Inversions of earthquake source slip from the recorded ground motions typically impose a number of restrictions on the source parameterization, which are needed to stabilize the inverse problem with sparse data. Such restrictions may include smoothing, causality considerations, predetermined shapes of the local source-time function, and constant rupture speed. The best regional networks have sensor spacing in the tens of kilometers range, much larger than the wavelengths relevant to key aspects of earthquake physics. Novel approaches to providing orders-of-magnitude denser sensing include low-cost sensors (Community Seismic Network) and space-based optical imaging (Geostationary Optical Seismometer). This thesis aims to understand whether the inversion results could be substantially improved, with fewer constraints, by the availability of much denser sensor networks than currently available.
Inversions that involve large number of sensors and 3D crustal velocity models are intractable with the current source inversion codes. Hence we have developed a new approach that can handle thousands of sensors in heterogeneous media. It employs iterative conjugate gradient optimization based on an adjoint method and involves iterative time-reversed 3D wave propagation simulations using the spectral element method (SPECFEM3D). We have also developed a variant of this adjoint-based method for layered media that utilizes pre-computed Green’s functions instead of the time-reversed wave propagation. The developed methods have been applied to two problems: impact of crustal structure uncertainties on source inversion and resolution of rise time as a function of network spacing and rupture velocity. In the first part, we show that typical uncertainties in crustal velocity models represented by a von Karman distribution of 5 km correlation length and 5% standard deviation (with Hurst exponent of zero), severely degrade the quality of source inversion. However, if the velocity uncertainties have a correlation of 500 m or a standard deviation of 1%, then source inversion has an adequate quality. In the second part we find that supershear ruptures show almost identical source recovery in terms of width of the slip pulse for network spacings ranging from few km to tens of km, even for rise times as short as 1 sec, while subshear ruptures require a network spacing finer than a penetration length that depends on rupture velocity and rise time, as their peak ground velocity decay rapidly with distance from the fault.
In summary, we have developed scalable source inversion tools that will enable exploiting the next generation of very dense earthquake observation systems, improvements in regional scale 3D tomography models and accelerated advancements in computing capabilities. These developments will be critical in resolving the fine spatio-temporal features of earthquake sources that are pertinent to fracture mechanics and earthquake physics. With the 3D iterative time-reversal imaging, one could aspire for extracting more information from the high frequency wavefield by considering joint improvement of source and structure.</p
