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 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 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 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.

Rupture parameters of dynamic source models compatible with NGA-West2 GMPEs

2020 ◽  
Author(s):  
Frantisek Gallovic ◽  
Lubica Valentova
Keyword(s):  
Ground Motions ◽  
Source Parameters ◽  
Strong Motion ◽  
Seismic Hazard Assessment ◽  
Response Spectra ◽  
Maximum Magnitude ◽  
Source Inversion ◽  
Dynamic Rupture ◽  
Heterogeneous Distribution ◽  
Dynamic Source

<p>Dynamic source inversions of individual earthquakes provide constraints on stress and frictional parameters, which are inherent to the studied event. However, general characteristics of both kinematic and dynamic rupture parameters are not well known, especially in terms of their variability. Here we constrain them by creating and analyzing a synthetic event database of dynamic rupture models that generate waveforms compatible with strong ground motions in a statistical sense.</p><p>We employ a framework that is similar to the Bayesian dynamic source inversion by Gallovič et al. (2019). Instead of waveforms of a single event, the data are represented by Ground Motion Prediction Equations (GMPEs), namely NGA-West2  (Boore et al., 2014). The Markov chain Monte Carlo technique produces samples of the dynamic source parameters with heterogeneous distribution on a fault. For all simulations, we assume a vertical 36x20km strike-slip fault, which limits our maximum magnitude to Mw<7. For dynamic rupture calculations, we employ upgraded finite-difference code FD3D_TSN (Premus et al., 2020) with linear slip-weakening friction law. Seismograms are calculated on a regular grid of phantom stations assuming a 1D velocity model using precalculated full wavefield Green's functions. The procedure results in a database with those dynamic rupture models that generate ground motions compatible with the GMPEs (acceleration response spectra in period band 0.5-5s) in terms of both median and variability.</p><p>The events exhibit various magnitudes and degrees of complexity (e.g. one or more asperities). We inspect seismologically determinable parameters, such as duration, moment rate spectrum, stress drop, size of the ruptured area, and energy budget, including their variabilities.  Comparison with empirically derived values and scaling relations suggests that the events are compatible with real earthquakes (Brune, 1970, Kanamori and Brodsky, 2004). Moreover, we investigate the stress and frictional parameters in terms of their scaling, power spectral densities, and possible correlations. The inferred statistical properties of the dynamic source parameters can be used for physics-based strong-motion modeling in seismic hazard assessment.</p>

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.

Proposed methodology for estimating the magnitude at which subduction megathrust ground motions and source dimensions exhibit a break in magnitude scaling: Example for 79 global subduction zones

2020 ◽  
Vol 36 (3) ◽  
pp. 1271-1297
Author(s):  
Kenneth W. Campbell
Keyword(s):  
Ground Motion ◽  
Subduction Zones ◽  
Ground Motions ◽  
Seismic Source ◽  
Scaling Relations ◽  
Megathrust Earthquakes ◽  
Source Dimensions ◽  
Magnitude Scaling ◽  
Aspect Ratios ◽  
Source Scaling

In this article, I propose a method for estimating the magnitude [Formula: see text] at which subduction megathrust earthquakes are expected to exhibit a break in magnitude scaling of both seismic source dimensions and earthquake ground motions. The methodology is demonstrated by applying it to 79 global subduction zones defined in the literature, including Cascadia. Breakpoint magnitude is estimated from seismogenic interface widths, empirical source scaling relations, and aspect ratios of physically unbounded earthquake ruptures and their uncertainties. The concept stems from the well-established observation that source-dimension and ground motion scaling decreases for shallow continental (primarily strike-slip) earthquakes when rupture exceeds the seismogenic width of the fault. Although a scaling break for megathrust earthquakes is difficult to observe empirically, all of the instrumentally recorded historical [Formula: see text] mega-earthquakes have occurred on subduction zones with [Formula: see text] (8.1–8.9), consistent with an observed break in source scaling relations derived from these same events. The breakpoint magnitudes derived in this study can be used to constrain the magnitude at which the scaling of ground motion is expected to decrease in subduction ground motion prediction equations.

Strong ground motion of mine tremors: Some implications for near-source ground motion parameters

1981 ◽  
Vol 71 (1) ◽  
pp. 295-319
Author(s):  
A. McGarr ◽  
R. W. E. Green ◽  
S. M. Spottiswoode
Keyword(s):  
Ground Motion ◽  
Source Parameters ◽  
Seismic Source ◽  
Shear Velocity ◽  
Recording System ◽  
Ground Acceleration ◽  
Hypocentral Distance ◽  
Earthquake Size ◽  
Mine Tremors ◽  
Stress Drops

abstract Ground acceleration was recorded at a depth of about 3 km in the East Rand Proprietary Mines, South Africa, for tremors with −1 ≦ ML ≦ 2.6 in the hypocentral distance range 50 m < R ≦ 1.6 km. The accelerograms typically had predominant frequencies of several hundred Hertz and peak accelerations, a, as high as 12 g. The peak accelerations show a dependence on magnitude, especially when expressed as dynamic shear-stress differences, defined as σ˜ = ρRa, where ρ is density. For the mine tremors, σ˜ varies from 2 to 500 bars and depends on magnitude according to log σ˜ = 1.40 + 0.38 · ML. Accelerograms for 12 events were digitized and then processed to determine velocity and, for seven events with especially good S/N, displacement and seismic source parameters. Peak ground velocities v ranged up to 6 cm/sec and show a well-defined dependence one earthquake size as measured by ML or by seismic moment, Mo. On the basis of regression fits to the mine data, with −0.76 ≦ ML ≦ 1.45, log Rv = 3.95 + 0.57 ML, where Rv is in cm2/sec, and log Rv = −4.68 + 0.49 log Mo. These regression lines agree excellently with the corresponding data for earthquakes of ML up to 6.4 or Mo to 1.4 × 1026 dyne-cm. At a given value of ML or Mo, a, at fixed R, shows considerably greater variation than v and appears to depend on the bandwidth of the recording system. The peak acceleration at small hypocentral distances is broadly consistent with ρRa = 1.14 Δτrofs/β, where Δτ is stress drop, ro is the source radius, β is shear velocity, and fs is the bandwidth of the recording system. The peak velocity data agree well with Rv = 0.57 βΔτro/μ, where μ is the modulus of rigidity; both expressions follow from Brune's model of the seismic source and were compared with data for events in the size range 5 × 1016 ≦ Mo ≦ 1.4 × 1026 dyne-cm. Measurements of the source parameters indicated that, as for earthquakes, the stress drops for the tremors range from 1 to 100 bars and show no consistent dependence on Mo down to Mo = 5 × 1016 dyne-cm.

Sign in / Sign up

Export Citation Format

Share Document