the approximate empirical Green's function (\egf) method. The former is computationally demanding and requires high-quality data, whereas the latter is limited by its accuracy and reliance on empirical assumptions. In this paper, we propose an alternative approach for estimating the \stf\ based on the time-reversal symmetry of the governing wave equation which can be used for routine analysis of antropogenic seismicity. The proposed method relies on the observation that, when far-field seismograms are back-propagated to the source location using time-reversal techniques (also known as adjoint methods), the reconstructed signal at the source approximates the original \stf. Consequently, the \stf\ can be efficiently recovered without the need…
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