Moment–Area Scaling Relationship Assuming Constant Stress Drop for Crustal Earthquakes

2020 ◽  
Vol 110 (1) ◽  
pp. 241-249
Author(s):  
Kazuhito Hikima ◽  
Akihiro Shimmura
Keyword(s):  
Stress Drop ◽  
Constant Stress ◽  
Event Data ◽  
Scaling Relation ◽  
Seismogenic Layer ◽  
Crustal Earthquakes ◽  
Rupture Area ◽  
Scaling Relationship ◽  
Static Stress Drop ◽  
Good Agreement

ABSTRACT For crustal earthquakes, the scaling relationship between the seismic moment M0 and rupture area S varies with the size of the earthquake, due to the limited thickness of the seismogenic layer. In those M0–S scaling relations, in most cases, the calculated static stress drop is altered with the size of earthquake, although the change depends on the assumed fault model. However, it is not clear whether the dependence of the stress drop on M0 is physically reasonable. In this study, the scaling relation between M0 and S, which assumes a constant stress drop over a wide M0 range, is discussed based on the analytical stress drop formula of a rectangular strike-slip fault. In the proposed relation, M0 is proportional to S3/2 for small and medium faults and to S1 for long faults. In addition, the relation between M0 and S varies in the intermediate range, depending on the aspect ratio. The scaling relation showed good agreement with past event data when the saturated rupture width was set to around 15–20 km and the stress drop was set to about 3 MPa.

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.

Source dimensions and stress drops of small earthquakes near Parkfield, California

1984 ◽  
Vol 74 (1) ◽  
pp. 27-40
Author(s):  
M. E. O'Neill
Keyword(s):  
Stress Drop ◽  
Small Region ◽  
Static Stress ◽  
Depth Range ◽  
Zero Crossing ◽  
Source Dimensions ◽  
Duration Magnitude ◽  
Short Period ◽  
Static Stress Drop ◽  
Stress Drops

Abstract Source dimensions and stress drops of 30 small Parkfield, California, earthquakes with coda duration magnitudes between 1.2 and 3.9 have been estimated from measurements on short-period velocity-transducer seismograms. Times from the initial onset to the first zero crossing, corrected for attenuation and instrument response, have been interpreted in terms of a circular source model in which rupture expands radially outward from a point until it stops abruptly at radius a. For each earthquake, duration magnitude MD gave an estimate of seismic moment MO and MO and a together gave an estimate of static stress drop. All 30 earthquakes are located on a 6-km-long segment of the San Andreas fault at a depth range of about 8 to 13 km. Source radius systemically increases with magnitude from about 70 m for events near MD 1.4 to about 600 m for an event of MD 3.9. Static stress drop ranges from about 2 to 30 bars and is not strongly correlated with magnitude. Static stress drop does appear to be spatially dependent; the earthquakes with stress drops greater than 20 bars are concentrated in a small region close to the hypocenter of the magnitude 512 1966 Parkfield earthquake.

Rotation of the principal stress directions due to earthquake faulting and its seismological implications

1995 ◽  
Vol 85 (5) ◽  
pp. 1513-1517
Author(s):  
Z.-M. Yin ◽  
G. C. Rogers
Keyword(s):  
Shear Stress ◽  
Normal Stress ◽  
Principal Stress ◽  
Stress Drop ◽  
Rotation Angle ◽  
Overburden Pressure ◽  
Rupture Area ◽  
Earthquake Faulting ◽  
Stress Directions ◽  
Before And After

Abstract Earthquake faulting results in stress drop over the rupture area. Because the stress drop is only in the shear stress and there is no or little stress drop in the normal stress on the fault, the principal stress directions must rotate to adapt such a change of the state of stress. Using two constraints, i.e., the normal stress on the fault and the vertical stress (the overburden pressure), which do not change before and after the earthquake, we derive simple expressions for the rotation angle in the σ1 axis. For a dip-slip earthquake, the rotation angle is only a function of the stress-drop ratio (defined as the ratio of the stress drop to the initial shear stress) and the angle between the σ1 axis and the fault plane, but for a strike-slip earthquake the rotation angle is also a function of the stress ratio. Depending on the faulting regimes, the σ1 axis can either rotate toward the direction of fault normal or rotate away from the direction of fault normal. The rotation of the stress field has several important seismological implications. It may play a significant role in the generation of heterogeneous stresses and in the occurrence and distribution of aftershocks. The rotation angle can be used to estimate the stress-drop ratio, which has been a long-lasting topic of debate in seismology.

Contribution of Gear Body to Tooth Deflections—A New Bidimensional Analytical Formula

2004 ◽  
Vol 126 (4) ◽  
pp. 748-752 ◽  
Author(s):  
P. Sainsot and ◽  
P. Velex ◽  
O. Duverger
Keyword(s):  
Finite Element ◽  
Analytical Formula ◽  
Constant Stress ◽  
Finite Element Models ◽  
Gear Dynamics ◽  
Computer Codes ◽  
Stress Variations ◽  
Tooth Pair ◽  
Good Agreement

The magnitude and variation of tooth pair compliance affects tooth loading and gear dynamics significantly. This paper presents an improved fillet/foundation compliance analysis based on the theory of Muskhelishvili applied to circular elastic rings. Assuming linear and constant stress variations at root circle, the above theory makes it possible to derive an analytical formula for gear body-induced tooth deflections which can be directly integrated into gear computer codes. The corresponding results are in very good agreement with those from finite element models and the formula is proved to be superior to Weber’s widely used equation, especially for large gears.

Lessons from a Small Local Earthquake (Mw 3.2) That Produced the Highest Acceleration Ever Recorded in Mexico City

2020 ◽  
Vol 91 (6) ◽  
pp. 3391-3406
Author(s):  
Shri Krishna Singh ◽  
Luis Quintanar-Robles ◽  
Danny Arroyo ◽  
Victor Manuel Cruz-Atienza ◽  
Victor Hugo Espíndola ◽  
...  
Keyword(s):  
Seismic Hazard ◽  
Mexico City ◽  
Stress Drop ◽  
Seismic Waves ◽  
Earthquake Swarm ◽  
Site Amplification ◽  
Function Technique ◽  
Ground Acceleration ◽  
Crustal Earthquakes ◽  
Variable Site

Abstract A reliable estimation of seismic hazard-facing Mexico City from local earthquakes has suffered from poor seismic instrumentation, complex crustal structure, large and variable site amplification, and lack of knowledge of recurrence period of earthquakes on the mapped faults. Owing to recent improvement in local seismic networks, an earthquake swarm activity, which occurred in June–August 2019, was well recorded. The largest event of the sequence, an Mw 3.2 earthquake, caused panic in the city and produced peak ground acceleration (PGA) exceeding 0.3g at the closest station (MHVM) about 1 km away. An analysis of the event shows that it had normal-faulting focal mechanism, consistent with northeast–southwest-oriented mapped faults in the region. It was located at a depth of ∼1  km and had a low stress drop (∼0.1  MPa). We find that the high PGA for this low stress-drop event resulted from high-frequency amplification at MHVM (about factor of ∼6 around 13 Hz), likely due to topographic site effects, superimposed on a pervasive broadband amplification of seismic waves at hill-zone sites in the Valley of Mexico (up to ∼10 in the frequency band of 0.2–10 Hz). Simulation of ground motion for a scenario Mw 5.0 earthquake, using an empirical Green’s function technique, reveals that such an event may give rise to significant seismic intensities in the lake-bed zone of Mexico City. The results emphasize the need to re-evaluate the seismic hazard to Mexico City from local crustal earthquakes in the Valley of Mexico.

Dominant strike-slip faulting and near-constant stress drop of induced earthquakes in the Kiskatinaw area, northeastern British Columbia, Canada

2021 ◽  
Author(s):  
Marco Pascal Roth ◽  
Kilian B Kemna ◽  
Rebecca M Harrington ◽  
Yajing Liu
Keyword(s):  
British Columbia ◽  
Stress Drop ◽  
Cross Correlation ◽  
Strike Slip ◽  
Constant Stress ◽  
Corner Frequency ◽  
Spectral Ratios ◽  
Thrust Faulting ◽  
Independent Events ◽  
Waveform Cross Correlation

<p><span>An increasing number of hydraulic fracturing (HF) operations in­ low-permeable tight shales in the Kiskatinaw area, northeastern British Columbia, have been associated with M3+ earthquakes in the last decade, including a M<sub>L</sub> 4.5 on 11/30/2018 near Dawson Creek. Here, we use a catalog of 8285 events ranging from magnitude ML -0.5 to 4.5 between July 2017 and July 2020 to investigate their source parameters. We identify event families using waveform cross-correlation and event temporal correlation, and estimate the focal mechanism solutions (FMS) of the highest-magnitude event within each family using the probabilistic earthquake source inversion framework </span><span><em>Grond</em></span><span>. We also estimate FMS for events with a magnitude larger than M</span><sub><span>L</span></sub><span> 2.5 that do not belong to a family (independent events). We compile a FMS catalog using the robustly constrained solutions for the largest events, and associate all smaller earthquakes with a cross-correlation coefficient (CCC) > 0.8 with the corresponding FMS. In addition, we estimate seismic moment and static stress drop values using spectral fitting methods on both single spectra and spectral ratios, and investigate their scaling relations.</span></p><p> </p><p><span>In total, we constrain 65 FMS, of which 53 are clustered events, and the remaining 12 are independent events. An additional 4255 events have a CCC > 0.8 with one of the constrained FMS and are listed accordingly in the catalog. Of the total 4320 FMS, 93% are strike-slip events with one nodal plane at low angles to S</span><sub><span>H</span></sub><span>, 3% are dominantly strike-slip with thrust-faulting components, and the remaining 4% have a dominantly thrust-faulting mechanisms perpendicular to S</span><sub><span>H. </span></sub><span> The thrust-style events comprise the relatively larger magnitudes contained in the catalog, and may indicate slip on pre-existing faults. Most strike-slip events are part of an event family with multiple matching waveforms, while most thrust-faulting events are isolated with a low number of matching waveforms. </span></p><p> </p><p><span>We fit the spectral corner frequency of 2360 P-phases and 1981 S-phases using single spectra estimates, and 1031 P-phases and 919 S-phases using the spectral ratios. While results from spectral ratios suggest a roughly constant stress drop of ~1 MPa for all magnitudes, the constant stress drop trend from single spectrum fitting breaks down at magnitudes smaller ~ M</span><sub><span>L</span></sub><span> 2.0, as has commonly been observed for events recorded by surface stations. We do not observe significant dependence of stress-drop values with the faulting style, nor with event depth. </span></p>

Matrix permeability and flow-derived DFN constrain reactivated natural fracture rupture area and stress drop — Marcellus Shale microseismic example

2021 ◽  
Vol 40 (9) ◽  
pp. 667-676
Author(s):  
Clay Kurison ◽  
Huseyin S. Kuleli
Keyword(s):  
Fluid Flow ◽  
Pore Pressure ◽  
Stress Drop ◽  
Marcellus Shale ◽  
Linear Flow ◽  
Matrix Permeability ◽  
Rupture Area ◽  
Microseismic Events ◽  
Shale Reservoirs ◽  
Stress Drops

Microseismic events associated with shale reservoir hydraulic fracturing stimulation (HFS) are interpreted to be reactivations of ubiquitous natural fractures (NFs). Despite adoption of discrete fracture network (DFN) models, accounting for NFs in fluid flow within shale reservoirs has remained a challenge. For an explicit account of NFs, this study introduced the use of seismology-based relations linking seismic moment, moment magnitude, fault rupture area, and stress drop. Microseismic data from HFS monitoring of Marcellus Shale horizontal wells had been used to derive planar hydraulic fracture geometry and source properties. The former was integrated with associated well production data found to exhibit transient linear flow. Analytical solutions led to linear flow parameters (LFPs) and system permeability for scenarios depicting flow through infinite and finite conductivity hydraulic fractures. Published core plug permeability was stress-corrected for in-situ conditions to estimate average matrix permeability. For comparison, the burial and thermal history for the study area was used in 1D Darcy-based modeling of steady and episodic expulsion of petroleum to account for geologic timescale persistence of abnormal pore pressure. Both evaluations resulted in matrix permeability in the same picodarcy (pD) range. Coupled with LFPs, reactivated NF surface area for stochastic DFNs was estimated. Subsequently, the aforementioned seismology-based relations were used for determining average stress drops needed to estimate NF rupture area matching flow-based DFN surface areas. Stress drops, comparable to values for tectonic events, were excluded. One of the determined values matched stress drops for HFS operations in past and recent seismological studies. In addition, calculated changes in pore pressure matched estimates in the aforementioned studies. This study unlocked the full potential of microseismic data beyond extraction of planar geometry attributes and stimulated reservoir volume (SRV). Here, microseismic events were explicitly used in the quantitative account of NFs in fluid flow within shale reservoirs.

Modeling of source rupture characteristics for the Saguenay earthquake of November 1988

1995 ◽  
Vol 85 (2) ◽  
pp. 525-551 ◽  
Author(s):  
R. A. W. Haddon
Keyword(s):  
North America ◽  
Stress Drop ◽  
High Stress ◽  
Strong Motion ◽  
Eastern North America ◽  
Fault Rupture ◽  
Rupture Area ◽  
Past Half Century ◽  
Acceleration Data ◽  
Strong Ground

Abstract The magnitude mb = 6.0 Saguenay earthquake of 25 November 1988 in Quebec, Canada, was one of the largest to have occurred in eastern North America during the past half-century. Recorded high-frequency ground motions exceeded anticipated values for an event of its size by a factor of 10 on both the regional network and strong-motion instruments. Two proposed explanations for the discrepancy are (1) that the source was a rare “high stress drop” event and (2) that it was an asymmetrical “fractional stress drop” rupture (involving only normal effective stresses). In this article, detailed fault-slip models are derived to fit characteristics of strong-motion displacement, velocity, and acceleration data. The results establish that the effective rupture stress was normal (less than 100 bars), that the fault rupture was highly asymmetrical with respect to the point of rupture initiation, and that the average slip time for points within the rupture area (approx. 0.2 sec) was considerably less than that associated with the standard Brune (1970) source spectral model. The rupture area developed in a number of episodes, each widening or lengthening the previously ruptured area, which may explain the short average slip time. The results indicate that the widely used assumption in hazard analyses that earthquake spectra are adequately represented by the standard Brune (1970) complete stress drop model may be seriously unreliable for prediction of strong ground motion in eastern North America.

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