Earthquake modeling in a homogeneous half-space

1978 ◽  
Vol 68 (2) ◽  
pp. 301-316 ◽  
Author(s):  
Stephen H. Hartzell ◽  
Gerald A. Frazier ◽  
James N. Brune
Keyword(s):  
Half Space ◽  
Transverse Component ◽  
Summation Method ◽  
Dynamic Rupture ◽  
Fault Surface ◽  
Homogeneous Half Space ◽  
Earthquake Modeling ◽  
Parkfield Earthquake ◽  
Homogeneous Block ◽  
Rubber Good

Abstract Ground motion produced by finite, kinematic fault surface is modeled at the surface of a homogeneous half-space. The Green's functions for point dislocations are summed to investigate the effects of different rupture velocities and source rise times. Displacements and velocities are compared for a bilateral and unilateral rupture. The method is used to model the displacements for a laboratory experiment involving a dynamic rupture in a homogeneous block of foam rubber. Good agreement between synthetic and model displacements is obtained at distances ranging from zero to somewhat greater than one fault length. The half-space Green's function summation method is then used to model the N65°E (transverse) component of displacement for the 1966 Parkfield earthquake. The 26-cm displacement pulse on this record is fit with a buried dislocation of 100 cm over a rectangular fault 30 km long and 6 km wide, with a depth of 3 km.

Inversion of slingram electromagnetic induction data using a Born approximation

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. E201-E212 ◽  
Author(s):  
Jochen Kamm ◽  
Michael Becken ◽  
Laust B. Pedersen
Keyword(s):  
Half Space ◽  
Born Approximation ◽  
High Efficiency ◽  
Three Dimensions ◽  
Background Model ◽  
Desktop Computer ◽  
Near Surface ◽  
Homogeneous Half Space ◽  
Integral Equation Formulation ◽  
Forward Operator

We present an efficient approximate inversion scheme for near-surface loop-loop EM induction data (slingram) that can be applied to obtain 2D or 3D models on a normal desktop computer. Our approach is derived from a volume integral equation formulation with an arbitrarily conductive homogeneous half-space as a background model. The measurements are not required to fulfill the low induction number condition (low frequency and conductivity). The high efficiency of the method is achieved by invoking the Born approximation around a half-space background. The Born approximation renders the forward operator linear. The choice of a homogeneous half-space yields closed form expressions for the required electromagnetic normal fields. It also yields a translationally invariant forward operator, i.e., a highly redundant Jacobian. In connection with the application of a matrix-free conjugate gradient method, this allows for very low memory requirements during the inversion, even in three dimensions. As a consequence of the Born approximation, strong conductive deviations from the background model are underestimated. Highly resistive anomalies are in principle overestimated, but at the same time difficult to resolve with induction methods. In the case of extreme contrasts, our forward model may fail in simultaneously explaining all the data collected. We applied the method to EM34 data from a profile that has been extensively studied with other electromagnetic methods and compare the results. Then, we invert three conductivity maps from the same area in a 3D inversion.

High-frequency ground-motion variability for rough-fault ruptures  

2021 ◽  
Author(s):  
Jagdish Chandra Vyas ◽  
Martin Galis ◽  
Paul Martin Mai
Keyword(s):  
Ground Motion ◽  
Large Scale ◽  
Earthquake Ground Motion ◽  
Small Scale ◽  
Dynamic Rupture ◽  
Roughness Effects ◽  
Ground Shaking ◽  
Fault Surface ◽  
Fault Roughness ◽  
Ground Motion Variability

<p>Geological observations show variations in fault-surface topography not only at large scale (segmentation) but also at small scale (roughness). These geometrical complexities strongly affect the stress distribution and frictional strength of the fault, and therefore control the earthquake rupture process and resulting ground-shaking. Previous studies examined fault-segmentation effects on ground-shaking, but our understanding of fault-roughness effects on seismic wavefield radiation and earthquake ground-motion is still limited.  </p><p>In this study we examine the effects of fault roughness on ground-shaking variability as a function of distance based on 3D dynamic rupture simulations. We consider linear slip-weakening friction, variations of fault-roughness parametrizations, and alternative nucleation positions (unilateral and bilateral ruptures). We use generalized finite difference method to compute synthetic waveforms (max. resolved frequency 5.75 Hz) at numerous surface sites  to carry out statistical analysis.  </p><p>Our simulations reveal that ground-motion variability from unilateral ruptures is almost independent of  distance from the fault, with comparable or higher values than estimates from ground-motion prediction equations (e.g., Boore and Atkinson, 2008; Campbell and Bozornia, 2008). However, ground-motion variability from bilateral ruptures decreases with increasing distance, in contrast to previous studies (e.g., Imtiaz et. al., 2015) who observe an increasing trend with distance. Ground-shaking variability from unilateral ruptures is higher than for bilateral ruptures, a feature due to intricate seismic radiation patterns related to fault roughness and hypocenter location. Moreover, ground-shaking variability for rougher faults is lower than for smoother faults. As fault roughness increases the difference in ground-shaking variabilities between unilateral and bilateral ruptures increases. In summary, our simulations help develop a fundamental understanding of ground-motion variability at high frequencies (~ 6 Hz) due small-scale geometrical fault-surface variations.</p>

Control of rupture by fault geometry during the 1966 parkfield earthquake

1981 ◽  
Vol 71 (1) ◽  
pp. 95-116 ◽  
Author(s):  
Allan G. Lindh ◽  
David M. Boore
Keyword(s):  
Main Shock ◽  
Fault Plane ◽  
San Andreas Fault ◽  
Strong Motion ◽  
P Wave ◽  
Fault Geometry ◽  
Dynamic Rupture ◽  
San Andreas ◽  
Hill Station ◽  
Parkfield Earthquake

abstract A reanalysis of the available data for the 1966 Parkfield, California, earthquake (ML=512) suggests that although the ground breakage and aftershocks extended about 40 km along the San Andreas Fault, the initial dynamic rupture was only 20 to 25 km in length. The foreshocks and the point of initiation of the main event locate at a small bend in the mapped trace of the fault. Detailed analysis of the P-wave first motions from these events at the Gold Hill station, 20 km southeast, indicates that the bend in the fault extends to depth and apparently represents a physical discontinuity on the fault plane. Other evidence suggests that this discontinuity plays an important part in the recurrence of similar magnitude 5 to 6 earthquakes at Parkfield. Analysis of the strong-motion records suggests that the rupture stopped at another discontinuity in the fault plane, an en-echelon offset near Gold Hill that lies at the boundary on the San Andreas Fault between the zone of aseismic slip and the locked zone on which the great 1857 earthquake occurred. Foreshocks to the 1857 earthquake occurred in this area (Sieh, 1978), and the epicenter of the main shock may have coincided with the offset zone. If it did, a detailed study of the geological and geophysical character of the region might be rewarding in terms of understanding how and why great earthquakes initiate where they do.

Numerical seismograms obtained using ω-κ integrals, for a point P source in a vertically inhomogeneous anelastic model

1996 ◽  
Vol 86 (3) ◽  
pp. 750-760
Author(s):  
F. Abramovici ◽  
L. H. T. Le ◽  
E. R. Kanasewich
Keyword(s):  
Half Space ◽  
Homogeneous Layer ◽  
Variable Step Size ◽  
Step Size ◽  
Adaptive Process ◽  
Cpu Time ◽  
Homogeneous Half Space ◽  
Linear Layer ◽  
Variable Step ◽  
Viscoelastic Layers

Abstract This article presents some numerical experiments in using a computer program for calculating the displacements due to a P source in a vertically inhomogeneous structure, based on the Fourier-Bessel representation. The structure may contain homogeneous, inhomogeneous, elastic, or viscoelastic layers. The source may act in any type of sublayer or in the half-space. Synthetic results for the simple case of a homogeneous layer overlaying a homogeneous half-space compare favorably with computations based on the Cagniard method. Numerical seismograms for an elastic layer having velocities and density varying linearly with depth were computed by integrating numerically the governing differential systems and compared with results based on the Haskell model of splitting the linear layer in homogeneous sublayers. Even an adaptive process with a variable step size based on the Haskell model has a poorer performance on the accuracy-cpu time scale than numerical integration.

Surface-wave dispersion computations

1970 ◽  
Vol 60 (2) ◽  
pp. 321-344 ◽  
Author(s):  
Fred Schwab ◽  
Leon Knopoff
Keyword(s):  
Half Space ◽  
Rayleigh Waves ◽  
Wave Dispersion ◽  
Reduction Technique ◽  
Surface Wave Dispersion ◽  
Single Precision ◽  
Homogeneous Half Space ◽  
Full Control ◽  
Significant Figures ◽  
Rayleigh Wave Dispersion

abstract Fundamental-mode Love- and Rayleigh-wave dispersion computations for multilayered, perfectly-elastic media were studied. The speed of these computations was improved, and the accuracy brought under full control. With sixteen decimal digits employed in these computations, fifteen significant-figure accuracy was found possible with Love waves and twelve to thirteen figure accuracy with Rayleigh waves. In order to ensure that the computed dispersion is correct to a specified accuracy, say σ significant figures, (σ + 1)/4 wavelengths of layered structure must be retained above a homogeneous half-space. To this accuracy, the homogeneous half-space is a sufficient model of the true layering it replaces. Using this result, it was possible to refine the usual layer-reduction technique so as to ensure retention of the specified accuracy while employing reduction. With this reduction technique in effect, and with σ specified below single-precision accuracy, the program can be run entirely in single precision; the specified accuracy is maintained without overflow or loss-of-precision problems being encountered during calculations.

Exact seismograms for a point force using generalized ray theory

Geophysics ◽  
1983 ◽  
Vol 48 (11) ◽  
pp. 1421-1427 ◽  
Author(s):  
E. R. Kanasewich ◽  
P. G. Kelamis ◽  
F. Abramovici
Keyword(s):  
Half Space ◽  
Near Field ◽  
Sedimentary Basins ◽  
Transverse Component ◽  
Point Force ◽  
Seismic Exploration ◽  
Head Wave ◽  
Vertical Force ◽  
Low Velocity ◽  
Head Waves

Exact synthetic seismograms are obtained for a simple layered elastic half‐space due to a buried point force and a point torque. Two models, similar to those encountered in seismic exploration of sedimentary basins, are examined in detail. The seismograms are complete to any specified time and make use of a Cagniard‐Pekeris method and a decomposition into generalized rays. The weathered layer is modeled as a thin low‐velocity layer over a half‐space. For a horizontal force in an arbitrary direction, the transverse component, in the near‐field, shows detectable first arrivals traveling with a compressional wave velocity. The radial and vertical components, at all distances, show a surface head wave (sP*) which is not generated when the source is compressive. A buried vertical force produces the same surface head wave prominently on the radial component. An example is given for a simple “Alberta” model as an aid to the interpretation of wide angle seismic reflections and head waves.

scholarly journals Displacement on the San Andreas fault subsequent to the 1966 Parkfield earthquake

1968 ◽  
Vol 58 (6) ◽  
pp. 1955-1973
Author(s):  
Stewart W. Smith ◽  
Max Wyss
Keyword(s):  
Shear Stress ◽  
Ground Motion ◽  
San Andreas Fault ◽  
High Rate ◽  
Aftershock Activity ◽  
Fault Surface ◽  
San Andreas ◽  
Parkfield Earthquake ◽  
Fault Displacement ◽  
Displacement Measurements

ABSTRACT Immediately following the 1966 Parkfield earthquake a continuing program of fault displacement measurements was undertaken, and several types of instruments were installed in the fault zone to monitor ground motion. In the year subsequent to the earthquake a maximum of at least 20 cm of displacement occurred on a 30 km section of the San Andreas fault, which far exceeded the surficial displacement at the time of the earthquake. The rate of displacement decreased logarithmically during this period in a manner similar to that of the decrease in aftershock activity. After the initial high rate of activity it could be seen that most of the displacement was occurring in 4–6 day epochs of rapid creep following local aftershocks. The variation of fault displacement along the surface trace was measured and shown to be consistent with a vertidal fault surface 44 km long and 14 km deep, along which a shear stress of 2.4 bars was relieved.

scholarly journals Rayleigh-type waves on a coated elastic half-space with a clamped surface

2019 ◽  
Vol 377 (2156) ◽  
pp. 20190111 ◽  
Author(s):  
J. Kaplunov ◽  
D. Prikazchikov ◽  
L. Sultanova
Keyword(s):  
Half Space ◽  
Numerical Solutions ◽  
Substrate Surface ◽  
Numerical Data ◽  
Elastic Half Space ◽  
Asymptotic Results ◽  
Homogeneous Half Space ◽  
Upper Face ◽  
Localized Waves ◽  
Perturbed Equation

Elastodynamics of a half-space coated by a thin soft layer with a clamped upper face is considered. The focus is on the analysis of localized waves that do not exist on a clamped homogeneous half-space. Non-traditional effective boundary conditions along the substrate surface incorporating the effect of the coating are derived using a long-wave high-frequency procedure. The derived conditions are implemented within the framework of the earlier developed specialized formulation for surface waves, resulting in a perturbation of the shortened equation of surface motion in the form of an integral or pseudo-differential operator. Non-uniform asymptotic formula for the speeds of the sought for Rayleigh-type waves, failing near zero frequency and the thickness resonances of a layer with both clamped faces, follow from the aforementioned perturbed equation. Asymptotic results are compared with the numerical solutions of the full dispersion relation for a clamped coated half-space. A similarity with Love-type waves proves to be useful for interpreting numerical data. This article is part of the theme issue ‘Modelling of dynamic phenomena and localization in structured media (part 1)’.

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