Dynamic rupture and seismic radiation in a damage-breakage rheology model

2020 ◽  
Author(s):  
Vladimir Lyakhovsky ◽  
Ittai Kurzon ◽  
Yehuda Ben-Zion
Keyword(s):  
Process Zone ◽  
Source Parameters ◽  
Damage Zone ◽  
Synthetic Seismograms ◽  
Rupture Zone ◽  
Corner Frequency ◽  
Far Field ◽  
Rupture Velocity ◽  
Fine Grid ◽  
Isotropic Source

<p>We present simulations of dynamic ruptures in a continuum damage-breakage rheological model and waves radiated by the ruptures observed in the far field. The model combines aspects of a continuum viscoelastic damage framework for brittle solids with a continuum breakage mechanics for granular flow. The brittle instability is associated with a phase transition between a damaged solid with distributed cracks and a granular medium within the generated rupture zone. The formulation significantly extends the ability to model brittle processes in structures with complex volumetric geometries and evolving elastic properties, compared to the traditional models of pre-existing frictional surface(s) in a solid with fixed properties. A set of numerical simulations examines the sensitivity of dynamic ruptures, seismic source properties and radiated waves to material properties controlling the coupled damage-breakage evolution, the thickness and geometry of the damage zone, and fluidity of the granular material. The simulations are performed in two stages. First, details of the rupture process are simulated using adaptive fine grid model. The results of these simulations include source parameters such as rupture velocity, potency, stress and strain drop, heat generation, and others. In the second stage, the obtained velocity source function is used for simulating radiated seismic waves and synthetic seismograms sampled by stations around the rupture zone and in the far field.</p><p>Detailed comparisons between the simulated source properties and those obtained by analyzing the synthetic seismograms demonstrate the relations between different source processes and inferred seismic parameters (potency, strain drop, directivity, rupture velocity, corner frequency, and others). One main effect shown in these simulations emphasizes the important role of rock damage and granulation process generating dynamic expansion-compaction around the process-zone. This expansion-compaction process leads to isotropic source term, while shear motion that accumulates behind the propagating front produces deviatoric deformation and shear heating behind the rupture front. Changing through our simulations, source geometries, and fault zone properties, we demonstrate that the process-zone dissipation due to the damage-breakage mechanism, and the isotropic source component, significantly affect the radiation pattern, rupture directivity, S/P energy partitioning, seismic potency and moment, and more. The results are significant for understanding better the proper usage and limitations of methods applied within the observational framework of earthquake seismology.</p>

Earthquake source properties from analysis of dynamic ruptures and far-field seismic waves in a damage-breakage model

2020 ◽  
Vol 224 (3) ◽  
pp. 1793-1810
Author(s):  
Ittai Kurzon ◽  
Vladimir Lyakhovsky ◽  
Yehuda Ben-Zion
Keyword(s):  
Seismic Waves ◽  
Source Parameters ◽  
Dominant Frequency ◽  
Earthquake Source ◽  
Corner Frequency ◽  
Far Field ◽  
Rupture Directivity ◽  
Rupture Velocity ◽  
S Waves ◽  
Dominant Frequencies

SUMMARY We present results on earthquake source properties using simulations of dynamic rupture and radiated seismic waves in a continuum damage-breakage rheological model. The source properties are derived by (1) calculation of source parameters directly from the simulated ruptures and (2) observational processing of the far-field radiated waves. The seismic potency, moment, damage-related source term, rupture velocity and effective rigidity are estimated directly from the simulated sources, while the radiation pattern, dominant frequency, directivity, rupture velocity and seismic potency are calculated through analysis of the radiated waves. The potencies calculated directly from the sources are used to validate those estimated by wave analysis. The effective rigidity at the rupture zone during failure is about four times smaller than that of the intact surrounding rocks. Rupture velocity can be estimated by far-field measurements for sources with unidirectional ruptures with prominent rupture directivity. The dominant frequencies for P and S waves $f_d^S/f_d^P$ reflect clearly the rupture duration and have a ratio in the range 0.87–1.12. Seismic potencies obtained through processing the P or S waves have an overall ±15 per cent difference from the source reference values. The calculated values of the coefficient ${\rm{\kappa }}$, relating rupture length to corner or dominant frequency, have strong dependency on the source geometry. Using a strain-rate dependent ${\rm{\kappa }}$, we obtain much weaker dependencies of strain-drop on the dominant frequencies, $\Delta {\rm{\varepsilon }} \propto {( {{f_d}} )^{3/4}}$, than the classical cube-dependency between stress drop and corner frequency, and corresponding weak dependency of average slip on dominant frequency, ${\rm{\bar{D}}} \propto {( {{f_d}} )^{1/2}}$. The obtained analysis procedure and relations can be used to reduce the uncertainty of source properties derived from far-field seismic waves.

A dynamic model for far-field acceleration

1982 ◽  
Vol 72 (4) ◽  
pp. 1049-1068
Author(s):  
John Boatwright
Keyword(s):  
Stress Drop ◽  
High Frequency ◽  
Dynamic Stress ◽  
The Body ◽  
Body Waves ◽  
Far Field ◽  
Rupture Velocity ◽  
Frequency Level ◽  
Average Change ◽  
Dynamic Stress Drop

abstract A model for the far-field acceleration radiated by an incoherent rupture is constructed by combining Madariaga's (1977) theory for the high-frequency radiation from crack models of faulting with a simple statistical source model. By extending Madariaga's results to acceleration pulses with finite durations, the peak acceleration of a pulse radiated by a single stop or start of a crack tip is shown to depend on the dynamic stress drop of the subevent, the total change in rupture velocity, and the ratio of the subevent radius to the acceleration pulse width. An incoherent rupture is approximated by a sample from a self-similar distribution of coherent subevents. Assuming the subevents fit together without overlapping, the high-frequency level of the acceleration spectra depends linearly on the rms dynamic stress drop, the average change in rupture velocity, and the square root of the overall rupture area. The high-frequency level is independent, to first order, of the rupture complexity. Following Hanks (1979), simple approximations are derived for the relation between the rms dynamic stress drop and the rms acceleration, averaged over the pulse duration. This relation necessarily depends on the shape of the body-wave spectra. The body waves radiated by 10 small earthquakes near Monticello Dam, South Carolina, are analyzed to test these results. The average change of rupture velocity of Δv = 0.8β associated with the radiation of the acceleration pulses is estimated by comparing the rms acceleration contained in the P waves to that in the S waves. The rms dynamic stress drops of the 10 events, estimated from the rms accelerations, range from 0.4 to 1.9 bars and are strongly correlated with estimates of the apparent stress.

10 July 1894 Istanbul Earthquake: Comparing Damages and Ground Motion Simulations

2021 ◽  
Author(s):  
Nesrin Yenihayat ◽  
Eser Çaktı ◽  
Karin Şeşetyan
Keyword(s):  
Ground Motion ◽  
Fault Simulation ◽  
Source Parameters ◽  
Historical Earthquakes ◽  
Corner Frequency ◽  
Simulation Approach ◽  
Ground Motion Simulations ◽  
Finite Fault ◽  
Intensity Map ◽  
Observed Damage

<p>One of the major earthquakes that resulted in intense damages in Istanbul and its neighborhoods took place on 10 July 1894. The 1894 earthquake resulted in 474 losses of life and 482 injuries. Around 21,000 dwellings were damaged, which is a number that corresponds to 1/7 of the total dwellings of the city at that time. Without any doubt, the exact loss of life was higher. Because of the censorship, the exact loss numbers remained unknown. There is still no consensus about its magnitude, epicentral location, and rupture of length. Even though the hardness of studying with historical records due to their uncertainties and discrepancies, researchers should enlighten the source parameters of the historical earthquakes to minimize the effect of future disasters especially for the cities located close to the most active fault lines as Istanbul. The main target of this study is to enlighten possible source properties of the 1894 earthquake with the help of observed damage distribution and stochastic ground motion simulations. In this paper, stochastic based ground motion scenarios will be performed for the 10 July 1894 Istanbul earthquake, using a finite fault simulation approach with a dynamic corner frequency and the results will be compared with our intensity map obtained from observed damage distributions. To do this, in the first step, obtained damage information from various sources has been presented, evaluated, and interpreted. Secondly, we prepared an intensity map associated with the 1894 earthquake based on macro-seismic information, and damage analysis and classification. For generating ground motions with a stochastic finite fault simulation approach, the EXSIM 2012 software has been used. Using EXSIM, several scenarios are modeled with different source, path, and site parameters. Initial source properties have been obtained from findings of our previous study on the simulation of the 26 September 2019 Silivri (Istanbul) earthquake with Mw 5.8. With the comparison of spatial distributions of the ground motion intensity parameters to the obtained damage and intensity maps, we estimate the optimum location and source parameters of the 1894 Earthquake.</p>

A Source Physics Interpretation of Nonself-Similar Double-Corner-Frequency Source Spectral Model JA19_2S

2022 ◽  
Author(s):  
Chen Ji ◽  
Ralph J. Archuleta
Keyword(s):  
Stress Drop ◽  
Wave Speed ◽  
Dynamic Stress ◽  
Corner Frequency ◽  
Rupture Velocity ◽  
Scaling Relation ◽  
Shear Wave Speed ◽  
Dynamic Stress Drop ◽  
Static Stress Drop ◽  
Frequency Source

Abstract We investigate the relation between the kinematic double-corner-frequency source spectral model JA19_2S (Ji and Archuleta, 2020) and static fault geometry scaling relations proposed by Leonard (2010). We find that the nonself-similar low-corner-frequency scaling relation of JA19_2S model can be explained using the fault length scaling relation of Leonard’s model combined with an average rupture velocity ∼70% of shear-wave speed for earthquakes 5.3 < M< 6.9. Earthquakes consistent with both models have magnitude-independent average static stress drop and average dynamic stress drop around 3 MPa. Their scaled energy e˜ is not a constant. The decrease of e˜ with magnitude can be fully explained by the magnitude dependence of the fault aspect ratio. The high-frequency source radiation is generally controlled by seismic moment, static stress drop, and dynamic stress drop but is further modulated by the fault aspect ratio and the relative location of the hypocenter. Based on these two models, the commonly quoted average rupture velocity of 70%–80% of shear-wave speed implies predominantly unilateral rupture.

scholarly journals Characteristics of local earthquake seismograms of varying dislocation sources in a stratified upper crust and modeling for P and S velocity structure: comparison with observations in the Koyna-Warna region, India

2016 ◽  
Vol 58 (6) ◽  
Author(s):  
V. G. Krishna
Keyword(s):  
Velocity Structure ◽  
Source Parameters ◽  
Velocity Model ◽  
Strike Slip ◽  
Synthetic Seismograms ◽  
Structure Comparison ◽  
Earthquake Sources ◽  
Crustal Velocity ◽  
Source Mechanisms ◽  
Local Earthquake

<p>Vertical component record sections of local earthquake seismograms from a state-of-the-art Koyna-Warna digital seismograph network are assembled in the reduced time versus epicentral distance frame, similar to those obtained in seismic refraction profiling. The record sections obtained for an average source depth display the processed seismograms from nearly equal source depths with similar source mechanisms and recorded in a narrow azimuth range, illuminating the upper crustal P and S velocity structure in the region. Further, the seismogram characteristics of the local earthquake sources are found to vary significantly for different source mechanisms and the amplitude variations exceed those due to velocity model stratification. In the present study a large number of reflectivity synthetic seismograms are obtained in near offset ranges for a stratified upper crustal model having sharp discontinuities with 7%-10% velocity contrasts. The synthetics are obtained for different source regimes (e.g., strike-slip, normal, reverse) and different sets of source parameters (strike, dip, and rake) within each regime. Seismogram sections with dominantly strike-slip mechanism are found to be clearly favorable in revealing the velocity stratification for both P and S waves. In contrast the seismogram sections for earthquakes of other source mechanisms seem to display the upper crustal P phases poorly with low amplitudes even in presence of sharp discontinuities of high velocity contrasts. The observed seismogram sections illustrated here for the earthquake sources with strike-slip and normal mechanisms from the Koyna-Warna seismic region substantiate these findings. Travel times and reflectivity synthetic seismograms are used for 1-D modeling of the observed virtual source local earthquake seismogram sections and inferring the upper crustal velocity structure in the Koyna-Warna region. Significantly, the inferred upper crustal velocity model in the region reproduces the synthetic seismograms comparable to the observed sections for earthquake sources with differing mechanisms in the Koyna and Warna regions.</p>

Far-field tsunami data assimilation for the 2015 Illapel earthquake

2019 ◽  
Vol 219 (1) ◽  
pp. 514-521 ◽  
Author(s):  
Y Wang ◽  
K Satake ◽  
R Cienfuegos ◽  
M Quiroz ◽  
P Navarrete
Keyword(s):  
Data Assimilation ◽  
Near Field ◽  
Source Parameters ◽  
Deep Ocean ◽  
Seismic Source ◽  
Far Field ◽  
Complementary Method ◽  
East Pacific ◽  
2015 Illapel Earthquake ◽  
Illapel Earthquake

SUMMARY The 2015 Illapel earthquake (Mw 8.3) occurred off central Chile on September 16, and generated a tsunami that propagated across the Pacific Ocean. The tsunami was recorded on tide gauges and Deep-ocean Assessment and Reporting of Tsunami (DART) tsunameters in east Pacific. Near-field and far-field tsunami forecasts were issued based on the estimation of seismic source parameters. In this study, we retroactively evaluate the potentiality of forecasting this tsunami in the far field based solely on tsunami data assimilation from DART tsunameters. Since there are limited number of DART buoys, virtual stations are assumed by interpolation to construct a more complete tsunami wavefront for data assimilation. The comparison between forecasted and observed tsunami waveforms suggests that our method accurately forecasts the tsunami amplitudes and arrival time in the east Pacific. This approach could be a complementary method of current tsunami warning systems based on seismic observations.

Improved approach for stress drop estimation and its application to an induced earthquake sequence in Oklahoma

2020 ◽  
Vol 223 (1) ◽  
pp. 233-253
Author(s):  
X Chen ◽  
R E Abercrombie
Keyword(s):  
Stress Drop ◽  
Source Parameters ◽  
High Stress ◽  
Temporal Variations ◽  
Earthquake Source ◽  
Average Stress ◽  
Corner Frequency ◽  
Resolution Limit ◽  
Spectral Fitting ◽  
Spatio Temporal

SUMMARY We calculate source parameters for fluid-injection induced earthquakes near Guthrie, Oklahoma, guided by synthetic tests to quantify uncertainties. The average stress drop during an earthquake is a parameter fundamental to ground motion prediction and earthquake source physics, but it has proved hard to measure accurately. This has limited our understanding of earthquake rupture, as well as the spatio-temporal variations of fault strength. We use synthetic tests based on a joint spectral-fitting method to define the resolution limit of the corner frequency as a function of the maximum frequency of usable signal, for both individual spectra and the average from multiple stations. Synthetic tests based on stacking analysis find that an improved stacking approach can recover the true input stress drop if the corner frequencies are within the resolution limit defined by joint spectral-fitting. We apply the improved approach to the Guthrie sequence, using different wave types and signal-to-noise criteria to understand the stability of the calculated stress drop values. The results suggest no systematic scaling relationship of stress drop for M ≤ 3.1 earthquakes, but larger events (M ≥ 3.5) tend to have higher average stress drops. Some robust spatio-temporal variations can be linked to the triggering processes and indicate possible stress heterogeneity within the fault zone. Tight clustering of low stress drop events at the beginning stage of the sequence suggests that pore pressure influences earthquake source processes. Events at shallow depth have lower stress drop compared to deeper events. The largest earthquake occurred within a cluster of high stress drop events, likely rupturing a strong asperity.

On the Energy of Dynamic Fractures

2012 ◽  
Vol 13 (2) ◽  
pp. 117-123
Author(s):  
Kaiwen Xia ◽  
Cangli Liu ◽  
Patrick Kanopoulos
Keyword(s):  
Fracture Energy ◽  
Dynamic Fracture ◽  
Material Parameter ◽  
Process Zone ◽  
Physical Reality ◽  
Impulsive Loading ◽  
Far Field ◽  
Hyperelastic Materials ◽  
Planar Impact ◽  
Dynamic Fractures

Abstract The validity of the constant propagation fracture energy postulation for dynamic fracture is discussed. As shown from existing direct and indirect experimental results, this assumption may not represent the physical reality. For spontaneous fractures, the fracture energy was shown to increase linearly with the crack length, and for dynamic fractures driven by known amplitude impulsive loading (generated by planar impact), the fracture energy was not a constant either. Despite of its phenomenogical origin, the Broberg's theory developed for self-similar crack growth works well for both spontaneous fractures and dynamic fractures produced by well defined dynamic loading. In this theory, the fracture energy is not a constant. Furthermore, with given far-field loading or equivalent far-field loading, the crack speed is uniquely determined by a strength-like material parameter. This parameter is related to the cohesive strength as proposed by H. J. Gao for hyperelastic materials in the crack-tip process zone. It is proposed in this work that the strength-like parameter (or equivalently the constant fracture speed) is a better material parameter to describe the dynamic fracture propagation process for most dynamic fractures.

The characteristic of source spectra and stress drop of earthquakes in the Bucaramanga nest

2020 ◽  
Author(s):  
Wenzheng Gong ◽  
Xiaofei Chen
Keyword(s):  
Focal Mechanism ◽  
Stress Drop ◽  
Source Parameters ◽  
Time Function ◽  
Corner Frequency ◽  
Ratio Method ◽  
Source Time Function ◽  
Spectra Analysis ◽  
Source Spectra ◽  
Very High

&lt;p&gt;Spectra analysis is helpful to understand earthquake rupture processes and estimate source parameters like stress drop. Obtaining real source spectra and source time function isn&amp;#8217;t easy, because the station recordings contain path effect and we usually can&amp;#8217;t get precise path information. Empirical Green&amp;#8217;s function (EGF) method is a popular way to cancel out the path effect, main two of which are the stacking spectra method (Prieto et al, 2006) and the spectral ratio method (Viegas et al, 2010; Imanishi et al, 2006). In our study, we apply the latter with multitaper spectral analysis method (Prieto et al, 2009) to calculate&amp;#160;relative source spectra and relative source time function. Target event and EGFs must have similar focal mechanism and be collocated, so we combine correlation coefficient of wave at all stations and focal mechanism similarity to select proper EGFs.&lt;/p&gt;&lt;p&gt;The Bucaramanga nest has&amp;#160;very high seismicity, so it&amp;#8217;s suitable to calculate&amp;#160;source spectra by using EGF method. We calculate&amp;#160;the source spectra and source time function of about 1540 earthquakes&amp;#160;(3-5.7ml, 135-160km depth) at Bucaramanga nest in Colombia. Simultaneously we also estimate corner frequency by fitting spectral source model (Brune, 1970; Boatwright, 1980) and stress drop using simple model (Eshelby, 1957) of earthquakes with multiple station recordings or EGFs. We obtain about 30000 events data with 12 stations&amp;#160;from National Seismological Network of Colombia (RSNC).&lt;/p&gt;&lt;p&gt;The result show that the source spectra of most earthquakes fitted well by omega-square model are smooth, and the source spectra of some have obvious &amp;#8216;holes&amp;#8217; near corner frequency, and the source time function of a few earthquakes appear two separate peeks. The first kind of earthquakes are style of self-arresting ruptures (Xu et al. 2015), which can be autonomously arrested by itself without any outside interference. Abercrombie (2014) and Wen et al. (2018) both researched the second kind of earthquakes and Wen think that this kind of earthquakes are style of the runaway ruptures including subshear and supershear&amp;#160;ruptures. The last kind of earthquakes maybe be caused by simultaneous slip on two close rupture zone. Stress drop appear to slightly increase with depth and are very high&amp;#160;(assuming rupture velocity/s wave velocity is 0.9). We also investigate the high-frequency falloff n, usually 2, of Brune model and Boatwright model by fitting all spectra, and find that the best value of n for Boatwright model is 2 and for Brune model is 3.5.&lt;/p&gt;

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