Internal co-seismic displacement and strain changes inside a homogeneous spherical Earth

2021 ◽  
Author(s):  
Jie Dong ◽  
Pengfei Cheng ◽  
Hanjiang Wen ◽  
Wenke Sun
Keyword(s):  
Epicentral Distance ◽  
Near Field ◽  
Strike Slip ◽  
Point Sources ◽  
Earth Model ◽  
Curvature Effect ◽  
Seismic Displacement ◽  
Analytical Foundation ◽  
Deformation Properties ◽  
Spherical Earth

Summary In this study, we devised a new set of analytical foundation solutions to compute the internal co-seismic displacement and strain changes caused by four independent point sources (strike-slip, dip-slip, horizontal tensile, and vertical tensile) inside a homogeneous spherical Earth model. Our model provides constraints on the deformation properties at depth, and reveals that the internal co-seismic deformation is larger than that on the surface. The deformation near the source is convergent with our formulae. For the internal deformation at radial section plane, the patterns of horizontal displacements ${u_\theta },{u_\phi }$ and strain changes ${e_{rr}},{e_{\theta \theta }},{e_{\phi \phi }},{e_{\theta \phi }}$ caused by strike-slip and tensile sources appear symmetric at the equidistance above and below the source. Their amplitudes are not identical but with a small discrepancy actually. Unlike these, the patterns of radial displacements ${u_r}$ for strike-slip and tensile sources exhibit point symmetry with the equidistance from the source. Also, the corresponding amplitudes are slightly different. The displacements ${u_\theta },{u_\phi }$ and strain changes ${e_{rr}},{e_{\theta \theta }},{e_{\phi \phi }},{e_{\theta \phi }}$ caused by dip-slip also appear the same properties as ${u_r}$ of strike-slip source. The magnitudes of the displacements and strain changes depend on the source types. The curvature effect on the near-field surface deformations is small, and it increases with the studied depth. But for the far-field deformation caused by the strike-slip source (ds = 20 km), the curvature effect can be as large as 77 per cent when the epicentral distance approximates to 1778 km.

Anomalously large near-field Rayleight waves excited by the 1992 Landers, California, earthquake

1994 ◽  
Vol 84 (3) ◽  
pp. 751-760
Author(s):  
Tatsuhiko Hara ◽  
Robert J. Geller
Keyword(s):  
Rayleigh Wave ◽  
Rayleigh Waves ◽  
Epicentral Distance ◽  
Moment Tensor ◽  
Near Field ◽  
Strike Slip ◽  
Field Amplitude ◽  
Earth Model ◽  
Symmetric Model ◽  
Spherically Symmetric

Abstract The epicenter of the Landers, California, earthquake (28 June 1992; MW = 7.3) was located near the TERRAscope network of broadband seismic stations. The direct Rayleigh wave arrivals, R1, were clipped, and the first two later arrivals, R2 and R3, were contaminated by the waves from a large aftershock, but, as reported by Kanamori et al. (1992a), the amplitudes of R4 and later great circle Rayleigh wave arrivals (fundamental mode spheroidal free oscillations) are about 10 times larger than predicted by synthetic seismograms for a spherically symmetric earth model. We show that, for the moment tensor of the Landers event (predominantly vertical strike slip), the amplitudes of synthetics at the TERRAscope stations for a laterally heterogeneous, rotating, elliptical model are about 10 times greater than those for a spherically symmetric model. Because the anomaly ratio is sensitive to both the source model and the three-dimensional (3D) earth model, we do not attempt to reproduce the exact anomaly ratios recorded by the various stations. To explain the existence of near-field amplitude anomalies in general, we use the first-order Born approximation to find the perturbation to the synthetic seismogram resulting from lateral heterogeneity, ellipticity, and the earth's rotation. In a coordinate system with the source on the z axis a point-source strike-slip earthquake on a vertical fault plane in a spherically symmetric medium excites Rayleigh waves with azimuthal order ±2 only; these waves have a near-field vertical displacement of zero at the source; the displacement increases with the square of epicentral distance for any given azimuth. Coupling as a result of asphericity allows such a source to excite Rayleigh waves with azimuthal order zero, whose near-field amplitude is independent of epicentral distance, thereby generating large near-field amplitude anomalies. We conduct numerical experiments to study the influence of various parameters on near-field amplitude anomalies.

Stress relaxation in a semi-infinite viscoelastic earth model

1973 ◽  
Vol 63 (6-1) ◽  
pp. 2145-2154
Author(s):  
Martin Rosenman ◽  
Sarva Jit Singh
Keyword(s):  
Free Surface ◽  
Stress Relaxation ◽  
Half Space ◽  
Epicentral Distance ◽  
Strike Slip ◽  
Strike Slip Fault ◽  
Earth Model ◽  
Contour Maps ◽  
Surface Stresses ◽  
Stress Components

Abstract Expressions for quasi-static surface stresses resulting from a finite, rectangular, vertical, strike-slip fault in a Maxwellian viscoelastic half-space are derived. Variation of the stresses with time and epicentral distance is studied. Contour maps are obtained in some representative cases. It is found that all nonvanishing stress components at the free surface die exponentially with time. This is in contrast to the behavior of the displacements and strains which, in general, do not vanish for large times.

Crustal deformation by earthquakes and explosions

1970 ◽  
Vol 60 (1) ◽  
pp. 193-215 ◽  
Author(s):  
Ari Ben-Menahem ◽  
Allon Gillon
Keyword(s):  
Half Space ◽  
Crustal Deformation ◽  
Surface Deformation ◽  
Epicentral Distance ◽  
Single Layer ◽  
Strike Slip ◽  
Earth Model ◽  
Homogeneous Half Space ◽  
Layer 2 ◽  
A New Technique

abstract Static displacements were calculated for an earth model which consists of a single layer of thickness H overlying a homogeneous half space. Localized sources simulating earthquake and explosion foci are placed at depths h=H2andh=32H. The ensuing surface deformation is evaluated as a function of the epicentral distance for a typical continental crust model. A new technique is used for the quadrature of the displacement integrals. By this method one is able to calculate 1000 layer-integrals of the type F m n ( x , t ) = ∫ 0 ∞ y n e − x y J m ( t y ) d y 1 + ( A + B y 2 ) e − 2 y + D e − 4 y , with an accuracy of 0.1 per cent, in less than 2 minutes. It is found that for epicentral distances r > 20H the displacements decay like (r/H)−α where 2 < α < 5. For compressional and strike-slip displacements at all depths and for dip-slip source above the layer, 2 < α < 3. For a dip-slip source located below the layer, 3 < α < 5. Maximal displacements for wr, ur, ux, uy and uz occur at approximately r ≃ 0.8h and decay with source's-depth like h−3/2.

Static deformation of a spherical earth model by internal dislocations

1969 ◽  
Vol 59 (2) ◽  
pp. 813-853
Author(s):  
Ari Ben-Menahem ◽  
Sarva Jit Singh ◽  
Faïza Solomon
Keyword(s):  
Poisson Ratio ◽  
Epicentral Distance ◽  
Source Parameters ◽  
Nodal Line ◽  
Earth Model ◽  
Lower Hemisphere ◽  
Surface Displacements ◽  
Spherical Earth ◽  
Global Deformation ◽  
Deformation Patterns

abstract A localized displacement dislocation is placed inside a homogeneous non-gravitating elastic sphere. The ensuing deformation is obtained in the form of rapidly converging series for arbitrary values of the Poisson ratio and the source parameters. Surface displacements and strains are computed for various sources for an average earth model. The numerical results are mapped on tangential planes and displayed in several forms. It is found that in the range 30° < θ < 120° the elongation strains fall off with the epicentral distance like Δ−α where 114 < α < 6, provided one proceeds along an arc which does not intersect a nodal line. In the lower hemisphere (90° < θ < 180°) relative to the source, seismic events such as the Chilean earthquake of May, 1960, should produce strains of the order of 10−9, which are on the threshold of detectability of modern extensometers, tiltmeters and rotationmeters. The range in which the half-space approximation is valid is determined. It is demonstrated that global deformation patterns of major earthquakes can serve as a useful diagnostic tool for recovering the source's spatial characteristics.

scholarly journals Co-Seismic Ionospheric Disturbance with Alaska Strike-Slip Mw7.9 Earthquake on 23 January 2018 Monitored by GPS

Atmosphere ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 83
Author(s):  
Yongming Zhang ◽  
Xin Liu ◽  
Jinyun Guo ◽  
Kunpeng Shi ◽  
Maosheng Zhou ◽  
...  
Keyword(s):  
Fault Location ◽  
Ionospheric Disturbance ◽  
Near Field ◽  
Singular Spectrum Analysis ◽  
Maximum Amplitude ◽  
Strike Slip ◽  
Ionospheric Disturbances ◽  
Total Electron ◽  
Total Electron Contents ◽  
Alaska Earthquake

The Mw7.9 Alaska earthquake at 09:31:40 UTC on 23 January 2018 occurred as the result of strike slip faulting within the shallow lithosphere of the Pacific plate. Global positioning system (GPS) data were used to calculate the slant total electron contents above the epicenter. The singular spectrum analysis (SSA) method was used to extract detailed ionospheric disturbance information, and to monitor the co-seismic ionospheric disturbances (CIDs) of the Alaska earthquake. The results show that the near-field CIDs were detected 8–12 min after the main shock, and the typical compression-rarefaction wave (N-shaped wave) appeared. The ionospheric disturbances propagate to the southwest at a horizontal velocity of 2.61 km/s within 500 km from the epicenter. The maximum amplitude of CIDs appears about 0.16 TECU (1TECU = 1016 el m−2) near the epicenter, and gradually decreases with the location of sub-ionospheric points (SIPs) far away from the epicenter. The attenuation rate of amplitude slows down as the distance between the SIPs and the epicenter increases. The direction of the CIDs caused by strike-slip faults may be affected by the horizontal direction of fault slip. The propagation characteristics of the ionospheric disturbance in the Alaska earthquake may be related to the complex conditions of focal mechanisms and fault location.

A theoretical study of the radiation from small strikeslip earthquakes at close distances

1983 ◽  
Vol 73 (1) ◽  
pp. 83-96 ◽  
Author(s):  
Michel Campillo ◽  
Michel Bouchon
Keyword(s):  
Ground Motion ◽  
Epicentral Distance ◽  
Homogeneous Medium ◽  
Source Model ◽  
Strike Slip ◽  
Peak Ground Velocity ◽  
Corner Frequency ◽  
Crack Model ◽  
Sharp Change ◽  
S Wave

abstract We present a study of the seismic radiation of a physically realistic source model—the circular crack model of Madariaga—at close distance range and for vertically heterogeneous crustal structures. We use this model to represent the source of small strike-slip earthquakes. We show that the characteristics of the radiated seismic spectra, like the corner frequency, are strongly affected by the presence of the free surface and by crustal layering, and that they can be considerably different from the ones of the homogeneous-medium far-field solution. The vertical and radial displacement spectra are the most strongly affected. We use this source model to calculate the decay of peak ground velocity with epicentral distance and source depth for small strike-slip earthquakes in California. For distances between 10 and 80 km, the peak horizontal velocity decay is of the form r−1.25 for a 4-km hypocentral depth and r−1.65 for deeper sources. The predominance of supercritically reflected arrivals beyond epicentral distances of 70 to 80 km produces a sharp change in the rate of decay of the ground motion. For most of the cases considered, the peak ground velocity increases between 80 and 100 km. We also show that the S-wave velocity in the source layer is the lower limit of phase velocities associated with significant ground motion.

Strain, tilt, and rotation associated with strong ground motion in the vicinity of earthquake faults

1982 ◽  
Vol 72 (5) ◽  
pp. 1717-1738 ◽  
Author(s):  
Michel Bouchon ◽  
Keiiti Aki
Keyword(s):  
Ground Motion ◽  
Rotational Velocity ◽  
Near Field ◽  
Strike Slip ◽  
Phase Velocities ◽  
Crustal Structures ◽  
Time Histories ◽  
San Fernando ◽  
Earthquake Faults ◽  
Strong Ground

abstract In the absence of near-field records of differential ground motion induced by earthquakes, we simulate the time histories of strain, tilt, and rotation in the vicinity of earthquake faults embedded in layered media. We consider the case of both strike-slip and dip-slip fault models and study the effect of different crustal structures. The maximum rotational motion produced by a buried 30-km-long strike-slip fault with slip of 1 m is of the order of 3 × 10−4 rad while the corresponding rotational velocity is about 1.5 × 10−3 rad/sec. A simulation of the San Fernando earthquake yields maximum longitudinal strain and tilt a few kilometers from the fault of the order of 8 × 10−4 and 7 × 10−4 rad. These values being small compared to the amplitude of ground displacement, the results suggest that most of the damage occurring in earthquakes is caused by translation motions. We also show that strain and tilt are closely related to ground velocity and that the phase velocities associated with strong ground motions are controlled by the rupture velocity and the basement rock shearwave velocity.

Multifault complex rupture and afterslip associated with the 2018 Mw 6.4 Hualien earthquake in northeastern Taiwan

2020 ◽  
Vol 224 (1) ◽  
pp. 416-434
Author(s):  
Dezheng Zhao ◽  
Chunyan Qu ◽  
Xinjian Shan ◽  
Roland Bürgmann ◽  
Wenyu Gong ◽  
...  
Keyword(s):  
Main Shock ◽  
Near Field ◽  
Active Faults ◽  
Fault Model ◽  
Body Waves ◽  
Coseismic Deformation ◽  
Coseismic Slip ◽  
Coulomb Stress Changes ◽  
Seismic Displacement ◽  
Stress Changes

SUMMARY We investigate the coseismic and post-seismic deformation due to the 6 February 2018 Mw 6.4 Hualien earthquake to gain improved insights into the fault geometries and complex regional tectonics in this structural transition zone. We generate coseismic deformation fields using ascending and descending Sentinel-1A/B InSAR data and GPS data. Analysis of the aftershocks and InSAR measurements reveal complex multifault rupture during this event. We compare two fault model joint inversions of SAR, GPS and teleseismic body waves data to illuminate the involved seismogenic faults, coseismic slip distributions and rupture processes. Our preferred fault model suggests that both well-known active faults, the dominantly left-lateral Milun and Lingding faults, and previously unrecognized oblique-reverse west-dipping and north-dipping detachment faults, ruptured during this event. The maximum slip of ∼1.6 m occurred on the Milun fault at a depth of ∼2–5 km. We compute post-seismic displacement time series using the persistent scatterer method. The post-seismic range-change fields reveal large surface displacements mainly in the near-field of the Milun fault. Kinematic inversions constrained by cumulative InSAR displacements along two tracks indicate that the afterslip occurred on the Milun and Lingding faults and the west-dipping fault just to the east. The maximum cumulative afterslip of 0.4–0.6 m occurred along the Milun fault within ∼7 months of the main shock. The main shock-induced static Coulomb stress changes may have played an important role in driving the afterslip adjacent to coseismic high-slip zones on the Milun, Lingding and west-dipping faults.

Spatial attenuation of intensities for central U.S. earthquakes

1976 ◽  
Vol 66 (3) ◽  
pp. 743-751
Author(s):  
Indra N. Gupta ◽  
Otto W. Nuttli
Keyword(s):  
United States ◽  
Ground Motion ◽  
Epicentral Distance ◽  
Near Field ◽  
Mississippi Valley ◽  
Average Value ◽  
Anelastic Attenuation ◽  
Central United States ◽  
Using Data ◽  
Spatial Attenuation

abstract Attenuation of ground motion in the central United States has to be determined principally using the Modified Mercalli (MM) intensity observations because of the absence of instrumental strong ground-motion data. Nuttli's previous studies of Mississippi Valley earthquakes indicate that higher-mode surface waves produce the largest ground motion except possibly in the near-field region. Particle velocity rather than acceleration correlates directly with intensity and the coefficient of anelastic attenuation has an average value of 0.10 per degree. Using data from isoseismals of the November 9, 1968, southern Illinois and the December 16, 1811, New Madrid, Missouri earthquakes and assuming a linear relationship between log(A/T) and MM intensity, attenuation is expressed by the equation, valid for I(R) ≧IV (MM), I ( R ) = I 0 + 3.7 − 0.0011 R − 2.7 log ⁡ R ; for R ≧ 20 k m where R is the epicentral distance in kilometers. This relationship shows fairly good agreement with isoseismals of many large earthquakes in the central United States and may therefore be useful in providing realistic estimates of spatial attenuation and hence of design earthquakes for a given site. It can also be sometimes useful in estimating the epicentral intensity of an earthquake whose maximum intensity is not reliably known.

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