Major research projects
This aims to be a compilation of my main research projects - those that I spent years working on and led to publications on peer-reviewed journals (including publications under review or in preparation).
• Full-waveform seismic tomography of the Alaskan lithosphere
Shear-wave velocity structure of the lithosphere across the entire Alaska is imaged by analyzing the seismic data recorded by ~ 400 stations, using the adjoint tomography method. By fitting > 1 million waveforms with 56 iterative model updates, a shear-wave velocity model is obtained, featuring several features of tectonic significance in the region. Despite the efforts in optimizing the imaging workflow, the project consumes ~ 2 million CPU hours on the supercomputer "Niagara" at University of Toronto.
• Wavefield injection based on interface discontinuity conditions
In seismic wave simulations, it is sometimes useful to inject a background wavefield into a domain of interest, so that the interaction between the incoming wavefield and the structure can be studied. This project studies the wavefield injection problem based on its equivalence to another seemingly unrelated problem - the interface discontinuity condition problem.
• Perfectly matched layer (PML) on curvilinear grids
Perfectly matched layer (PML) is known to have superior performance in absorbing waves at the truncation boundaries of computational domains. However, PML is usually derived and implemented on Cartesian grids, and therefore requires the computational domain to align with the (x, y, z) coordinates. Such requirement restricts the use of PML in wave simulations with deformed geometries (e.g., spherical geometry of the Earth). This project attempts to implement PML on curvilinear grids based on coordinate transformations between the curvilinear and Cartesian coordinates.
Research notes
Brainstorms, random notes, implementation of new algorithms, etc. Not chunky enough for publication, but in my view, creative and interesting as well.
The gradient of the objective function with respect to the structural parameters, or the sensitivity kernel, is a key component in full-waveform inversion (FWI). Two decades ago, derived by Lagrangian multipliers or Born scattering, it is shown that thesensitivity kernel can be calculated using the adjoint method, which involves the correlation between a forward and an adjoint wavefield (e.g., the seminal paper by Tromp, Tape & Liu, 2005), triggering the development of FWI in the following years. On the other hand, backpropagation and auto-differentiation enables efficient calculation of the gradient of a deep learning model with respect to its parameters. This note reveals that (1) the seismic wave equation can be seen as a special recurrent neural network, and (2) the adjoint method can be derived from the backpropagation algorithm. To further illustrate this connection, a sensitivity kernel shown in Tromp, Tape & Liu (2005) is reproduced using PyTorch.
For surface-wave FWI, it is sometimes desirable to measure and fit multiple surface-wave modes (fundamental and overtone) within one window. Different modes may exhibit different dispersion, and therefore it is hard to use frequency-dependent phase-shift measurement to fit all the modes. This note attempts to explore the use of frequency-time-dependent phase-shift measurement based on continuous wavelet transform to fit multi-mode surface waves. A very simple toy experiment is provided using PyTorch.