Join us 11am–12pm Thursday 11th November for this week’s EarthByte seminar, featuring Lutz Gross from the University of Queensland. The seminar will be held online via Zoom, at https://uni-sydney.zoom.us/j/84686822190. Further details are below:
FEM-based Geophysical Data Inversion using esys-escript for Python
Inversion is the art to turn – in the best case – two-dimensional data into a three-dimensional map. Besides the obvious ingredient `data`, this process also relies on a physical forward model delivering a prediction of a spatial realization of the target property (or properties). Sadly the existence and uniqueness of a solution are not guaranteed and additional assumptions on the spatial correlation need to be introduced which depending on the inversion approach are regularization constraints for deterministic inversion or marginal distribution plus variogram when following a stochastic approach. When applying maximum likelihood estimation for the latter both inversion approaches – deterministic as well as stochastic – are falling back to solving an optimization problem with the forward model(s) as constraint with a cost function comprised of data misfit and (differential) norm of the target property. In the context of geophysical inversion, the forward model for instance for gravity and magnetic anomalies are given in form of partial differential equations (PDEs). The resulting PDE constraint optimization problem can be expressed as a system of PDEs. For this presentation, the finite element method (FEM) is the method of choice to solve these PDEs.
In the first part of the presentation, the use of the FEM method with unstructured meshes to solve large scale inversion problems for potential field data (gravity and magnetic) is discussed. In this application case, an individual data set can be inverted using a preconditioned conjugate method which provides scalability on parallel computing platforms. The extension to a joint inversion of both data sets using a structural correlation is discussed.
The implementations of these inversion algorithms are using the esys-escript module in Python which is discussed in the second part of the presentation. It provides an environment to implement the solution of a single PDE but also to link the solution of several PDEs as it is required for time-dependent, non-linear or optimization problems. Data structures of the underlying discretization method, such as FEM, and sparse matrix solvers are hidden from the user. This high level of abstraction also allows users to easily develop model scripts that can efficiently run on desktops as well as massive parallel computers (without redesign). The presentation will give an overview of the esys-escript and discuss a simple example script.