Dept. of Geosciences Colloquium: Earthquake Slip Inversions: Addressing the Non-Uniqueness and the Ill-Conditioning of the Inverse Problem

​Abstract:

Inverting seismic and geodetic data for earthquake slip distribution is key for understanding earthquake mechanics and assessing future fault failures. A well-resolved slip model may be used for calculating the stress changes in the crust and determining the probability of earthquake occurrence on adjacent faults. Often, however, the slip inversions are non-unique and/or ill-conditioned. The problem is said to be non-unique when it results in a suite of very different slip models that fit the data similarly well, and is said to be ill-conditioned when small changes to the data space cause big changes to the solution space. The non-uniqueness of the problem may be addressed by combining different types of datasets, such as interferometric synthetic-aperture radar (InSAR), pixel offset tracking and GPS. The ill-conditioning may be addressed by reconditioning the inverse problem in a manner that
reduces the solution sensitivity to noise and data processing errors. Implementing both approaches eliminates the need for a-priori regularisation, and results in a trustable slip model.

In this work we will present methodologies for setting up well-conditioned and well-resolved earthquake slip inversions. We will first address the ill-conditioning of the inverse problem by optimizing the data and model discretization in a manner that improves the inversion stability. In order to improve the non-uniqueness of the inverse we will augment the traditional data used in slip inversions with SAR Burst Overlap Interferometry(BOI). The BOI is applied to strips that are measured twice in each satellite pass, once in a forward and once in a backward looking direction. Using this double interferometry, displacements can be calculated along the satellite flight direction, a component that is not resolved by traditional SAR interferometry and is most important for ~N-S striking earthquake faults.

We will apply these approaches to three earthquakes. First, the Mw6.3, 6 April 2009 L’Aquila earthquake in Italy, where we jointly invert InSAR data, GPS displacement results, and geological offset field observations. This approach results in a better agreement between the source model and the precise relocated aftershock sequence. We then examine the Mw6.4 and Mw7.1 foreshock-mainshock Ridgecrest earthquake pair, revealing that a section of the fault has ruptured twice and an off-fault post-seismic transient occurred to the north-west of the earthquake rupture. Finally, we will investigate the Mw7.8 and Mw7.6 February 2023 Turkish earthquake doublet, showing that although they are temporally and spatially close, they are on opposite ends of the earthquake spectrum in stress drop terms.

By combining different types of datasets and optimising the inversion process, we can obtain a trustable slip model reducing the need for a priori regularisation. These results provide valuable insights into earthquake mechanics and the assessment of future fault failures.
 

Event Organizer: Dr. Roy Barkan