scholarly journals Fully probabilistic seismic source inversion – Part 2: Modelling errors and station covariances

2016 ◽  
Author(s):  
Simon C. Stähler ◽  
Karin Sigloch
Keyword(s):  
Bayesian Inference ◽  
Cross Correlation ◽  
Likelihood Function ◽  
Body Wave ◽  
Source Parameters ◽  
Seismic Source ◽  
Noise Distribution ◽  
Source Inversion ◽  
Earthquake Source Parameters ◽  
Waveform Cross Correlation

Abstract. Seismic source inversion, a central task in seismology, is concerned with the estimation of earthquake source parameters and their uncertainties. Estimating uncertainties is particularly challenging because source inversion is a non-linear problem. In a companion paper, Stähler & Sigloch (2014) developed a method of fully Bayesian inference for source parameters, based on measurements of waveform cross-correlation between broadband, teleseismic body-wave observations and their modeled counterparts. This approach yields not only depth and moment tensor estimates but also source time functions. A prerequisite for Bayesian inference is the proper characterization of the noise distribution afflicting the measurements, a problem we address here. We show that for realistic broadband body-wave seismograms, the systematic error due to an incomplete physical model affects waveform misfits more strongly than random, ambient background noise. In this situation, the waveform cross-correlation coefficient CC or rather its decorrelation D = 1 − CC, performs more robustly as a misfit criterion than LP-norms, more commonly used measures of misfit based on distances between individual time samples. From a set of over 900 user-supervised, deterministic source solutions treated as a quality-controlled reference, we derive the noise distribution on signal decorrelation D = 1 − CC of the broadband seismogram fits. The noise on D is found to approximately follow a log-normal distribution, a fortunate fact that readily accommodates the formulation of a likelihood function for D for our multivariate problem. The first and second moments of this multivariate distribution are shown to depend mostly on the signal-to-noise ratio of the CC measurements and on the back-azimuthal distances of seismic stations. By identifying and quantifying its likelihood function, we make D and thus waveform cross-correlation measurements usable for fully probabilistic sampling strategies, in source inversion and related applications such as seismic tomography.

scholarly journals Fully probabilistic seismic source inversion – Part 2: Modelling errors and station covariances

Solid Earth ◽  
2016 ◽  
Vol 7 (6) ◽  
pp. 1521-1536 ◽  
Author(s):  
Simon C. Stähler ◽  
Karin Sigloch
Keyword(s):  
Bayesian Inference ◽  
Cross Correlation ◽  
Likelihood Function ◽  
Body Wave ◽  
Source Parameters ◽  
Seismic Source ◽  
Earthquake Source ◽  
Source Inversion ◽  
Earthquake Source Parameters ◽  
Waveform Cross Correlation

Abstract. Seismic source inversion, a central task in seismology, is concerned with the estimation of earthquake source parameters and their uncertainties. Estimating uncertainties is particularly challenging because source inversion is a non-linear problem. In a companion paper, Stähler and Sigloch (2014) developed a method of fully Bayesian inference for source parameters, based on measurements of waveform cross-correlation between broadband, teleseismic body-wave observations and their modelled counterparts. This approach yields not only depth and moment tensor estimates but also source time functions. A prerequisite for Bayesian inference is the proper characterisation of the noise afflicting the measurements, a problem we address here. We show that, for realistic broadband body-wave seismograms, the systematic error due to an incomplete physical model affects waveform misfits more strongly than random, ambient background noise. In this situation, the waveform cross-correlation coefficient CC, or rather its decorrelation D = 1 − CC, performs more robustly as a misfit criterion than ℓp norms, more commonly used as sample-by-sample measures of misfit based on distances between individual time samples. From a set of over 900 user-supervised, deterministic earthquake source solutions treated as a quality-controlled reference, we derive the noise distribution on signal decorrelation D = 1 − CC of the broadband seismogram fits between observed and modelled waveforms. The noise on D is found to approximately follow a log-normal distribution, a fortunate fact that readily accommodates the formulation of an empirical likelihood function for D for our multivariate problem. The first and second moments of this multivariate distribution are shown to depend mostly on the signal-to-noise ratio (SNR) of the CC measurements and on the back-azimuthal distances of seismic stations. By identifying and quantifying this likelihood function, we make D and thus waveform cross-correlation measurements usable for fully probabilistic sampling strategies, in source inversion and related applications such as seismic tomography.

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.

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.

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.

Synthetic Source Inversion Tests with the Damped Isochrone Inversion Approach

2020 ◽  
pp. 2150002
Author(s):  
Wahyu Srigutomo ◽  
I G. P. F. S. Djaja ◽  
Nanang T. Puspito
Keyword(s):  
Focal Mechanism ◽  
Projection Method ◽  
Source Parameters ◽  
Least Square ◽  
Slip Distribution ◽  
Damping Factor ◽  
Test Model ◽  
Back Projection ◽  
Source Inversion ◽  
Earthquake Source Parameters

Earthquake source parameters such as slip distribution and slip rate are useful information for understanding the physical processes behind earthquakes. The isochrone back-projection method, or isochrone-BPM, is one of the methods used to obtain slip distribution in the fault plane by incorporating the isochrone concept with back-projection method. Isochrone-BPM has advantages in its ease of implementation. However, it appears that the resulted slip distribution images always contain artifacts causing the images to be smeared. The emergence of these artifacts may lead to misinterpretation of the slip distribution, thus becoming a major weakness of isochrone-BPM. In this work, an alternative approach is proposed by utilizing least-square inversion scheme with the addition of damping factor as an alternative to the isochrone-BPM, which is then referred to as damped isochrone inversion since it still utilizes the core formulation of isochrone-BPM. The application of isochrone-BPM slip inversion to synthetic data generated from a test model shows that the quality of the resulted image will highly depend on the set of receiving stations used. In addition, the isochrone-BPM image will also depend on the focal mechanism of the earthquake, which is indicated by the difference in patterns on different mechanisms. Contrary to isochrone-BPM, the damped isochrone inversion produces slip distribution images that do not depend on the set of receiving stations used and do exhibit dependence on the focal mechanism. These results may suggest that as an alternative to the isochrone-BPM, the damped isochrone inversion offers better performance in recovering the slip distribution images.

scholarly journals The use of body-wave spectra in the determination of seismic-source parameters

1972 ◽  
Vol 62 (2) ◽  
pp. 561-589 ◽  
Author(s):  
Thomas C. Hanks ◽  
Max Wyss
Keyword(s):  
Body Wave ◽  
Source Parameters ◽  
Seismic Source ◽  
Source Model ◽  
Radiated Energy ◽  
Vertical Fault ◽  
Seismic Source Model ◽  
Minimum Estimate ◽  
Stress Drops

abstract Teleseismic determinations of body-wave (P, S) spectra, interpreted in terms of the Brune (1970) seismic-source model, are used to estimate the parameters seismic moment (Mto) and source dimension (r) for three large, shallow, strike-slip earthquakes occurring on nearly vertical fault planes and for which the same parameters can be determined from field (F) data. These earthquakes are (1) the Borrego Mountain, California, earthquake (April 9, 1968) for which [Mo(P) = 10, Mo(S) = 6.6, and Mo(F) = 3.6] × 1025 dyne-cm and [r(p) = 14, r(S) = 23, and L/2(F) = 17] km; (2) the Mudurnu Valley, Turkey, earthquake (July 22, 1967) for which [-Mo(P) = 9.1, Mo(S) = 8.5, and Mo(F) = 7.4] × 1026 dyne-cm, and [r(P) = 39, r(S) = 48, and L/2(F) = 40] km; and (3) the Dasht-e-Bayāz, Iran, earthquake (August 31, 1968) for which [Mo(P) = 4.8, Mo(S) = 8.6, and Mo(F) = 18] × 1026 dyne-cm, and [r(P) = S1, r(S) = 48, and L/2(F) = 40] km. The Brune (1970) model is well-calibrated with respect to the determination of these parameters for the earthquakes considered. A minimum estimate for the radiated energy can be expressed in terms of Mo and r; this estimate is low by a factor of 10 with respect to the estimate obtained from energy-magnitude relations for these three earthquakes. The stress drops of these events are of the order of 10 bars.

scholarly journals Teleseismic body wave inversion

2018 ◽  
Vol 40 (3) ◽  
pp. 1177
Author(s):  
A. Moshou ◽  
P. Papadimitriou ◽  
K. Makropoulos
Keyword(s):  
Body Wave ◽  
Moment Tensor ◽  
Source Parameters ◽  
Singular Value Decomposition Method ◽  
Wave Inversion ◽  
Generalized Inversion ◽  
Earthquake Source Parameters ◽  
Generalized Inversion Technique ◽  
Double Couple ◽  
Value Decomposition

Body wave inversion methodology is developed to determine the earthquake source parameters in teleseismic distances. The generalized inversion technique, based on the singular value decomposition method, is applied to determine the deviatone moment tensor which is decomposed in two parts. The first one is related to the pure Double Couple (DC) and the second one to the compensated linear vector dipoles (CLVD). The best solution of the overdetermined problem is obtained by minimizing the misfit between observed and synthetic seismograms. The proposed methodology is applied for the four strongest earthquakes that occurred recently in Greece (2001-2006)

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

Solid Earth ◽  
2016 ◽  
Vol 7 (5) ◽  
pp. 1467-1477 ◽  
Author(s):  
Michael Reinwald ◽  
Moritz Bernauer ◽  
Heiner Igel ◽  
Stefanie Donner
Keyword(s):  
Inverse Problem ◽  
Numerical Study ◽  
Ground Motions ◽  
Source Parameters ◽  
Normal Fault ◽  
Seismic Source ◽  
Vertical Gradient ◽  
Vertical Displacement ◽  
Source Inversion ◽  
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 of how this type of ground motion observation can be used to solve the seismic source inverse problem. In this paper, we focus on the question of 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 three-component translational sensors (classic seismometers) with those obtained with 22 six-component sensors (with additional three-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 to 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 inversions with a random distribution of receivers. Since our previous results are achieved with a regular spacing of the receivers, we try to answer the question of whether the results are dependent on the spatial distribution of the receivers. The results show that with the six-component subnetworks, kinematic source inversions for source properties (such as rupture velocity, rise time, and slip amplitudes) are not only equally successful (even that would be beneficial because of the substantially reduced logistics installing half the sensors) but also statistically inversions for some source properties are almost always improved. 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.

scholarly journals Assessment of glacial-earthquake source parameters

2017 ◽  
Vol 63 (241) ◽  
pp. 867-876 ◽  
Author(s):  
STEPHEN A. VEITCH ◽  
MEREDITH NETTLES
Keyword(s):  
Source Parameters ◽  
Seismic Source ◽  
Earthquake Source ◽  
Source Modeling ◽  
Front Position ◽  
Earthquake Source Parameters ◽  
Slow Earthquakes ◽  
Earthquake Force ◽  
Single Force ◽  
Remote Sensing Techniques

ABSTRACTGlacial earthquakes are slow earthquakes of magnitude M~5 associated with major calving events at near-grounded marine-terminating glaciers. These globally detectable earthquakes provide information on the grounding state of outlet glaciers and the timing of large calving events. Seismic source modeling of glacial earthquakes provides information on the size and orientation of forces associated with calving events. We compare force orientations estimated using a centroid-single-force technique with the calving-front orientations of the source glaciers at or near the time of earthquake occurrence. We consider earthquakes recorded at four glaciers in Greenland – Kangerdlugssuaq Glacier, Helheim Glacier, Kong Oscar Glacier, and Jakobshavn Isbræ – between 1999 and 2010. We find that the estimated earthquake force orientations accurately represent the orientation of the calving front at the time of the earthquake, and that seismogenic calving events are produced by a preferred section of the calving front, which may change with time. We also find that estimated earthquake locations vary in a manner consistent with changes in calving-front position, though with large scatter. We conclude that changes in glacial-earthquake source parameters reflect true changes in the geometry of the source glaciers, providing a means for identifying changes in glacier geometry and dynamics that complements traditional remote-sensing techniques.

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