Seismic source representations for spall

1991 ◽  
Vol 81 (1) ◽  
pp. 191-201
Author(s):  
Steven M. Day ◽  
Keith L. McLaughlin
Keyword(s):  
Seismic Waves ◽  
Moment Tensor ◽  
Time History ◽  
Seismic Source ◽  
Point Force ◽  
Crack Model ◽  
Secondary Source ◽  
Tension Crack ◽  
Waveform Data ◽  
The Moment

Abstract Spall may be a significant secondary source of seismic waves from underground explosions. The proper representation of spall as a seismic source is important for forward and inverse modeling of explosions for yield estimation and discrimination studies. We present a new derivation of a widely used point force representation for spall, which is based on a horizontal tension crack model. The derivation clarifies the relationship between point force and moment tensor representations of the tension crack. For wavelengths long compared with spall depth, the two representations are equivalent, and the moment tensor time history is proportional to the doubly integrated time history of the point force. Numerical experiments verify that, for regional seismic phases, this equivalence is valid for all frequencies for which the point-source (long wavelength) approximation is valid. Further analysis shows that the moment tensor and point force representations retain their validity for nonplanar spall surfaces, provided that the average dip of the surface is small. The equivalency of the two representations implies that a singular inverse problem will result from attempts to infer simultaneously the spectra of both of these source terms from seismic waveforms. If the spall moment tensor alone is estimated by inversion of waveform data, the inferred numerical values of its components will depend inversely upon the source depth that is assumed in the inversion formalism.

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.

Uncertainty in FPSs from moment-tensor inversion

Geophysics ◽  
2011 ◽  
Vol 76 (6) ◽  
pp. WC65-WC75 ◽  
Author(s):  
Jing Du ◽  
Norm R. Warpinski
Keyword(s):  
Moment Tensor ◽  
Failure Process ◽  
Uncertainty Propagation ◽  
Moment Tensor Inversion ◽  
Hydraulic Fractures ◽  
Mechanism Analysis ◽  
Fault Plane Solutions ◽  
Waveform Data ◽  
Amplitude Data ◽  
The Moment

Although microseismic monitoring of hydraulic fractures has primarily been concerned with the dimensions, complexity, and growth of fractures or fracture systems, there is an ever-increasing desire to extract more information about the hydraulic-fracturing and/or natural fractures from microseismic data. Source mechanism analysis, which is concerned with deducing details of the failure process from the microseismic waveform data, is, therefore, attracting more attention. However, most of the studies focus more on the moment-tensor inversion than on extracting fault-plane solutions (FPSs) from inverted moment tensors. The FPSs can be extracted from the inverted moment-tensor, but there remains a question regarding how errors associated with the inversion of the moment-tensor affect the accuracy of the FPSs. We examine the uncertainties of FPS, given the uncertainties of the amplitude data, by looking into the uncertainty propagation from amplitude data into the moment-tensor and then into the resultant FPS. The uncertainty propagation method will be demonstrated using two synthetic examples.

scholarly journals Seismic Moment Tensor Solutions from GeoNet Data to Provide a Moment Magnitude Scale for New Zealand

2021 ◽  
Author(s):  
◽  
Elizabeth de Joux Robertson
Keyword(s):  
New Zealand ◽  
Seismic Moment ◽  
Moment Tensor ◽  
Velocity Model ◽  
Moment Tensor Inversion ◽  
Moment Magnitude ◽  
Seismic Moment Tensor ◽  
Waveform Data ◽  
Moment Tensors ◽  
The Moment

<p>The aim of this project is to enable accurate earthquake magnitudes (moment magnitude, MW) to be calculated routinely and in near real-time for New Zealand earthquakes. This would be done by inversion of waveform data to obtain seismic moment tensors. Seismic moment tensors also provide information on fault-type. I use a well-established seismic moment tensor inversion method, the Time-Domain [seismic] Moment Tensor Inversion algorithm (TDMT_INVC) and apply it to GeoNet broadband waveform data to generate moment tensor solutions for New Zealand earthquakes. Some modifications to this software were made. A velocity model can now be automatically used to calculate Green's functions without having a pseudolayer boundary at the source depth. Green's functions can be calculated for multiple depths in a single step, and data are detrended and a suitable data window is selected. The seismic moment tensor solution that has either the maximum variance reduction or the maximum double-couple component is automatically selected for each depth. Seismic moment tensors were calculated for 24 New Zealand earthquakes from 2000 to 2005. The Global CMT project has calculated CMT solutions for 22 of these, and the Global CMT project solutions are compared to the solutions obtained in this project to test the accuracy of the solutions obtained using the TDMT_INVC code. The moment magnitude values are close to the Global CMT values for all earthquakes. The focal mechanisms could only be determined for a few of the earthquakes studied. The value of the moment magnitude appears to be less sensitive to the velocity model and earthquake location (epicentre and depth) than the focal mechanism. Distinguishing legitimate seismic signal from background seismic noise is likely to be the biggest problem in routine inversions.</p>

scholarly journals Penentuan Karakteristik Mekanisme Gempa Tahun 2018-2019 Di Nusa Tenggara Menggunakan Metode Inversi Momen Tensor

Kappa Journal ◽  
2021 ◽  
Vol 5 (1) ◽  
pp. 31-39
Author(s):  
Sri Rizki Eka Putri ◽  
◽  
Hiden Hiden ◽  
Suhayat Minardi ◽  
◽  
...  
Keyword(s):  
Moment Tensor ◽  
Inversion Method ◽  
Eurasian Plate ◽  
Waveform Data ◽  
Fault Parameters ◽  
The Indian Ocean ◽  
The Moment ◽  
High Level ◽  
Earthquake Characteristics ◽  
Orientation Parameters

Nusa Tenggara is one of the areas with a high level of seismic activity in Indonesia because this area is located between the Indian Ocean plate, which moves northward and pushes the Eurasian plate. One method that is often used to determine an earthquake's epicentre is the Tensor Moment Inversion method. This study aims to determine the moment tensor magnitude of each earthquake event and determine earthquake characteristics based on the earthquake focus mechanism in Nusa Tenggara from 2018 to 2019. The earthquake with a magnitude of ≥ 5.7 SR and to find out the fault parameters, namely strike, dip, and rake using waveform data. One method that is often used to determine an earthquake's epicentre is the Tensor Moment Inversion method. The results showed that the fault planes formed were reverse faults and oblique faults. It has been calculated the moment tensor for each of the six components, namely Mxx, Myy, Mzz, Mxy, Myz and Mxz. From the results of the focal analysis of the 2018-2019 Nusa Tenggara earthquake mechanism, the values of the fault plane orientation parameters such as strike, dip and rake are obtained. For strikes in Nusa Tenggara on area 1, namely: 73° to 122°, Dip: 20° to 72° and Rake: 53° to 139°. While in field 2 for a strike, it is 232° to 280°, Dip 28° to 75°, Rake: 52° to 102°.

The Meckering earthquake of 14 October 1968: A possible downward propagating rupture

1987 ◽  
Vol 77 (5) ◽  
pp. 1558-1578
Author(s):  
Kristín S. Vogfjörd ◽  
Charles A. Langston
Keyword(s):  
Moment Tensor ◽  
Source Parameters ◽  
Time History ◽  
Vertical Displacement ◽  
Body Waves ◽  
Finite Fault ◽  
Short Period ◽  
Double Couple ◽  
The Moment ◽  
Fault Length

Abstract Average source parameters of the 1968 Meckering, Australia earthquake are obtained by the inversion of body waves. The objectives of the inversion are the elements of the moment tensor and the source-time history. An optimum source depth of 3 km is determined, but because of source complexity the point source assumption fails and the moment tensor obtained at that depth has a large nondouble-couple term, compensated linear vector dipole = 34 per cent. The source parameters of the major double-couple are: strike = 341°; dip = 37°; rake = 61°; and seismic moment = 8.2 ×1025 dyne-cm. The source-time function is of approximately 4 sec duration, with a long rise time and a sharp fall-off. The fault length is constrained on the surface by the observed surface break, and results from vertical displacement modeling suggest a width of approximately 10 km in the middle, assuming a dip of 37°. That restricts the entire faulted area to lie above 6 km depth. Two finite fault models for the earthquake are presented, with rupture initiating at a point (1) near the top of the fault and (2) at the bottom of the fault. Both models produce similar long-period synthetics, but based on the short-period waveforms, model 1 is favored. It is argued that such a rupture process is the most reasonable in this cold shield region.

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

&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;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.&lt;/p&gt;&lt;p&gt;Grond can be used to optimise simultaneously seismic waveforms, amplitude spectra, waveform features, phase picks, static displacements from InSAR and GNSS, and gravitational signals.&lt;/p&gt;&lt;p&gt;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).&lt;/p&gt;

Defining the scalar moment of a seismic source with a general moment tensor

1999 ◽  
Vol 89 (5) ◽  
pp. 1390-1394 ◽  
Author(s):  
David Bowers ◽  
John A. Hudson
Keyword(s):  
Seismic Moment ◽  
Moment Tensor ◽  
Seismic Source ◽  
Second Order ◽  
Seismic Moment Tensor ◽  
Total Moment ◽  
Double Couple ◽  
The Moment ◽  
Deviatoric Part ◽  
Scalar Moment

Abstract We compare several published definitions of the scalar moment M0, a measure of the size of a seismic disturbance derived from the second-order seismic moment tensor M (with eigenvalues m1 ≥ m3 ≥ m2). While arbitrary, a useful definition is in terms of a total moment, MT0 = MI + MD, where MI = |M|, with M = (m1 + m2 + m3)/3, is the isotropic moment, and MD = max(|mj − M|; j = 1, 2, 3), is the deviatoric moment. This definition is consistent with other definitions of M0 if M is a double couple. This definition also gives physically appealing and simple results for the explosion and crack sources. Furthermore, our definitions of MT0, MI and MD are in accord with the parameterization of the moment tensor into a deviatoric part (represented by T which lies in [−1,1]) and a volumetric part (represented by k which lies in [−1, 1]) proposed by Hudson et al. (1989).

scholarly journals Seismic Moment Tensor Solutions from GeoNet Data to Provide a Moment Magnitude Scale for New Zealand

2021 ◽  
Author(s):  
◽  
Elizabeth de Joux Robertson
Keyword(s):  
New Zealand ◽  
Seismic Moment ◽  
Moment Tensor ◽  
Velocity Model ◽  
Moment Tensor Inversion ◽  
Moment Magnitude ◽  
Seismic Moment Tensor ◽  
Waveform Data ◽  
Moment Tensors ◽  
The Moment

<p>The aim of this project is to enable accurate earthquake magnitudes (moment magnitude, MW) to be calculated routinely and in near real-time for New Zealand earthquakes. This would be done by inversion of waveform data to obtain seismic moment tensors. Seismic moment tensors also provide information on fault-type. I use a well-established seismic moment tensor inversion method, the Time-Domain [seismic] Moment Tensor Inversion algorithm (TDMT_INVC) and apply it to GeoNet broadband waveform data to generate moment tensor solutions for New Zealand earthquakes. Some modifications to this software were made. A velocity model can now be automatically used to calculate Green's functions without having a pseudolayer boundary at the source depth. Green's functions can be calculated for multiple depths in a single step, and data are detrended and a suitable data window is selected. The seismic moment tensor solution that has either the maximum variance reduction or the maximum double-couple component is automatically selected for each depth. Seismic moment tensors were calculated for 24 New Zealand earthquakes from 2000 to 2005. The Global CMT project has calculated CMT solutions for 22 of these, and the Global CMT project solutions are compared to the solutions obtained in this project to test the accuracy of the solutions obtained using the TDMT_INVC code. The moment magnitude values are close to the Global CMT values for all earthquakes. The focal mechanisms could only be determined for a few of the earthquakes studied. The value of the moment magnitude appears to be less sensitive to the velocity model and earthquake location (epicentre and depth) than the focal mechanism. Distinguishing legitimate seismic signal from background seismic noise is likely to be the biggest problem in routine inversions.</p>

The Time History Analysis of the Frame Structure with Special-Shaped Columns Considering Torsional Component of the Earthquake

2011 ◽  
Vol 368-373 ◽  
pp. 777-780
Author(s):  
Dong Qiang Xu ◽  
Pin Li
Keyword(s):  
Seismic Wave ◽  
Seismic Waves ◽  
Time History ◽  
Regular Structure ◽  
Structure Design ◽  
Frame Structure ◽  
Irregular Structure ◽  
History Analysis ◽  
Moment Effect ◽  
The Moment

This paper is concerned with the study on internal forces of structure by building model in ANSYS under unidirectional seismic wave, bi-directional seismic waves and two-way and reverse seismic wave. The results revealed that the moment effect of frame structure under bi-directional seismic waves and two-way and reverse seismic wave is bigger around 30% than it under unidirectional seismic wave. And the torque accretion multiple of irregular structure is bigger around 1 than the corresponding regular structure. Therefore, we should take into account the effect of multi-dimensional seismic and the torsional effect of the irregular structure in structure design.

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