Inverting elastic dislocations using the Weakly-enforced Slip Method
Gertjan van Zwieten, E. Harald van Brummelen*, Ramon F. Hanssen
Mathematical Geodesy and Positioning
Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an earthquake's faulting mechanism. This inverse problem requires a numerical forward model that is both accurate and fast, as typical inverse procedures require many evaluations. The Weakly-enforced Slip Method (WSM) was developed to meet these needs, but it was not before applied in an inverse problem setting. Consequently, it was unknown what affects particular properties of the WSM, notably its inherent continuity, have on the inversion process. Here we show that the WSM can accurately recover slip distributions in a Bayesian-inference setting, provided that data points in the vicinity of the fault are removed. In a representative scenario, an element size of 1 km was found to be sufficiently fine to generate a posterior probability distribution that is close to the theoretical optimum. For rupturing faults a masking zone of 10 km sufficed to avoid numerical disturbances that would otherwise be induced by the discretization error. These results demonstrate that the WSM is a viable forward method for earthquake inversion problems. While our synthesized scenario is basic for reasons of validation, our results are expected to generalize to the wider gamut of scenarios that finite element methods are able to capture. This has the potential to bring modeling flexibility to a field that is often forced to impose model restrictions in a concession to computability.
International Journal for Numerical and Analytical Methods in Geomechanics
https://doi.org/10.1002/nag.3365
Bayesian inference
elastic dislocation
inverse problem
10.1002/nag.3365
Num Anal Meth Geomechanics - 2022 - van Zwieten - Inverting elastic dislocations using the Weakly‐enforced Slip MethodFinal published version, 3.57 MBLicence: CC BY-NC
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Dislocation Mathematics 100%
Slip Mathematics 95%
dislocation Earth & Environmental Sciences 79%
Earthquakes Engineering & Materials Science 70%
Earthquake Mathematics 63%
Error Chemical Compounds 61%
Inverse problems Engineering & Materials Science 58%
van Zwieten, G., van Brummelen, E. H., & Hanssen, R. F. (2022). Inverting elastic dislocations using the Weakly-enforced Slip Method. International Journal for Numerical and Analytical Methods in Geomechanics, 46(9), 1729-1753. https://doi.org/10.1002/nag.3365
van Zwieten, Gertjan ; van Brummelen, E. Harald ; Hanssen, Ramon F. / Inverting elastic dislocations using the Weakly-enforced Slip Method. In: International Journal for Numerical and Analytical Methods in Geomechanics. 2022 ; Vol. 46, No. 9. pp. 1729-1753.
@article{548590afad9b4cbba88d328d4ff2a0dd,
title = "Inverting elastic dislocations using the Weakly-enforced Slip Method",
abstract = "Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an earthquake's faulting mechanism. This inverse problem requires a numerical forward model that is both accurate and fast, as typical inverse procedures require many evaluations. The Weakly-enforced Slip Method (WSM) was developed to meet these needs, but it was not before applied in an inverse problem setting. Consequently, it was unknown what affects particular properties of the WSM, notably its inherent continuity, have on the inversion process. Here we show that the WSM can accurately recover slip distributions in a Bayesian-inference setting, provided that data points in the vicinity of the fault are removed. In a representative scenario, an element size of 1 km was found to be sufficiently fine to generate a posterior probability distribution that is close to the theoretical optimum. For rupturing faults a masking zone of 10 km sufficed to avoid numerical disturbances that would otherwise be induced by the discretization error. These results demonstrate that the WSM is a viable forward method for earthquake inversion problems. While our synthesized scenario is basic for reasons of validation, our results are expected to generalize to the wider gamut of scenarios that finite element methods are able to capture. This has the potential to bring modeling flexibility to a field that is often forced to impose model restrictions in a concession to computability.",
keywords = "Bayesian inference, elastic dislocation, inverse problem",
author = "{van Zwieten}, Gertjan and {van Brummelen}, {E. Harald} and Hanssen, {Ramon F.}",
doi = "10.1002/nag.3365",
journal = "International Journal for Numerical and Analytical Methods in Geomechanics",
publisher = "John Wiley & Sons",
van Zwieten, G, van Brummelen, EH & Hanssen, RF 2022, 'Inverting elastic dislocations using the Weakly-enforced Slip Method', International Journal for Numerical and Analytical Methods in Geomechanics, vol. 46, no. 9, pp. 1729-1753. https://doi.org/10.1002/nag.3365
Inverting elastic dislocations using the Weakly-enforced Slip Method. / van Zwieten, Gertjan; van Brummelen, E. Harald; Hanssen, Ramon F.
In: International Journal for Numerical and Analytical Methods in Geomechanics, Vol. 46, No. 9, 2022, p. 1729-1753.
T1 - Inverting elastic dislocations using the Weakly-enforced Slip Method
AU - van Zwieten, Gertjan
AU - van Brummelen, E. Harald
AU - Hanssen, Ramon F.
N2 - Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an earthquake's faulting mechanism. This inverse problem requires a numerical forward model that is both accurate and fast, as typical inverse procedures require many evaluations. The Weakly-enforced Slip Method (WSM) was developed to meet these needs, but it was not before applied in an inverse problem setting. Consequently, it was unknown what affects particular properties of the WSM, notably its inherent continuity, have on the inversion process. Here we show that the WSM can accurately recover slip distributions in a Bayesian-inference setting, provided that data points in the vicinity of the fault are removed. In a representative scenario, an element size of 1 km was found to be sufficiently fine to generate a posterior probability distribution that is close to the theoretical optimum. For rupturing faults a masking zone of 10 km sufficed to avoid numerical disturbances that would otherwise be induced by the discretization error. These results demonstrate that the WSM is a viable forward method for earthquake inversion problems. While our synthesized scenario is basic for reasons of validation, our results are expected to generalize to the wider gamut of scenarios that finite element methods are able to capture. This has the potential to bring modeling flexibility to a field that is often forced to impose model restrictions in a concession to computability.
AB - Earthquakes cause lasting changes in static equilibrium, resulting in global deformation fields that can be observed. Consequently, deformation measurements such as those provided by satellite based InSAR monitoring can be used to infer an earthquake's faulting mechanism. This inverse problem requires a numerical forward model that is both accurate and fast, as typical inverse procedures require many evaluations. The Weakly-enforced Slip Method (WSM) was developed to meet these needs, but it was not before applied in an inverse problem setting. Consequently, it was unknown what affects particular properties of the WSM, notably its inherent continuity, have on the inversion process. Here we show that the WSM can accurately recover slip distributions in a Bayesian-inference setting, provided that data points in the vicinity of the fault are removed. In a representative scenario, an element size of 1 km was found to be sufficiently fine to generate a posterior probability distribution that is close to the theoretical optimum. For rupturing faults a masking zone of 10 km sufficed to avoid numerical disturbances that would otherwise be induced by the discretization error. These results demonstrate that the WSM is a viable forward method for earthquake inversion problems. While our synthesized scenario is basic for reasons of validation, our results are expected to generalize to the wider gamut of scenarios that finite element methods are able to capture. This has the potential to bring modeling flexibility to a field that is often forced to impose model restrictions in a concession to computability.
KW - Bayesian inference
KW - elastic dislocation
KW - inverse problem
U2 - 10.1002/nag.3365
DO - 10.1002/nag.3365
JO - International Journal for Numerical and Analytical Methods in Geomechanics
JF - International Journal for Numerical and Analytical Methods in Geomechanics
van Zwieten G, van Brummelen EH, Hanssen RF. Inverting elastic dislocations using the Weakly-enforced Slip Method. International Journal for Numerical and Analytical Methods in Geomechanics. 2022;46(9):1729-1753. https://doi.org/10.1002/nag.3365