Mathematical Geophysics

Seismic surface waves superimposed on the Earth.

Earth’s internal structure and processes, which cannot be observed directly, must be inferred from data that can be collected at (or above) Earth’s surface. Our research in Mathematical Geophysics at ANU attempts to address the question of `How to do this?' `How robust are the results? '. Projects at all levels are available with a computational and mathematical focus in inverse theory and parameter estimation.


Nature of Project(s):

Computational (making use of observational data from a variety of fields); mathematical/theoretical.

Essential Background:

PHYS3070 Physics of the Earth; EMSC8023 Advanced Data Sciences; EMSC80XX Computational Geosciences.


We wish to understand the Earth’s internal structure and processes, but we cannot observe these directly: everything must be inferred from data that can be collected at (or above) Earth’s surface. How should we do this? How robust are the results? Our research in Mathematical Geophysics at ANU attempts to address these questions. We develop new techniques for inference and inversion, and apply these to imaging of Earth systems. 

We are interested in a wide range of Earth phenomena, including the imaging of Earth structure at all scales (from global down to local), and understanding dynamic processes including earthquakes and mantle convection. Some of the projects we offer will involve developing new theory or methodology; others will focus on applying these techniques to new datasets. All our work is computer-intensive, and will suit students who enjoyed EMSC80XX Computational Geosciences, Advanced Data Sciences EMSC8023 and/or Physics of the Earth PHYS3070. For some projects, a certain level of mathematical fluency will be required. 

Some projects may provide opportunities for students to work with researchers and data from Geoscience Australia and CSIRO, by participation in ongoing collaborative projects.

Possible Research Avenues: 

Imaging of the Australian continent – Using a variety of datasets (especially seismological observations) and novel imaging techniques to infer details of the structure of the lithosphere and upper mantle in the Australian region. In particular, we are interested in probabilistic imaging techniques, which help capture the full range of structures that could be compatible with observations including quantification of uncertainty. This information helps to guide resource exploration, especially for the Australian minerals industry.

Machine learning in geophysics – In recent years, the fields of ‘machine learning’ and ‘artificial intelligence’ have seen massive growth.  They provide tools and techniques for discovering, assimilating and applying useful information hidden within complex datasets. How do these relate to established geophysical inference techniques? How can we use ideas from machine learning to solve geophysical problems? Potential applications range from data classification and quality control tasks through to real-time analysis of data to provide earthquake early warning.

Inversion problem with sparsity regularization – Mathematicians have recently demonstrated a number of intriguing results surrounding ‘sparse’ matrices: that is, matrices for which most elements are zero. It seems that these may offer an attractive route to building high-quality images of earth systems. Many of the details remain to be worked out, and could be explored by a mathematically-inclined student. This is likely to involve numerical experiments using a programming language such as Python.

Normal mode seismology – Often, when we think about seismic waves, we imagine an isolated wave-packet travelling around the Earth. However, at very low frequencies the earth ‘rings like a bell’, and normal mode seismology provides the mathematical framework for studying this. In particular, normal modes are thought to be the only dataset that provides any sensitivity to Earth’s large-scale density structure. Projects in this area may involve both observational and computational work.