Non-double-couple mechanisms of microearthquakes induced during the 2000 injection experiment at the KTB site, Germany: A result of tensile faulting or anisotropy of a rock?

Vavryčuk, Václav; Bohnhoff, Marco; Jechumtálová, Zuzana; Kolář, Petr; Šı́lený, Jan

doi:10.1016/j.tecto.2007.08.019

Cited by 83 publications

(33 citation statements)

References 39 publications

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“…Therefore, first the source tensors must be calculated from moment tensors and then interpreted. If the elastic properties of the medium in the focal zone needed for calculating the source tensors are not known, they can be inverted from the non-DC components of the moment tensors (Vavryčuk 2004(Vavryčuk , 2011Vavryčuk et al 2008). Note that the retrieved medium parameters do not refer to local material properties of the fault but to the medium surrounding the fault and depend on the wavelength of the analysed radiated waves.…”

Section: Source Tensor Decompositionmentioning

confidence: 99%

Moment tensor decompositions revisited

2014

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The decomposition of moment tensors into isotropic (ISO), double-couple (DC) and compensated linear vector dipole (CLVD) components is a tool for classifying and physically interpreting seismic sources. Since an increasing quantity and quality of seismic data allow inverting for accurate moment tensors and interpreting details of the source process, an efficient and physically reasonable decomposition of moment and source tensors is necessary. In this paper, the most common moment tensor decompositions are revisited, new equivalent formulas of the decompositions are derived, suitable norms of the moment tensors are discussed and the properties of commonly used source-type plots are analysed. The Hudson skewed diamond plot is introduced in a much simpler way than originally proposed. It is shown that not only the Hudson plot but also the diamond CLVD-ISO plot and the Riedesel-Jordan plot conserve the uniform distribution probability of moment eigenvalues if the appropriate norm of moment tensors is applied. When analysing moment tensor uncertainties, no source-type plot is clearly preferable. Since the errors in the eigenvectors and eigenvalues of the moment tensors cannot be easily separated, the moment tensor uncertainties project into the source-type plots in a complicated way. As a consequence, the moment tensors with the same uncertainties project into clusters of a different size. In case of an anisotropic focal area, the complexity of moment tensors of earthquakes prevents their direct interpretation, and the decomposition of moment tensors must be substituted by that of the source tensors.Keywords Dynamics and mechanics of faulting . Earthquake source observations . Seismic anisotropy . Theoretical seismology IntroductionThe moment tensor describes equivalent body forces acting at a seismic point source (Burridge and Knopoff 1964) and is a basic quantity evaluated for earthquakes on all scales from acoustic emissions to large devastating earthquakes. The most common type of the moment tensor is the double-couple (DC) source which represents the force equivalent of shear faulting on a planar fault in isotropic media. However, many studies reveal that seismic sources often display more general moment tensors with significant non-double-couple (non-DC) components ). An explosion is an obvious example of a non-DC source, but non-DC components can also be produced by the collapse of a cavity in mines (Rudajev and Šílený 1985;Šílený and Milev 2008), by shear faulting on a nonplanar (curved or irregular) fault (Sipkin 1986), by tensile faulting induced by fluid injection in geothermal or volcanic areas (Ross et al. 1996;Julian et al. 1997) when the slip vector is inclined from the fault and causes its opening (Vavryčuk 2001(Vavryčuk , 2011 Roessler et al. 2004Roessler et al. , 2007. Complications also arise if the source is situated at a material interface (Vavryčuk 2013).In order to identify which type of seismic source is physically represented by the retrieved moment tensor, Knopoff and Randall (1970...

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Section: Source Tensor Decompositionmentioning

confidence: 99%

Moment tensor decompositions revisited

2014

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“…We have been working with recordings of seismic events induced by hydraulic load at the KTB deep hole (e.g. Baish et al, 2002;Vavryčuk et al, 2007;Kolář, 2007). The modelling procedure (Backus and Mulcahy, 1976;Aki and Richards,1980) is formulated for true P and S amplitudes decomposed into NS-EW-Z directions as [P n , P e , P z ] and [S n , S e , S z ]:…”

Section: Examples Of Im Computationsmentioning

confidence: 99%

Isometric method: Efficient tool for solving non-linear inverse problems

2007

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A novel algorithm called Isometric Method (IM) for solving smooth real-valued nonlinear inverse problems has been developed. Model and data spaces are represented by using m + 1 corresponding vectors at a time (m is the dimension of model space). Relations among vectors in the data space are set up and then transferred into the model space thus generating a new model. If the problem is truly linear, this new model is the exact solution of the inverse problem.If the problem is non-linear, the whole procedure has to be repeated iteratively. The basic underlying idea of IM is to postulate the distance in the model space in such a way that the model and data spaces are isometric, i.e. distances in both spaces have the same measure. As all model-data vector pairs are used many times in successive iterations, the number of the forward problem computations is minimized. There is no necessity to deal with derivatives. The requirement for the computer memory is low. IM is suitable especially for solving smooth medium non-linear problems when forward modelling is time-consuming and minimizing the number of function evaluations is topical. Applications of IM on synthetic and real geophysical problems are also presented.K e y w o r d s : non-linear inversion, optimization, isometric algorithm

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“…Non-DC source mechanisms have also been reported in induced seismicity. For example, non-DC events have been observed among earthquakes induced by wastewater injection in Geysers, California (Ross et al 1996(Ross et al , 1999 and southeast Germany (Vavryčuk et al 2008). Mining-induced earthquakes (e.g., Ford et al 2008) are also reported to have non-DC mechanisms.…”

Section: Introductionmentioning

confidence: 99%

Mathematical review on source-type diagrams

2016

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A source-type diagram is a visualization tool used to display earthquake sources, including double-couples, compensated linear vector dipoles, and isotropic deformation. Together with recent observations of non-double-couple events in a variety of tectonic settings, it is important to be able to recognize the source type intuitively from a representative diagram. Since previous works have proposed diagrams created using a range of projections, we review these diagrams in the framework of the moment tensor eigenvalue space. For further applications, we also provide complete formulas for conversion between moment tensor representation and the coordinate system of each diagram style. Using both a global catalog and synthetic data, we discuss differences between types of diagrams and the relative effectiveness of each.

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Non-double-couple mechanisms of microearthquakes induced during the 2000 injection experiment at the KTB site, Germany: A result of tensile faulting or anisotropy of a rock?

Cited by 83 publications

References 39 publications

Moment tensor decompositions revisited

Moment tensor decompositions revisited

Isometric method: Efficient tool for solving non-linear inverse problems

Mathematical review on source-type diagrams

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