Representation of complex seismic sources by orthogonal moment-tensor fields

Jordan, Thomas H.; Juarez, Alan

doi:10.1093/gji/ggy492

Cited by 5 publications

(2 citation statements)

References 68 publications

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“…Backus and Mulcahy (1976) termed stress glut the stress mismatch of a purely elastic medium and the true physical stress. The stress glut method was first established within the context of kinematic earthquake source descriptions, where the region of non‐zero stress glut is the internal source (Bukchin, 1995; Chen et al., 2005; Clévédé et al., 2004; Jordan & Juarez, 2019, 2020, 2021; McGuire, 2017; McGuire et al., 2001, 2002). The stress glut (Andrews, 1999) and the thick fault zone (Madariaga et al., 1998) methods in the context of dynamic rupture modeling have been implemented in the finite difference method (Andrews, 1976, 1999; Dalguer & Day, 2006; Herrendörfer et al., 2018; Madariaga et al., 1998; Preuss et al., 2019).…”

Section: Introductionmentioning

confidence: 99%

A Diffuse Interface Method for Earthquake Rupture Dynamics Based on a Phase‐Field Model

Hayek,

May,

Pranger

et al. 2023

JGR Solid Earth

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In traditional modeling approaches, earthquakes are often depicted as displacement discontinuities across zero‐thickness surfaces embedded within a linear elastodynamic continuum. This simplification, however, overlooks the intricate nature of natural fault zones and may fail to capture key physical phenomena integral to fault processes. Here, we propose a diffuse interface description for dynamic earthquake rupture modeling to address these limitations and gain deeper insight into fault zones' multifaceted volumetric failure patterns, mechanics, and seismicity. Our model leverages a steady‐state phase‐field, implying time‐independent fault zone geometry, which is defined by the contours of a signed distance function relative to a virtual fault plane. Our approach extends the classical stress glut method, adept at approximating fault‐jump conditions through inelastic alterations to stress components. We remove the sharp discontinuities typically introduced by the stress glut approach via our spatially smooth, mesh‐independent fault representation while maintaining the method's inherent logical simplicity within the well‐established spectral element method framework. We verify our approach using 2D numerical experiments in an open‐source spectral element implementation, examining both a kinematically driven Kostrov‐like crack and spontaneous dynamic rupture in diffuse fault zones. The capabilities of our methodology are showcased through mesh‐independent planar and curved fault zone geometries. Moreover, we highlight that our phase‐field‐based diffuse rupture dynamics models contain fundamental variations within the fault zone. Dynamic stresses intertwined with a volumetrically applied friction law give rise to oblique plastic shear and fault reactivation, markedly impacting rupture front dynamics and seismic wave radiation. Our results encourage future applications of phase‐field‐based earthquake modeling.

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Section: Introductionmentioning

confidence: 99%

A Diffuse Interface Method for Earthquake Rupture Dynamics Based on a Phase‐Field Model

Hayek,

May,

Pranger

et al. 2023

JGR Solid Earth

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“…For large sources, the point source approximation is challenged and the extension from a point source to something more general is not trivial. The existing solutions, such as higher order moment tensors (Clévédé et al 2004;Jordan and Juarez 2018) or finite source inversions (Mai et al 2016), are difficult to implement in tomographic full waveform inversion in a automated way for example.…”

Section: Introductionmentioning

confidence: 99%

Homogenization of seismic point and extended sources

Capdeville

2021

Geophysical Journal International

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SUMMARY Seismic sources are mostly modelled as point sources: moment tensors associated with the gradient of a Dirac distribution. Such sources contain an infinite range of scales and induce a discontinuity in the displacement wavefield. This makes the near-source wavefield expensive to model and the event location complex to invert, in particular for large events for which many point sources are required. In this work, we propose to apply the non-periodic two-scale homogenization method to the wave equation source term for both force and couple-sources. We show it is possible to replace the Dirac point source with a smooth source term, valid in a given seismic signal frequency band. The discontinuous wavefield near-source wavefield can be recovered using a corrector that needs to be added to the solution obtained solving the wave equation with the smooth source term. We show that, compared to classical applications of the two-scale homogenization method to heterogeneous media, the source term homogenization has some interesting particularities: for couple-sources, the leading term of the homogenization asymptotic expansion is dependent on the fine spatial scale, depending on the source type, only one or two first terms of the expansion are non-zero and there is no periodic case equivalent (the source term cannot be made spatially periodic). For heterogeneous media, two options are developed. In the first one, only the source is homogenized while the medium itself remains the same, including its discontinuities. In the second one, both the source and the medium are homogenized successively: first the medium and then the source. We present a set of tests in 1-D and 2-D, showing accurate results both in the far-source and near-source wavefields, before discussing the interest of this work in the forward and inverse problem contexts.

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Erratum: ‘Representation of complex seismic sources by orthogonal moment–tensor fields’

Jordan

Juarez

2020

Geophysical Journal International

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Representation of complex seismic sources by orthogonal moment-tensor fields

Cited by 5 publications

References 68 publications

A Diffuse Interface Method for Earthquake Rupture Dynamics Based on a Phase‐Field Model

A Diffuse Interface Method for Earthquake Rupture Dynamics Based on a Phase‐Field Model

Homogenization of seismic point and extended sources

Erratum: ‘Representation of complex seismic sources by orthogonal moment–tensor fields’

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