An introduction to the two-scale homogenization method for seismology

Capdeville, Yann; Cupillard, Paul; Singh, Sarvpreet

doi:10.1016/bs.agph.2020.07.001

Cited by 15 publications

(10 citation statements)

References 79 publications

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“…shows a singularity at the source location. The imprint of the elastic structure is visible, as expected (the strain is discontinuous in discontinuous models (Capdeville et al 2020)).…”

Section: Numerical Preliminary Observationssupporting

confidence: 79%

“…In this section, we summarize the results of Capdeville et al (2010a) on the twoscale homogenization method applied to the elastic wave equation when the mechanical property heterogeneities do not present any natural scale separation. Many mathematical subtleties have been omitted here but can be found in Capdeville et al (2010a) and Capdeville et al (2020).…”

Section: Two-scale Homogenization Of the Mechanical Properties With No Scale Separationmentioning

confidence: 99%

“…F wavenumber cutoff is always 1/λ min . More details about this technical aspect can be found in Capdeville et al (2020), section 2.3.…”

Section: Two-scale Homogenization Of the Mechanical Properties With No Scale Separationmentioning

confidence: 99%

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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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“…shows a singularity at the source location. The imprint of the elastic structure is visible, as expected (the strain is discontinuous in discontinuous models (Capdeville et al 2020)).…”

Section: Numerical Preliminary Observationssupporting

confidence: 79%

Section: Two-scale Homogenization Of the Mechanical Properties With No Scale Separationmentioning

confidence: 99%

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Homogenization of seismic point and extended sources

Capdeville

2021

Geophysical Journal International

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“…Given that strain measurements are acutely sensitive to very small-scale structure, the distinction between true instrument response, coupling between the instrument and the ground, and very local path effects are less distinct for DAS (and other strain-sensing modalities) than they are for point seismometers acting at typical 1 Hz frequencies (e.g. King et al 1976;Ringler et al 2019;Capdeville et al 2020). Attempting to ascribe the apparent response of the cable to any one of these factors using only the predicted ground motions is difficult, however by studying the characteristics of response across the whole array it may be possible to build a hypothesis as to the predominant factors by searching for a correlation (or lack of correlation) with other data sets, such as tomographic models of the subsurface.…”

Section: N V E R S I O N O F Da S R E C O R D S F O R Pa Rt I C L E V E L O C I T Ymentioning

confidence: 99%

Wavefield-based evaluation of DAS instrument response and array design

Muir

Zhan

2021

Geophysical Journal International

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Summary Distributed Acoustic Sensing (DAS) networks promise to revolutionize observational seismology by providing cost-effective, highly dense spatial sampling of the seismic wavefield, especially by utilizing pre-deployed telecomm fiber in urban settings for which dense seismic network deployments are difficult to construct. However, each DAS channel is sensitive only to one projection of the horizontal strain tensor and therefore gives an incomplete picture of the horizontal seismic wavefield, limiting our ability to make a holistic analysis of instrument response. This analysis has therefore been largely restricted to pointwise comparisons where a fortuitious coincidence of reference three-component seismometers and co-located DAS cable allows. We evaluate DAS instrument response by comparing DAS measurements from the PoroTomo experiment with strain-rate wavefield reconstructed from the nodal seismic array deployed in the same experiment, allowing us to treat the entire DAS array in a systematic fashion irrespective of cable geometry relative to the location of nodes. We found that, while the phase differences are in general small, the amplitude differences between predicted and observed DAS strain-rates average a factor of 2 across the array and correlate with near-surface geology, suggesting that careful assessment of DAS deployments is essential for applications that require reliable assessments of amplitude. We further discuss strategies for empirical gain corrections and optimal placement of point sensor deployments to generate the best combined sensitivity with an already deployed DAS cable, from a wavefield reconstruction perspective.

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“…Under specific circumstances the data are usable only when they are corrected for local side effects, especially strain-rotation-coupling. investigated the coupling in more detail using the theory of homogenisation (Capdeville et al, 2020). They introduced the coupling vector J which is a characteristic of the receiver location and not dependent on source or time.…”

Section: Strain-rotation Coupling and Local Side Effectsmentioning

confidence: 99%

Rotational Ground Motion Measurements for Regional Seismic Moment Tensors: a Review

Donner¹

2021

Preprint

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Seismic moment tensors are an important tool in geosciences on all spatial scales and for a broad range of applications. The basic underlying theory is established since decades. However, various factors influence the reliability of the inversion result, several of them are mutually dependent. Hence, a reliable retrieval of seismic moment tensors is still hampered in many cases, especially at regional event-receiver distances.To sample the entire wavefield due to a seismic source we need six components: three translational and three rotational ones. Up to now, only translational ground motion recordings were used for moment tensor retrieval, missing out valuable information. Using rotational in addition to the classical translational ground motions during waveform inversion for moment tensors mainly adds information on the vertical displacement gradient to the inversion problem. Furthermore, having available six instead of only three components per receiver location provides additional constraints on the sampling of the radiation pattern. As a result, the moment tensor components are resolved with higher precision and accuracy, even when the number of recording receivers is considerably reduced. Especially, components with a dependence to depth as well as the centroid depth can benefit significantly from additional rotational ground motion. Up to the time of writing this review only a few studies are published on the topic. Here, I summarise their findings and provide an overview over the possible capabilities of including rotational ground motion measurements to waveform inversion for seismic moment tensor retrieval.

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An introduction to the two-scale homogenization method for seismology

Cited by 15 publications

References 79 publications

Homogenization of seismic point and extended sources

Homogenization of seismic point and extended sources

Wavefield-based evaluation of DAS instrument response and array design

Rotational Ground Motion Measurements for Regional Seismic Moment Tensors: a Review

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