Model Uncertainties and Joint Inversion in Geophysics

Solid Earth geophysics is based on different types of data, such as magnetic, gravitational, electrical and seismic generally collected near or at the surface of the Earth, and is used to estimate physical parameters of the subsurface. The related parameter estimation problems are typically characterized as inverse problems. Other types of data may include petrophysical data from borehole (core) drilling. All these types of data are then used to decide, for example, where to carry out further drilling, which is an expensive undertaking. The standard way of modelling different types of data uses oversimpli ed likelihood models, which can be interpreted as being induced by white noise, zero mean and uncorrelated with the unknowns. The problem is that the use of these trivial likelihood models tends to underestimate the underlying uncertainties of the parameters. However, the so-called Bayesian Approximation Error (BAE) approach has shown that feasible likelihood models are typically non-trivial. In this thesis, we use the BAE approach to construct feasible likelihood models for the case of di erent data types and jointly correlated parameters. We show that the associated joint likelihood functions are coupled and that the errors are heavily correlated with the unknowns. We also show that the assimilation of di erent measurement modalities with properly constructed covariance structures may increase accuracy in the estimates. As examples, we use linear and non-linear geophysical forward problems, namely, gravity and magnetics, to estimate the large scale representation of the associated physical parameters. As joint prior models, we use jointly correlated Whittle-Mat ern random eld models with crosscovariance constructed using statistical constitutive models. We add borehole data which is inherently represented in a smaller spatial scale. We show that straightforward incorporation of the small scale borehole data with the large scale model can underestimate the posterior uncertainty and can render parameter estimates useless.

Name thesis:degree_name

PhD

Level thesis:degree_level

Doctoral

Discipline thesis:degree_discipline

Mathematics

Grantor dc:publisher

ResearchSpace@Auckland

Year dc:date.issued

2019

Author dc:creator

• Guzman Carballo, Susana Scarlett

Advisors dc:contributor.advisor

• Kaipio, Jari
• Rowland, Julie

Statement dc:rights

• Items in ResearchSpace are protected by copyright, with all rights reserved, unless otherwise indicated. Previously published items are made available in accordance with the copyright policy of the publisher.

Licence dc:rights.uri

• https://researchspace.auckland.ac.nz/docs/uoa-docs/rights.htm

Handle dc:identifier.uri

https://hdl.handle.net/2292/52405

OAI identifier oai:identifier

oai:researchspace.auckland.ac.nz:2292/52405