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Paleomagnetic measurements of natural remanent magnetization were – until recently -- performed on large, millimeter to centimeter-sized rock samples using classical rock magnetometers. Developments of magnetic imaging (i.e., quantum diamond microscope (QDM) and scanning SQUID microscope) allow for the measurement of individual, weakly magnetic (10-16 Am2) particle clusters within a sample. However, this increased spatial resolution adds to the complexity of the magnetic signal and requires novel approaches in analyzing the data.Commonly, the magnetic moment of sources within a sample are analyzed by dipole inversion, meaning fitting a dipole signal to a cropped part of a magnetic map. While this gives accurate results for sources that are well separated and dipole-like in character, recovering net magnetic moments from complex maps proved difficult. Machine learning (ML) has been used to study a vast number of problems and has become a part of our daily lives. Here, we present the first ML model to predict net magnetic moments from magnetic maps. Our ML models consist of three simple convolutional neural networks for source declination, inclination, moment magnitude, each of which has been trained on a large (500k) synthetic map dataset. The models are tested against several datasets, varying in size, source distribution and resolution. Our models can quickly and accurately recover the magnetic moment, even for very complex (i.e., low dipolarity) maps. The accuracy of the models is < 8˚ for inclination and declination and < 10 % for moment. Surprisingly, we find little correlation in the prediction accuracy to the dipolarity of the map. These results show that ML is a promising alternative to dipole inversions, especially for maps with low dipolarity parameters, where traditional dipole inversions can fail.

The Cascadia subduction zone hosts great $\mathrm{M}_\mathrm{W} > 8.5$ earthquakes, but studying these events is hindered by our short observational record. Earthquake cycle simulation provides an alternative window into the behavior of the subduction zone. Here, we present simulations over 3,800 years, 14 ruptures and hundreds of slow slip events on a high-fidelity geometric representation of the Cascadia subduction zone beneath surface topography. The boundaries of these ruptures are defined by ephemeral stress barriers that last for several cycles but are eliminated by a barrier-crossing rupture. Thus, it is possible that many real world rupture barriers are due to remnant stress shadows from previous slip events and may not persist over several earthquake cycles. In addition, we see ``fast' slow slip events with $\mathrm{M}_\mathrm{W} \approx 8$. These events may occur in nature and reduce the seismically available moment or they may be a spurious feature of an unrealistic friction law.

Boundary element methods have become a foundational tool in earthquake science for the modeling of earthquake cycle kinematics. Despite their wide use and convenience typical rectangular and triangular constant slip dislocation methods produce stress singularities at the edges of every element rendering these models physically unrealistic. As we demonstrate, in an earthquake cycle simulation where the stress influences the fault slip through a friction relationship, these un-physical stress singularities manifest in severe numerical artifacts which limit their applicability to the calculation of on fault stresses and dynamic earthquake cycle modeling. To solve this problem, we develop a singularity free Galerkin boundary element method using continuous linear displacement and slip basis functions. We use Gaussian and Sauter-Schwab quadrature combined with a Stokes theorem based regularization approach in lieu of analytical formulae. In order to solve the large dense linear systems that emerge from boundary element methods, we use a fast multipole method to accurately approximate far-field element interactions. Combining these theoretical approaches with an optimized parallel implementation and GPU acceleration, we are able to solve one million element problems in seconds on a desktop computer.