scholarly journals Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation

Solid Earth ◽  
2014 ◽  
Vol 5 (2) ◽  
pp. 1055-1069 ◽  
Author(s):  
S. C. Stähler ◽  
K. Sigloch
Keyword(s):  
Moment Tensor ◽  
Source Parameters ◽  
Practical Importance ◽  
Principal Component ◽  
Seismic Source ◽  
Empirical Orthogonal Functions ◽  
Time Function ◽  
Source Inversion ◽  
Source Time Function ◽  
Earthquake Parameters

Abstract. Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference) is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Seismic source Mechanisms (PRISM) that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 source time functions (STFs) by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits propagating these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.

scholarly journals Fully probabilistic seismic source inversion – Part 1: Efficient parameterisation

2013 ◽  
Vol 5 (2) ◽  
pp. 1125-1162 ◽  
Author(s):  
S. C. Stähler ◽  
K. Sigloch
Keyword(s):  
Moment Tensor ◽  
Source Parameters ◽  
Practical Importance ◽  
Principal Component ◽  
Seismic Source ◽  
Empirical Orthogonal Functions ◽  
Time Function ◽  
Source Inversion ◽  
Source Time Function ◽  
Earthquake Parameters

Abstract. Seismic source inversion is a non-linear problem in seismology where not just the earthquake parameters themselves, but also estimates of their uncertainties are of great practical importance. Probabilistic source inversion (Bayesian inference) is very adapted to this challenge, provided that the parameter space can be chosen small enough to make Bayesian sampling computationally feasible. We propose a framework for PRobabilistic Inference of Source Mechanisms (PRISM) that parameterises and samples earthquake depth, moment tensor, and source time function efficiently by using information from previous non-Bayesian inversions. The source time function is expressed as a weighted sum of a small number of empirical orthogonal functions, which were derived from a catalogue of >1000 STFs by a principal component analysis. We use a likelihood model based on the cross-correlation misfit between observed and predicted waveforms. The resulting ensemble of solutions provides full uncertainty and covariance information for the source parameters, and permits to propagate these source uncertainties into travel time estimates used for seismic tomography. The computational effort is such that routine, global estimation of earthquake mechanisms and source time functions from teleseismic broadband waveforms is feasible.

Deriving source-time functions using principal component analysis

1989 ◽  
Vol 79 (3) ◽  
pp. 711-730
Author(s):  
D. W. Vasco
Keyword(s):  
Principal Component Analysis ◽  
Moment Tensor ◽  
Principal Component ◽  
Singular Values ◽  
Singular Value ◽  
Time Function ◽  
Basis Functions ◽  
Single Source ◽  
Source Time Function ◽  
The Moment

Abstract Factors such as source complexity, microseismic noise, and lateral heterogeneity all introduce nonuniqueness into the source-time function. The technique of principal component analysis is used to factor the moment tensor into a set of orthogonal source-time functions. This is accomplished through the singular value decomposition of the time-varying moment tensor. The adequacy of assuming a single source-time function may then be examined through the singular values of the decomposition. The F test can also be used to assess the significance of the various principal component basis functions. The set of significant basis functions can be used to test models of the source-time functions, including multiple sources. Application of this technique to the Harzer nuclear explosion indicated that a single source-time function was found to adequately explain the moment tensor. It consists of a single pulse appearing on the diagonal elements of the moment-rate tensor. The decomposition of the moment tensor for a deep teleseism in the Bonin Islands revealed three basis functions associated with relatively large singular values. The F test indicated that only two of the principal components were significant. The principal component associated with the largest singular value consists of a large pulse followed 16-sec later by a diminished pulse. The second principal component, a long-period oscillation, appears to be a manifestation of the poor resolution of the moment-rate tensor at low frequencies.

The characteristic of source spectra and stress drop of earthquakes in the Bucaramanga nest

2020 ◽  
Author(s):  
Wenzheng Gong ◽  
Xiaofei Chen
Keyword(s):  
Focal Mechanism ◽  
Stress Drop ◽  
Source Parameters ◽  
Time Function ◽  
Corner Frequency ◽  
Ratio Method ◽  
Source Time Function ◽  
Spectra Analysis ◽  
Source Spectra ◽  
Very High

<p>Spectra analysis is helpful to understand earthquake rupture processes and estimate source parameters like stress drop. Obtaining real source spectra and source time function isn’t easy, because the station recordings contain path effect and we usually can’t get precise path information. Empirical Green’s function (EGF) method is a popular way to cancel out the path effect, main two of which are the stacking spectra method (Prieto et al, 2006) and the spectral ratio method (Viegas et al, 2010; Imanishi et al, 2006). In our study, we apply the latter with multitaper spectral analysis method (Prieto et al, 2009) to calculate relative source spectra and relative source time function. Target event and EGFs must have similar focal mechanism and be collocated, so we combine correlation coefficient of wave at all stations and focal mechanism similarity to select proper EGFs.</p><p>The Bucaramanga nest has very high seismicity, so it’s suitable to calculate source spectra by using EGF method. We calculate the source spectra and source time function of about 1540 earthquakes (3-5.7ml, 135-160km depth) at Bucaramanga nest in Colombia. Simultaneously we also estimate corner frequency by fitting spectral source model (Brune, 1970; Boatwright, 1980) and stress drop using simple model (Eshelby, 1957) of earthquakes with multiple station recordings or EGFs. We obtain about 30000 events data with 12 stations from National Seismological Network of Colombia (RSNC).</p><p>The result show that the source spectra of most earthquakes fitted well by omega-square model are smooth, and the source spectra of some have obvious ‘holes’ near corner frequency, and the source time function of a few earthquakes appear two separate peeks. The first kind of earthquakes are style of self-arresting ruptures (Xu et al. 2015), which can be autonomously arrested by itself without any outside interference. Abercrombie (2014) and Wen et al. (2018) both researched the second kind of earthquakes and Wen think that this kind of earthquakes are style of the runaway ruptures including subshear and supershear ruptures. The last kind of earthquakes maybe be caused by simultaneous slip on two close rupture zone. Stress drop appear to slightly increase with depth and are very high (assuming rupture velocity/s wave velocity is 0.9). We also investigate the high-frequency falloff n, usually 2, of Brune model and Boatwright model by fitting all spectra, and find that the best value of n for Boatwright model is 2 and for Brune model is 3.5.</p>

scholarly journals Improved finite-source inversion through joint measurements of rotational and translational ground motions: A theoretical study

2016 ◽  
Author(s):  
Michael Reinwald ◽  
Moritz Bernauer ◽  
Heiner Igel ◽  
Stefanie Donner
Keyword(s):  
Inverse Problem ◽  
Ground Motions ◽  
Source Parameters ◽  
Normal Fault ◽  
Seismic Source ◽  
Vertical Gradient ◽  
Vertical Displacement ◽  
Source Inversion ◽  
Additional Information ◽  
Finite Source

Abstract. With the prospects of seismic equipment being able to measure rotational ground motions in a wide frequency and amplitude range in the near future we engage in the question how this type of ground motion observation can be used to solve the seismic inverse problem. In this paper, we focus on the question, whether finite source inversion can benefit from additional observations of rotational motion. Keeping the overall number of traces constant, we compare observations from a surface seismic network with 44 3-component translational sensors (classic seismometers) with those obtained with 22 6-component sensors (with additional 3-component rotational motions). Synthetic seismograms are calculated for known finite-source properties. The corresponding inverse problem is posed in a probabilistic way using the Shannon information content as measure how the observations constrain the seismic source properties. We minimize the influence of the source receiver geometry around the fault by statistically analyzing six-component (three velocity and three rotation rate) inversions with a random distribution of receivers. The results show that with the 6-C subnetworks the source properties are not only equally well recovered (even that would be benefitial because of the substantially reduced logistics installing half the sensors) but statistically some source properties are almost always better resolved. We assume that this can be attributed to the fact that the (in particular vertical) gradient information is contained in the additional motion components. We compare these effects for strike-slip and normal-faulting type sources and confirm that the increase in inversion quality for kinematic source parameters is even higher for the normal fault. This indicates that the inversion benefits from the additional information provided by the horizontal rotation rates, i.e. information about the vertical displacement gradient.

A user-friendly probabilistic earthquake source inversion framework for joint inversion of seismic, geodetic, and gravitational signals - The Grond toolkit

2020 ◽  
Author(s):  
Sebastian Heimann ◽  
Marius Isken ◽  
Daniela Kühn ◽  
Hannes Vasyura-Bathke ◽  
Henriette Sudhaus ◽  
...  
Keyword(s):  
Open Source ◽  
Joint Inversion ◽  
Moment Tensor ◽  
Source Parameters ◽  
Seismic Source ◽  
Magma Ascent ◽  
Caldera Collapse ◽  
Waveform Data ◽  
Trade Offs ◽  
Finite Fault

<p>Seismic source and moment tensor waveform inversion is often ill-posed or non-unique if station coverage is poor or signals are weak. Three key ingredients can help in these situations: (1) probabilistic inference and global search of the full model space, (2) joint optimisation with datasets yielding complementary information, and (3) robust source parameterisation or additional source constraints. These demands lead to vast technical challenges, on the performance of forward modelling, on the optimisation algorithms, as well as on visualisation, optimisation configuration, and management of the datasets. Implementing a high amount of automation is inevitable.</p><p>To tackle all these challenges, we are developing a sophisticated new seismic source optimisation framework, Grond. With its innovative Bayesian bootstrap optimiser, it is able to efficiently explore large model spaces, the trade-offs and the uncertainties of source parameters. The program is highly flexible with respect to the adaption to specific source problems, the design of objective functions, and the diversity of empirical datasets.</p><p>It uses an integrated, robust waveform data processing, and allows for interactive visual inspection of many aspects of the optimisation problem, including visualisation of the result uncertainties. Grond has been applied to CMT moment tensor and finite-fault optimisations at all scales, to nuclear explosions, to a meteorite atmospheric explosion, and to volcano-tectonic processes during caldera collapse and magma ascent. Hundreds of seismic events can be handled in parallel given a single optimisation setup.</p><p>Grond can be used to optimise simultaneously seismic waveforms, amplitude spectra, waveform features, phase picks, static displacements from InSAR and GNSS, and gravitational signals.</p><p>Grond is developed as an open-source package and community effort. It builds on and integrates with other established open-source packages, like Kite (for InSAR) and Pyrocko (for seismology).</p>

Seismic Source Processes of 25 Earthquakes (Mw>5) in the Gulf of California

2022 ◽  
Author(s):  
Eduardo Huesca-Pérez ◽  
Edahí Gutierrez-Reyes ◽  
Luis Quintanar
Keyword(s):  
Gulf Of California ◽  
Moment Tensor ◽  
Source Parameters ◽  
Seismic Source ◽  
Focal Mechanisms ◽  
Process Models ◽  
Moment Tensors ◽  
Time Space ◽  
Double Couple ◽  
Broadband Seismograms

ABSTRACT The Gulf of California (GoC) is a complex tectonic boundary that has been instrumented in the past several decades to record broadband seismograms. This volume of data has allowed us to study several source parameters systematically. Before, only a few source parameters of earthquakes greater than magnitude five had been studied in the GoC area. We re-examined the focal mechanisms of several earthquakes in the southern GoC that occurred over the last 20 yr using local–regional distance broadband seismograms. These focal mechanisms were then used as input data to retrieve the time–space history of the rupture for each earthquake. This work contributes to the study of 25 rupture-process models computed with the method proposed by Yagi et al. (1999). To investigate more about the nature of the seismicity in the GoC, we also calculated the non-double-couple component of moment tensors for 45 earthquakes. Previous studies (e.g., Ortega et al., 2013, 2016) have shown that non-double-couple components from moment tensors in this region are associated with complex faulting, suggesting that oblique faults or several parallel faults are interacting simultaneously. Our results show that, at least for moderate earthquakes (5 < M < 6), rupture processes in the GoC show a complex interaction between fault systems. It is revealed on the important contribution of non-double-couple component obtained in the full moment tensor analysis.

Wavelet estimation from marine pressure measurements

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2108-2119 ◽  
Author(s):  
Are Osen ◽  
Bruce G. Secrest ◽  
Lasse Amundsen ◽  
Arne Reitan
Keyword(s):  
Pressure Field ◽  
Estimation Method ◽  
Seismic Source ◽  
Time Function ◽  
Pressure Measurements ◽  
Source Time Function ◽  
Wavelet Estimation ◽  
The Earth ◽  
Scattered Energy ◽  
Direct Pressure

A new and alternative procedure for the deterministic estimation of the seismic source time function (wavelet) is proposed. This paper follows a series of reports on source signature estimation, requiring neither statistical assumptions on the signature nor any knowledge about the earth below the receivers. The proposed estimation method, which in principle is exact, uses conventional recordings of the pressure on a surface below the source and recordings of the pressure at one or more locations above the receiver surface. The derivation of the method is based on the Kirchhoff‐Helmholtz integral equation. The formulation ensures that the scattered energy is filtered from the wavelet estimation, enabling the wavelet to be detected from the direct pressure field. Along with the derivation, we present a numerical example.

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