Inversion of seismograms to determine simultaneously the moment tensor components and source time function for a point source buried in a horizontally layered medium

1991 ◽  
Vol 35 (3) ◽  
pp. 166-183 ◽  
Author(s):  
Jan Šílený ◽  
Giuliano F. Panza
Keyword(s):  
Point Source ◽  
Layered Medium ◽  
Moment Tensor ◽  
Time Function ◽  
Source Time Function ◽  
The Moment

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.

Seismic moment and long-period radiation of underground nuclear explosions

1973 ◽  
Vol 63 (3) ◽  
pp. 847-857
Author(s):  
Gerhard Müller
Keyword(s):  
Point Source ◽  
Seismic Moment ◽  
Time Function ◽  
Moment Function ◽  
P Wave ◽  
Underground Explosion ◽  
Source Time Function ◽  
Nuclear Explosions ◽  
Long Period ◽  
The Moment

abstract The moment function of an explosion is introduced, using the equivalence of an explosive point source and three mutually perpendicular linear dipoles. The seismic moment of an explosion is the final value, for large times, of the moment function. Its relation to source parameters is similar to that of the moment of an earthquake: M1 = (λ + 2μ)S1D1 (λ, μ = Lamé's parameters, S1 = surface area of a sphere surrounding the explosion in the elastic zone, D1 = static radial displacement on this sphere). From strain observations of other authors (Romig et al., 1969; Smith et al., 1969), the moment of the underground nuclear explosion BENHAM is estimated to be about 1024 dyne cm. This moment value supports the assumption that the source-time function for the long-period radiation from large nuclear explosions (periods greater than about 10 sec) is essentially a step-function. On the other hand, a quantitative estimate of the long-period P-wave spectrum of the explosions JORUM, HANDLEY and MILROW and a comparison with observed spectra of Molnar (1971) for JORUM and HANDLEY and Wyss et al. (1971) for MILROW support the assumption of an impulsive source-time function. This discrepancy, which is typical of current opinions among seismologists, is not resolved. It is concluded that an explosive point source is possibly not a sufficient model for the long-time radiation and the static displacement field of a nuclear underground explosion whose elastic radius is about equal to its depth and which is detonated in a prestressed medium.

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 Long-period mechanism of the 8 November 1980 Eureka, California, earthquake

1982 ◽  
Vol 72 (2) ◽  
pp. 439-456
Author(s):  
Thorne Lay ◽  
Jeffrey W. Given ◽  
Hiroo Kanamori
Keyword(s):  
Point Source ◽  
Seismic Moment ◽  
Moment Tensor ◽  
Strike Slip ◽  
The Body ◽  
Body Waves ◽  
Long Period ◽  
Amplitude Data ◽  
The Moment ◽  
Scalar Moment

Abstract The seismic moment and source orientation of the 8 November 1980 Eureka, California, earthquake (Ms = 7.2) are determined using long-period surface and body wave data obtained from the SRO, ASRO, and IDA networks. The favorable azimuthal distribution of the recording stations allows a well-constrained mechanism to be determined by a simultaneous moment tensor inversion of the Love and Rayleigh wave observations. The shallow depth of the event precludes determination of the full moment tensor, but constraining Mzx = Mzy = 0 and using a point source at 16-km depth gives a major double couple for period T = 256 sec with scalar moment M0 = 1.1 · 1027 dyne-cm and a left-lateral vertical strike-slip orientation trending N48.2°E. The choice of fault planes is made on the basis of the aftershock distribution. This solution is insensitive to the depth of the point source for depths less than 33 km. Using the moment tensor solution as a starting model, the Rayleigh and Love wave amplitude data alone are inverted in order to fine-tune the solution. This results in a slightly larger scalar moment of 1.28 · 1027 dyne-cm, but insignificant (<5°) changes in strike and dip. The rake is not well enough resolved to indicate significant variation from the pure strike-slip solution. Additional amplitude inversions of the surface waves at periods ranging from 75 to 512 sec yield a moment estimate of 1.3 ± 0.2 · 1027 dyne-cm, and a similar strike-slip fault orientation. The long-period P and SH waves recorded at SRO and ASRO stations are utilized to determine the seismic moment for 15- to 30-sec periods. A deconvolution algorithm developed by Kikuchi and Kanamori (1982) is used to determine the time function for the first 180 sec of the P and SH signals. The SH data are more stable and indicate a complex bilateral rupture with at least four subevents. The dominant first subevent has a moment of 6.4 · 1026 dyne-cm. Summing the moment of this and the next three subevents, all of which occur in the first 80 sec of rupture, yields a moment of 1.3 · 1027 dyne-cm. Thus, when the multiple source character of the body waves is taken into account, the seismic moment for the Eureka event throughout the period range 15 to 500 sec is 1.3 ± 0.2 · 1027 dyne-cm.

A Student’s Guide to and Review of Moment Tensors

1989 ◽  
Vol 60 (2) ◽  
pp. 37-57 ◽  
Author(s):  
M. L. Jost ◽  
R. B. Herrmann
Keyword(s):  
Point Source ◽  
Moment Tensor ◽  
Tensor Decomposition ◽  
Seismic Source ◽  
Order Moment ◽  
Review Of Literature ◽  
Moment Tensors ◽  
Numerical Examples ◽  
Testing Algorithms ◽  
The Moment

Abstract A review of a moment tensor for describing a general seismic point source is presented to show a second order moment tensor can be related to simpler seismic source descriptions such as centers of expansion and double couples. A review of literature is followed by detailed algebraic expansions of the moment tensor into isotropic and deviatoric components. Specific numerical examples are provided in the appendices for use in testing algorithms for moment tensor decomposition.

Inversion of teleseismic body waves for the moment tensor of the 1978 Thessaloniki, Greece, earthquake

1981 ◽  
Vol 71 (5) ◽  
pp. 1423-1444
Author(s):  
Jeffrey S. Barker ◽  
Charles A. Langston
Keyword(s):  
Point Source ◽  
Moment Tensor ◽  
Source Parameters ◽  
Source Model ◽  
Body Waves ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Initial Rupture ◽  
Short Period ◽  
The Moment

abstract Seismograms from WWSSN and Canadian network stations were modeled to determine the source parameters of the 20 June 1978 Thessaloniki, Greece, earthquake (Ms = 6.4). The depth of the initial rupture was constrained to 11 ± 1 km by comparison of the arrival times of surface reflections with synthetic short-period seismograms. A focal sphere plot of first motion polarities provided little constraint on other focal parameters, except to indicate that predominantly normal faulting was involved. A generalized inverse technique utilizing the moment tensor formalism was applied to teleseismic P and SH waves for six increments of depth. The moment tensor obtained indicated a nearly horizontal, N-trending tension axis and a nearly vertical compression axis, and yielded the following double-couple source parameters: strike 280° ± 7°; dip 55° ± 3°; rake −65° ± 5°; seismic moment 5.7 × 1025 dyne-cm; and a skewed triangular source time function with a rise time of about 1 sec and duration of 6 to 8 sec. Due to indications of multiple or finite source effects for this event, and the assumption in the moment tensor formalism of a point source, a low-pass filter was applied to the data and the inversions were repeated. The results were nearly identical with those of the original inversion, suggesting that any individual sources had similar mechanisms, or that the point source model is sufficient for this earthquake.

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.

Observations and modeling of the rupture development based on the analysis of Source Time Functions

2020 ◽  
Author(s):  
Julien Renou ◽  
Martin Vallée ◽  
Hideo Aochi
Keyword(s):  
Dynamic Models ◽  
Large Population ◽  
Time Function ◽  
Development Phase ◽  
Rupture Velocity ◽  
Source Time Function ◽  
Generic Properties ◽  
Dynamic Source ◽  
Source Models ◽  
The Moment

<p>Our knowledge of earthquake source physics, giving rise to events of very different magnitudes, requires observations of a large population of earthquakes. The development of systematic analysis tools for the global seismicity meets these expectations, and allows us to extract the generic properties of earthquakes, which can then be integrated into models of the rupture process. Following this approach, the SCARDEC method is able to retrieve source time functions of events over a large range of magnitude (Mw > 5.7). The source time function (which describes the temporal evolution of the moment rate) is suitable for the analysis of transient rupture properties which provide insights into the generation of earthquakes of various sizes. Our study aims at observing the rupture development of such earthquakes in order to add better constraints on dynamic source models. We first focus on the development of earthquakes through the analysis of the SCARDEC catalog. The phase leading to the peak of the source time function ("development phase'') is extracted to characterize its evolution. From the computation of moment accelerations at prescribed moment rates, we observe that the evolution of the moment rate during the developement phase is independent of the final magnitude. A quantitative analysis of the moment rate increase as a function of time further indicates that this phase does not respect the steady t² self-similar growth. These observations are then compared with dynamic source models. We develop heterogeneous dynamic models which take into consideration rupture physics. Heterogeneous distributions of the friction parameter and the initial stress contribute to generate highly realistic rupture scenarios. Rupture propagation is strongly influenced by these two dynamic parameters which induce a clear preferential direction of propagation together with a local variability of the rupture velocity. Variability of the kinematic parameters also tends to correlate rupture velocity and slip velocity, which is a key feature for the transient behavior of the development phase previously observed. These findings are expected to put further constraints on future realistic dynamic rupture scenarios.</p>

SYNTHESIS OF A LAYERED MEDIUM FROM ITS ACOUSTIC TRANSMISSION RESPONSE

Geophysics ◽  
1968 ◽  
Vol 33 (2) ◽  
pp. 264-269 ◽  
Author(s):  
Jon F. Claerbout
Keyword(s):  
Plane Wave ◽  
Layered Medium ◽  
Time Function ◽  
Wave Incident ◽  
Acoustic Transmission ◽  
Source Time Function ◽  
Plane Wave Incident ◽  
Deep Source ◽  
Impulsive Source

A direct (noniterative) method is presented to determine an acoustic layered medium from the seismogram due to a time‐limited plane wave incident from the lower halfspace. It is shown that one side of the autocorrelation of the seismogram due to an impulsive source at depth is the seismogram due to an impulsive source on the surface. This transforms the problem to the acoustic reflections problem as solved by Kunetz. Both the deep source time function and the layering can be determined from a surface seismogram.

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