The deformation of mantle and crustal rocks in response to stress plays a crucial role in the distribution of seismic and volcanic hazards, controlling tectonic processes ranging from continental drift to earthquake triggering. However, the spatial variation of these dynamic properties is poorly understood as they are difficult to measure. We exploited the large stress perturbation incurred by the 2016 earthquake sequence in Kumamoto, Japan, to directly image localized and distributed deformation. The earthquakes illuminated distinct regions of low effective viscosity in the lower crust, notably beneath the Mount Aso and Mount Kuju volcanoes, surrounded by larger-scale variations of viscosity across the back-arc. This study demonstrates a new potential for geodesy to directly probe rock rheology in situ across many spatial and temporal scales.

SUMMARY Inverse problems play a central role in data analysis across the fields of science. Many techniques and algorithms provide parameter estimation including the best-fitting model and the parameters statistics. Here, we concern ourselves with the robustness of parameter estimation under constraints, with the focus on assimilation of noisy data with potential outliers, a situation all too familiar in Earth science, particularly in analysis of remote-sensing data. We assume a linear, or linearized, forward model relating the model parameters to multiple data sets with a priori unknown uncertainties that are left to be characterized. This is relevant for global navigation satellite system and synthetic aperture radar data that involve intricate processing for which uncertainty estimation is not available. The model is constrained by additional equalities and inequalities resulting from the physics of the problem, but the weights of equalities are unknown. We formulate the problem from a Bayesian perspective with non-informative priors. The posterior distribution of the model parameters, weights and outliers conditioned on the observations are then inferred via Gibbs sampling. We demonstrate the practical utility of the method based on a set of challenging inverse problems with both synthetic and real space-geodetic data associated with earthquakes and nuclear explosions. We provide the associated computer codes and expect the approach to be of practical interest for a wide range of applications.

The source characteristics of slow and fast earthquakes provide a window into the mechanical properties of faults. In particular, the average stress drop controls the evolution of friction, fault slip, and event magnitude. However, this important source property is typically inferred from the analysis of seismic waves and is subject to many epistemic uncertainties. Here, we investigate the source properties of 53 earthquakes and 17 slow-slip events on thrust and strike-slip faults in various tectonic settings using slip distributions constrained by geodesy in combination with other data. We determine the width, potency, and potency density of slow and fast earthquake sources based on static slip distributions. The potency density, defined conceptually as the ratio of average slip to rupture radius, is a measure of anelastic deformation with limited bias from rigidity differences across depths and tectonic settings. Strike-slip earthquakes have the highest potency density, varying from 20 to 500 microstrain. The potency density is on average lower on continental thrust faults and megathrusts, from 10 to 200 microstrain, with an algebraic decrease with centroid depth, indicative of systematic changes in dominant rupture processes with depth. Slow slip events represent an end-member style of rupture with low potency density and large rupture width. Significant variability in potency density of slow-slip events affects their moment-duration scaling. The variations of source properties across tectonic settings, depth, and rupture styles can be used to better constrain numerical simulations of seismicity and to assess the source characteristics of future earthquakes and slow slip events. Plain Language Summary Natural earthquakes reduce the stress that accumulates on faults due to plate tectonics. To better understand the variability of seismic hazards around active faults, we survey the properties of slow and fast earthquakes around the world. The potential of faults to concentrate large slip in the rupture area differs depending on the geological setting, the depth of the source, and the type of rupture. Earthquakes in a continental setting condense more slip in a given rupture area, particularly in transform faults like the San Andreas fault. Subduction zone earthquakes, although some of the largest events on Earth, generally distribute less slip over a wider area, but this varies as a function of depth. Slow earthquakes represent an extreme case of little slip distributed over a large area. The propensity of rupture characteristics to vary with fault type and depth may help forecast the hazards posed by future seismicity.

Please select one of the following; *delete as appropriate: *(B) This thesis contains material from [3 number] paper(s) published in the following peer-reviewed journal(s) / from papers accepted at conferences in which I am listed as an author/ under preparation where I am an author.Chapter 2 is submitted as P. Nanjundiah, S.Barbot, and S.Wei. Static source prope1ties of slow and fast earthquakes. Journal of Geophysical Research-Solid Earth. The contributions of the co-authors are as follows:• A/Prof Barbot provided the initial project direction and edited the manuscript drafts.• I prepared the manuscript drafts. The manuscript was revised by A/Prof Shengji Wei.• I co-designed the study with A/Prof Barbot. I also analyzed the data.• The catalogue of slip distribution was collected by Prof Barbot and me.• The processing of slip-distributions and calculations of source parameters were done by me • A/Prof Wei assisted in the collection of joint inversion models and provided guidance in the interpretation of the collected data.• A/Prof Barbot, A/Prof Wei and Mr P.Adamek helped proofread the document to improve the language and construction of the manuscript Chapter 3 is under preparations as P. Nanjundiah, S. Wei, S. Barbot, W. Feng, P. Tapponnier and W. Teng, Source characteristics of the 2015 Mw 7.2 Lake Sarez,Tajikistan, earthquake sequence The contributions of the co-authors are as follows:• A/Prof Barbot suggested the study area • A/Prof Wei and I carried out the joint inversion between geodetic and seismic data for the mainshock and edited the manuscript drafts.• I performed the relative relocation of the aftershocks using Cut-and-Paste technique as well as my own relative relocation code.• The persistent scatter pixel offset tracking images of the near field deformation of the 2015 Mw 7.2 Lake Sarez, Tajikistan earthquake from Sentinel-IA satellite were processed using SAR!mgGeodesy by Dr Wang Teng of the University of Peking.• The Synthetic aperture radar data from Sentinal-1 A satellite for the mainshock was processed by Dr Wanpeng Feng using glnSAR technique to produce the interferograms.• I performed the relative relocation of the aft ershocks using CUT-and-Paste technique as well as my own relative relocation code • Prof P.Tapponnier helped provide insights into the tectonic setting of the Pamir plateau and the role of this eatthquake sequence in the same.