Overview of a range of solution methods for elastic dislocation problems in geophysics

Zwieten, G. J. van; Hanssen, Ramon F.; Gutiérrez, Miguel

doi:10.1029/2012jb009278

Cited by 13 publications

(24 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The second term in the final expression in (21) then vanishes if Γ ε collapses on Γ. Therefore, formally passing to the limit in (21), we obtain…”

Section: Collapsing the Liftmentioning

confidence: 93%

“…The model embeds a displacement discontinuity of given location and magnitude in an elastic medium, causing the entire medium to deform under the locked-in stress. Many different solution methods have been developed for this particular problem, based on analytical solutions or numerical approximations; see for instance [21] for an overview of the most prominent methods. However, methods founded on analytical solutions generally dictate severe model simplifications, such as elastic homogeneity or generic geometries, which restricts their validity.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Discontinuities without discontinuity: The Weakly-enforced Slip Method

Zwieten

Brummelen

Zee

et al. 2014

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

Tectonic faults are commonly modelled as Volterra or Somigliana dislocations in an elastic medium. Various solution methods exist for this problem. However, the methods used in practice are often limiting, motivated by reasons of computational efficiency rather than geophysical accuracy. A typical geophysical application involves inverse problems for which many different fault configurations need to be examined, each adding to the computational load. In practice, this precludes conventional finite-element methods, which suffer a large computational overhead on account of geometric changes. This paper presents a new non-conforming finite-element method based on weak imposition of the displacement discontinuity. The weak imposition of the discontinuity enables the application of approximation spaces that are independent of the dislocation geometry, thus enabling optimal reuse of computational components. Such reuse of computational components renders finite-element modeling a viable option for inverse problems in geophysical applications. A detailed analysis of the approximation properties of the new formulation is provided. The analysis is supported by numerical experiments in 2D and 3D.Comment: Submitted for publication in CMAM

show abstract

“…The second term in the final expression in (21) then vanishes if Γ ε collapses on Γ. Therefore, formally passing to the limit in (21), we obtain…”

Section: Collapsing the Liftmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Discontinuities without discontinuity: The Weakly-enforced Slip Method

Zwieten

Brummelen

Zee

et al. 2014

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…It is supposed that the considered system experiences a new minimum energy state of self-stressed equilibrium. The magnitude and direction of the displacement jump (or slip) is a vector field over the dislocation plane, where a slip vector has normal components, the material opens, and is added to fill the void, just as it happens when a dyke intrudes a fault (van Zwieten et al 2013). The displacements are discontinuous at the dislocation plane and continuous elsewhere.…”

Section: Introductionmentioning

confidence: 99%

“…There are several approaches to model elastic dislocation of an active fault (van Zwieten et al 2013). Analytical methods are rapid and accurate, but are often restricted to simple problems without complexity.…”

Section: Introductionmentioning

confidence: 99%

“…This method may be implemented in finite element method (FEM) to consider the discontinuity effects of fault without direct modeling of the discontinuity. Even though the SNT was proposed in 1981, this idea is still a robust tool as it can handle anisotropy, heterogeneity, topography, distributed slip and curved fault effects (Melosh and Raefsky 1983;Melosh and Williams 1989;Andrews 1999;Day 2006, 2007;van Zwieten et al 2013). Recently, van Zwieten et al (2014) developed the weaklyenforced slip method to model tectonic faults without explicitly simulating discontinuities.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A Monte Carlo adapted finite element method for dislocation simulation of faults with uncertain geometry

2017

View full text Add to dashboard Cite

Dislocation modelling of an earthquake fault is of great importance due to the fact that ground surface response may be predicted by the model. However, geological features of a fault cannot be measured exactly, and therefore these features and data involve uncertainties. This paper presents a Monte Carlo based random model of faults with finite element method incorporating split node technique to impose the effects of discontinuities. Length and orientation of the fault are selected as random parameters in the domain model, and hence geometrical uncertainties are encountered. Mean and standard deviation values, as well as probability density function of ground surface responses due to the dislocation are computed. Based on analytical and numerical calculation of dislocation, two approaches of Monte Carlo simulations are proposed. Various comparisons are examined to illustrate the capability of both methods for random simulation of faults.

show abstract

Inverting elastic dislocations using the Weakly‐enforced Slip Method

Zwieten

Brummelen

Hanssen

2022

Num Anal Meth Geomechanics

View full text Add to dashboard Cite

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.

show abstract

Overview of a range of solution methods for elastic dislocation problems in geophysics

Cited by 13 publications

References 25 publications

Discontinuities without discontinuity: The Weakly-enforced Slip Method

Discontinuities without discontinuity: The Weakly-enforced Slip Method

A Monte Carlo adapted finite element method for dislocation simulation of faults with uncertain geometry

Inverting elastic dislocations using the Weakly‐enforced Slip Method

Contact Info

Product

Resources

About