Acoustic emissions from penny‐shaped cracks in glass. II. Moment tensor and source‐time function

1986 ◽  
Vol 59 (8) ◽  
pp. 2711-2715 ◽  
Author(s):  
Kwang Yul Kim ◽  
Wolfgang Sachse
Keyword(s):  
Moment Tensor ◽  
Acoustic Emissions ◽  
Time Function ◽  
Source Time Function

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.

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.

Waveform Energy Focusing Tomography for Passive Sources

2020 ◽  
Author(s):  
Yueqiao Hu ◽  
Junlun Li ◽  
Haijiang Zhang
Keyword(s):  
Moment Tensor ◽  
Waveform Inversion ◽  
Velocity Model ◽  
Time Function ◽  
Source Information ◽  
Source Time Function ◽  
Origin Time ◽  
Small Magnitude ◽  
Short Period ◽  
Energy Focusing

<p>Full waveform inversion (FWI) is one of the most attractive geophysical inversion methods that reconstruct models with higher quality by exploiting the information of full wave-field. Despite its high resolution and successful practical applications, there still exist several obstacles to the successful application of FWI for passive earthquake sources, such as the high non-linearity for model convergence and demand for accurate source information, such as the moment tensor, the source time function, etc. To alleviate the requirement for a priori source information in waveform inversion, we propose a new method called Waveform Energy Focusing Tomography (WEFT), which backpropagates the observed wavefield from the receivers, not the data residuals like in conventional FWI, and tries to maximize the back-propagated wavefield energy around the source location over a short period around the origin time. Therefore, there is no need to provide the focal mechanism and source time function in advance. To better reconstruct the passive sources, the least-squares moment tensor migration approach is used, and the Hessian matrix is approximated using either analytic expression or raytracing. Since waveform fitting is superseded by simpler energy maximization, the nonlinearity of WEFT is weaker than that of FWI, and even less-accurate initial velocity model can be used. These advantages of WEFT make it more practical  for challenging earthquake data, especially for local small magnitude earthquakes where both velocity model and earthquake source information are unknown.</p>

scholarly journals The Cephalonia, Ionian Sea (Greece), sequence of strong earthquakes of January-February 2014: a first report

2014 ◽  
Vol 3 (1) ◽  
Author(s):  
Gerassimos A. Papadopoulos ◽  
Vassilios K. Karastathis ◽  
Ioannis Koukouvelas ◽  
Maria Sachpazi ◽  
Ioannis Baskoutas ◽  
...  
Keyword(s):  
Fault Plane ◽  
Moment Tensor ◽  
Time Function ◽  
P Wave ◽  
Ionian Sea ◽  
Fault Rupture ◽  
Source Time Function ◽  
Ground Acceleration ◽  
Strong Earthquakes ◽  
Source Duration

On 26.1.2014 and 3.2.2014 two strong earthquakes of M<sub>w</sub>6.0 and M<sub>w</sub>5.9 ruptured the western Cephalonia Isl., Ionian Sea (Greece), at the SSW-wards continuation of the Lefkada segment of the Cephalonia Transform Fault Zone (CTFZ), causing considerable damage and a variety of ground failures. High-precision relocation of the aftershocks implies that the seismogenic layer was of 35 km in length (L) striking NNE-SSW, of 10 km maximum in width and 15 km in thickness. Two aftershock spatial clusters were revealed at north (<em>L<sub>1</sub></em>~10 km) and at south (<em>L<sub>2</sub></em>~25 km). However, no time correlation was found between the two clusters and the two strong earthquakes. Fitting the temporal evolution of aftershocks to the Omori-law showed slow aftershock decay. Fault plane solutions produced by moment tensor inversions indicated that the strong earthquakes as well as a plenty of aftershocks (M<sub>w</sub>≥4.0) were associated with dextral strikeslip faulting with some thrust component and preferred fault planes striking about NNE-SSW. Average fault plane parameters obtained for the three largest events are: strike 21(±2)<sup>0</sup>, dip 65.5(±3)<sup>0</sup>, slip 173(±3)<sup>0</sup>. Broadband P-wave teleseismic records were inverted for understanding the rupture histories. It was found that the earthquake of 26.1.2014 had a complex source time function with c. 62 cm maximum slip, source duration of ~12 s and downwards rupture. Most of the slip was concentrated on a 13x9 km fault rupture. The earthquake of 3.2.2014 had a relatively simple source time function related with one big patch of slip with maximum slip c. 45 cm, with 10 s source duration. The rupture was directed upwards which along with the shallow focus (~5 km) and the simple source time function may explain the significantly larger (0.77 g) PGA recorded with the second earthquake with respect to the one recorded (0.56 g) with the first earthquake. Most of the slip was concentrated on a 12x6 km fault rupture. Maximum seismic intensity (<em>I<sub>m</sub></em>) of level VII and VIII to VIII+ was felt in Lixouri town and the nearby villages from the first and the second earthquake, respectively. The rupture histories and the increased building vulnerability after the damage caused by the first shock may account for the larger <em>I<sub>m</sub></em> caused by the second shock. However, the ground failures area of the second earthquake was nearly half of that of the first earthquake, which is consistent with the faster attenuation of ground acceleration away from the meizoseismal area caused by the second earthquake with respect to the first one. From that the 2014 earthquakes ruptured on land western Cephalonia we suggested to revise the CTFZ geometry in the sense that the Lefkada CTFZ segment does not terminates offshore NW Cephalonia but extends towards SSW in western Cephalonia.

The 14 September 1995 (M = 7.3) Copala, Mexico, earthquake: A source study using teleseismic, regional, and local data

1997 ◽  
Vol 87 (4) ◽  
pp. 999-1010
Author(s):  
F. Courboulex ◽  
M. A. Santoyo ◽  
J. F. Pacheco ◽  
S. K. Singh
Keyword(s):  
Time Window ◽  
Time Function ◽  
Source Process ◽  
Source Time Function ◽  
Nonlinear Method ◽  
Local Data ◽  
Plate Interface ◽  
Linear Inversion ◽  
Field Source ◽  
Mexico Earthquake

Abstract We analyze source characteristics of the 14 September 1995, Copala, Mexico, earthquake (M = 7.3) using teleseismic, regional, and local seismograms. In the analysis of the teleseismic and the regional seismic waves, we apply the empirical Green's function (EGF) technique. The recording of an appropriate aftershock is taken as the EGF and is used to deconvolve the mainshock seismogram, thus obtaining an apparent far-field source-time function at each station. The deconvolution has been done using surface waves. For teleseismic data, we apply a spectral deconvolution method that enables us to obtain 37 apparent source-time functions (ASTFs) at 29 stations. In the analysis of the regional broadband seismograms, we use two different aftershocks as EGF, and the deconvolution is performed in the time domain with a nonlinear method, imposing a positivity constraint, and the best azimuth for the directivity vector is obtained through a grid-search approach. We also analyze two near-source accelerograms. The traces are inverted for the slip distribution over the fault plane by applying a linear inversion technique. With the aid of a time-window analysis, we obtain an independent estimation of the source-time function and a more detailed description of the source process. The analysis of the three datasets permits us to deduce the main characteristics of the source process. The rupture initiated at a depth of 16 km and propagated in two directions: updip along the plate interface toward 165° N and toward 70° N. The source duration was between 12 and 14 sec, with the maximum of energy release occurring 8 sec after the initiation of the rupture. The estimated rupture dimension of 35 × 45 km is about one-fourth of the aftershock area. The average dislocation over the fault was 1.4 m (with a maximum dislocation of 4.1 m located 10 km south of the hypocenter), which gives roughly 1 MPa as the average static stress drop.

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