Inversion of Surface Deformation Data for Rapid Estimates of Source Parameters and Uncertainties: A Bayesian Approach

Abstract

New satellite missions (e.g., the European Space Agency's Sentinel‐1 constellation), advances in data downlinking, and rapid product generation now provide us with the ability to access space‐geodetic data within hours of their acquisition. To truly take advantage of this opportunity, we need to be able to interpret geodetic data in a prompt and robust manner. Here we present a Bayesian approach for the inversion of multiple geodetic data sets that allows a rapid characterization of posterior probability density functions (PDFs) of source model parameters. The inversion algorithm efficiently samples posterior PDFs through a Markov chain Monte Carlo method, incorporating the Metropolis‐Hastings algorithm, with automatic step size selection. We apply our approach to synthetic geodetic data simulating deformation of magmatic origin and demonstrate its ability to retrieve known source parameters. We also apply the inversion algorithm to interferometric synthetic aperture radar data measuring co‐seismic displacements for a thrust‐faulting earthquake (2015 Mw 6.4 Pishan earthquake, China) and retrieve optimal source parameters and associated uncertainties. Given its robustness and rapidity in estimating deformation source parameters and uncertainties, our Bayesian framework is capable of taking advantage of real‐time geodetic measurements. Thus, our approach can be applied to geodetic data to study magmatic, tectonic, and other geophysical processes, especially in rapid‐response operational settings (e.g., volcano observatories). Our algorithm is fully implemented in a MATLAB®‐based software package (Geodetic Bayesian Inversion Software) that we make freely available to the scientific community.

Integrated Petrological and Geophysical Constraints on Magma System Architecture in the Western Galápagos Archipelago: Insights From Wolf Volcano

“…Patterns of ground deformation similar to those identified before the 2015 Wolf eruption have recently been identified elsewhere in the western Galápagos Archipelago (e.g., at Fernandina and Cerro Azul), with shallow intereruptive inflation and significant deflation of a deeper magma storage region during eruptions or major dike intrusion events (Bagnardi & Amelung, ; Bagnardi & Hooper, ; Bagnardi et al, ; Geist, Harpp, et al, ). Based on our observations from Wolf volcano, these deep deflationary sources must reflect melt extraction from large lower crustal magma storage regions or mush columns, from which most of the erupted material is sourced.…”

“…Long‐term subsidence, possibly related to crystallization and contraction of a shallow magma body at ~3‐km depth, has also been observed at Alcedo (Hooper et al, ). Evidence for additional, deeper magma storage at >5 km has been identified in InSAR data from Fernandina (Bagnardi et al, ; Bagnardi & Amelung, ; Chadwick et al, ), Cerro Azul (Bagnardi & Hooper, ), and Wolf volcano (Xu et al, ), and by seismicity patterns at Sierra Negra (Davidge et al, ). There are currently no geodetic constraints on magma storage depths beneath volcanoes in the eastern Galápagos Archipelago, due to the infrequency of historic eruptions (Siebert et al, ) and the apparent absence of clear intereruptive deformation.…”

The 2017 Eruption of Erta 'Ale Volcano, Ethiopia: Insights Into the Shallow Axial Plumbing System of an Incipient Mid‐Ocean Ridge

“…To find this solution, we subsampled the data using a quadtree approach (Jónsson et al, ), with a variance threshold of 9 × 10 −4 m 2 . We optimized the geometry and opening of the dislocation and estimated uncertainties using the Geodetic Bayesian Inversion Software, which implements the Markov Chain Monte Carlo method and Metropolis‐Hastings algorithm to create probability density functions of model source parameters (Bagnardi & Hooper, ).…”

Did Anthropogenic Activities Trigger the 3 April 2017 Mw 6.5 Botswana Earthquake?

“…1.0, Centre for Observation and Modelling of Earthquakes, Volcanoes and Tectonics (COMET), Leeds, England, available at: http://comet.nerc.ac.uk/gbis/) [24] to infer the model parameters by Some atmospheric artifacts are present in the interferogram, which are mainly due to turbulent effects. However, a rough estimation of the LoS tropospheric delay ( Figure S1) [22], estimated between the days of the two SAR acquisitions (http://ceg-research.ncl.ac.uk/v2/gacos/), shows that the area surrounding the earthquake epicenter presents a negligible tropospheric delay, which does not affect the observed displacement pattern.…”

“…1.0, Centre for Observation and Modelling of Earthquakes, Volcanoes and Tectonics (COMET), Leeds, England, available at: http://comet.nerc.ac.uk/gbis/) [24] to infer the model parameters by means of the descending interferogram obtained from the S1B satellite data. The inversion code uses a Markov-chain Monte Carlo algorithm, incorporating the Metropolis-Hastings algorithm [25][26][27] to estimate the multivariate posterior probability distribution for all model parameters.…”