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Journal ArticleDOI

Internal deformation due to shear and tensile faults in a half-space

01 Apr 1992-Bulletin of the Seismological Society of America (GeoScienceWorld)-Vol. 82, Iss: 2, pp 1018-1040
TL;DR: A complete set of closed analytical expressions for the internal displacements and strains due to shear and tensile faults in a half-space for both point and finite rectangular sources is presented in this paper.
Abstract: A complete set of closed analytical expressions is presented in a unified manner for the internal displacements and strains due to shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and systematically composed of terms representing deformations in an infinite medium, a term related to surface deformation and that is multiplied by the depth of observation point. Several practical suggestions to avoid mathematical singularities and computational instabilities are also presented. The expressions derived here represent powerful tools both for the observational and theoretical analyses of static field changes associated with earthquake and volcanic phenomena.
Citations
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Journal ArticleDOI
TL;DR: In this article, a Coulomb failure criterion was proposed for the production of aftershocks, where faults most likely to slip are those optimally orientated for failure as a result of the prevailing regional stress field and the stress change caused by the mainshock.
Abstract: To understand whether the 1992 M = 7.4 Landers earthquake changed the proximity to failure on the San Andreas fault system, we examine the general problem of how one earthquake might trigger another. The tendency of rocks to fail in a brittle manner is thought to be a function of both shear and confining stresses, commonly formulated as the Coulomb failure criterion. Here we explore how changes in Coulomb conditions associated with one or more earthquakes may trigger subsequent events. We first consider a Coulomb criterion appropriate for the production of aftershocks, where faults most likely to slip are those optimally orientated for failure as a result of the prevailing regional stress field and the stress change caused by the mainshock. We find that the distribution of aftershocks for the Landers earthquake, as well as for several other moderate events in its vicinity, can be explained by the Coulomb criterion as follows: aftershocks are abundant where the Coulomb stress on optimally orientated faults rose by more than one-half bar, and aftershocks are sparse where the Coulomb stress dropped by a similar amount. Further, we find that several moderate shocks raised the stress at the future Landers epicenter and along much of the Landers rupture zone by about a bar, advancing the Landers shock by 1 to 3 centuries. The Landers rupture, in turn, raised the stress at site of the future M = 6.5 Big Bear aftershock site by 3 bars. The Coulomb stress change on a specified fault is independent of regional stress but depends on the fault geometry, sense of slip, and the coefficient of friction. We use this method to resolve stress changes on the San Andreas and San Jacinto faults imposed by the Landers sequence. Together the Landers and Big Bear earthquakes raised the stress along the San Bernardino segment of the southern San Andreas fault by 2 to 6 bars, hastening the next great earthquake there by about a decade.

2,100 citations

Journal ArticleDOI
TL;DR: This paper reviewed many published works and presented a compilation of quantitative earthquake interaction studies from a stress change perspective, which provided some clues about certain aspects of earthquake mechanics, but much work remains before we can understand the complete story of how earthquakes work.
Abstract: Many aspects of earthquake mechanics remain an enigma as we enter the closing years of the twentieth century. One potential bright spot is the realization that simple calculations of stress changes may explain some earthquake interactions, just as previous and on going studies of stress changes have begun to explain human-induced seismicity. This paper, which introduces the special section “Stress Triggers, Stress Shadows, and Implications for Seismic Hazard,” reviews many published works and presents a compilation of quantitative earthquake interaction studies from a stress change perspective. This synthesis supplies some clues about certain aspects of earthquake mechanics. It also demonstrates that much work remains before we can understand the complete story of how earthquakes work.

1,031 citations

Journal ArticleDOI
TL;DR: The ITRF2014 is generated with an enhanced modeling of nonlinear station motions, including seasonal (annual and semiannual) signals of station positions and postseismic deformation for sites that were subject to major earthquakes.
Abstract: For the first time in the International Terrestrial Reference Frame (ITRF) history, the ITRF2014 is generated with an enhanced modeling of nonlinear station motions, including seasonal (annual and semiannual) signals of station positions and postseismic deformation for sites that were subject to major earthquakes. Using the full observation history of the four space geodetic techniques (very long baseline interferometry (VLBI), satellite laser ranging (SLR), Global Navigation Satellite Systems (GNSS), and Doppler orbitography and radiopositioning integrated by satellite (DORIS)), the corresponding international services provided reprocessed time series (weekly from SLR and DORIS, daily from GNSS, and 24 h session-wise from VLBI) of station positions and daily Earth Orientation Parameters. ITRF2014 is demonstrated to be superior to past ITRF releases, as it precisely models the actual station trajectories leading to a more robust secular frame and site velocities. The ITRF2014 long-term origin coincides with the Earth system center of mass as sensed by SLR observations collected on the two LAGEOS satellites over the time span between 1993.0 and 2015.0. The estimated accuracy of the ITRF2014 origin, as reflected by the level of agreement with the ITRF2008 (both origins are defined by SLR), is at the level of less than 3 mm at epoch 2010.0 and less than 0.2 mm/yr in time evolution. The ITRF2014 scale is defined by the arithmetic average of the implicit scales of SLR and VLBI solutions as obtained by the stacking of their respective time series. The resulting scale and scale rate differences between the two solutions are 1.37 (±0.10) ppb at epoch 2010.0 and 0.02 (±0.02) ppb/yr. While the postseismic deformation models were estimated using GNSS/GPS data, the resulting parametric models at earthquake colocation sites were applied to the station position time series of the three other techniques, showing a very high level of consistency which enforces more the link between techniques within the ITRF2014 frame. The users should be aware that the postseismic deformation models are part of the ITRF2014 products, unlike the annual and semiannual signals, which were estimated internally with the only purpose of enhancing the velocity field estimation of the secular frame.

925 citations

Journal ArticleDOI
TL;DR: Using the measurements of ∼726 GPS stations around the Tibetan Plateau, Wang et al. as discussed by the authors determined the rigid rotation of the entire plateau in a Eurasia-fixed reference frame, which can be best described by an Euler vector of (24.38° ± 0.42°N, 102.37° ± 1.0206°/Ma).
Abstract: [1] Using the measurements of ∼726 GPS stations around the Tibetan Plateau, we determine the rigid rotation of the entire plateau in a Eurasia-fixed reference frame which can be best described by an Euler vector of (24.38° ± 0.42°N, 102.37° ± 0.42°E, 0.7096° ± 0.0206°/Ma). The rigid rotational component accommodates at least 50% of the northeastward thrust from India and dominates the eastward extrusion of the northern plateau. After removing the rigid rotation to highlight the interior deformation within the plateau, we find that the most remarkable interior deformation of the plateau is a “glacier-like flow” zone which starts at somewhere between the middle and western plateau, goes clockwise around the Eastern Himalayan Syntaxis (EHS), and ends at the southeast corner of the plateau with a fan-like front. The deformation feature of the southern plateau, especially the emergence of the flow zone could be attributed to an eastward escape of highly plastic upper crustal material driven by a lower crust viscous channel flow generated by lateral compression and gravitational buoyancy at the later developmental stage of the plateau. The first-order feature of crustal deformation of the northeastern plateau can be well explained by a three-dimensional elastic half-space dislocation model with rates of dislocation segments comparable to the ones from geological observations. In the eastern plateau, although GPS data show no significant convergence between the eastern margin of the plateau and the Sichuan Basin, a small but significant compressional strain rate component of ∼10.5 ± 2.8 nstrain/yr exists in a relatively narrow region around the eastern margin. In addition, a large part of the eastern plateau, northeast of the EHS, is not undergoing shortening along the northeastward convergence direction of the EHS but is stretching.

844 citations


Cites background or methods from "Internal deformation due to shear a..."

  • ...D elastic half-space dislocation model [Okada, 1992] to best fit the observed two horizontal components of GPS velocity at each site around the area....

    [...]

  • ...…assume that the crustal deformation of the northeastern plateau is dominated by deep slip of a series of major active faults which are approximated as simple dislocation segments locked 20 km to the surface and slipping below to an infinite depth in an elastic half-space [Okada, 1992] (Figure 8)....

    [...]

  • ...[30] As a tentative experiment, we assume that the crustal deformation of the northeastern plateau is dominated by deep slip of a series of major active faults which are approximated as simple dislocation segments locked 20 km to the surface and slipping below to an infinite depth in an elastic half-space [Okada, 1992] (Figure 8)....

    [...]

  • ...(rather than dip slip) and strike-slip rates for each of the faults using a 3-D elastic half-space dislocation model [Okada, 1992] to best fit the observed two horizontal components of GPS velocity at each site around the area....

    [...]

Journal ArticleDOI
11 Jun 1993-Science
TL;DR: The most promising explanations involve nonlinear interactions between large dynamic strains accompanying seismic waves from the mainshock and crustal fluids (perhaps including crustal magma).
Abstract: The magnitude 7.3 Landers earthquake of 28 June 1992 triggered a remarkably sudden and widespread increase in earthquake activity across much of the western United States. The triggered earthquakes, which occurred at distances up to 1250 kilometers (17 source dimensions) from the Landers mainshock, were confined to areas of persistent seismicity and strike-slip to normal faulting. Many of the triggered areas also are sites of geothermal and recent volcanic activity. Static stress changes calculated for elastic models of the earthquake appear to be too small to have caused the triggering. The most promising explanations involve nonlinear interactions between large dynamic strains accompanying seismic waves from the mainshock and crustal fluids (perhaps including crustal magma).

825 citations

References
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Book
01 Jan 1892
TL;DR: Webb's work on elasticity as mentioned in this paper is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity.
Abstract: The present treatise is the outcome of a suggestion made to me some years ago by Mr R. R. Webb that I should assist him in the preparation of a work on Elasticity. He has unfortunately found himself unable to proceed with it, and I have therefore been obliged to take upon myself the whole of the work and the whole of the responsibility. I wish to acknowledge at the outset the debt that I owe to him as a teacher of the subject, as well as my obligation for many valuable suggestions chiefly with reference to the scope and plan of the work, and to express my regret that other engagements have prevented him from sharing more actively in its production. The division of the subject adopted is that originally made by Clebsch in his classical treatise, where a clear distinction is ill-awn between exact solutions for bodies all whose dimensions are finite and approximate solutions for bodies some of whose dimensions can be regarded as infinitesimal. The present volume contains the general mathematical theory of the elastic properties of the first class of bodies, and I propose to treat the second class in another volume. At Mr Webb's suggestion, the exposition of the theory is preceded by an historical sketch of its origin and development. Anything like an exhaustive history has been rendered unnecessary by the work of the late Dr Todhunter as edited by Prof Karl Pearson, but it is hoped that the brief account given will at once facilitate the comprehension of the theory and add to its interest. Readers of the historical work referred to will appreciate the difficulty of giving within a reasonable compass a complete account of all the valuable researches that have been made; and the aim of this book is rather to present a connected account of the theory in its present state, and an indication of the way in which that state has been attained, avoiding on the one hand merely analytical developments, and on the other purely technical details.

7,269 citations

Journal ArticleDOI
TL;DR: In this paper, a suite of closed analytical expressions for the surface displacements, strains, and tilts due to inclined shear and tensile faults in a half-space for both point and finite rectangular sources are presented.
Abstract: A complete suite of closed analytical expressions is presented for the surface displacements, strains, and tilts due to inclined shear and tensile faults in a half-space for both point and finite rectangular sources. These expressions are particularly compact and free from field singular points which are inherent in the previously stated expressions of certain cases. The expressions derived here represent powerful tools not only for the analysis of static field changes associated with earthquake occurrence but also for the modeling of deformation fields arising from fluid-driven crack sources.

4,057 citations

Journal ArticleDOI

2,316 citations


"Internal deformation due to shear a..." refers background in this paper

  • ...The remaining term, U/B(Xl, X2,0), reduces to the formula for the surface displacement field due to a point force in a half-space (Okada, 1985)....

    [...]

  • ...In a previous paper (Okada, 1985), we have obtained a complete set of compact closed analytical expressions for the surface deformation due to inclined shear and tensile faults in a half-space....

    [...]

Journal ArticleDOI
01 May 1936-Physics
TL;DR: In this paper, a solution of the three-dimensional elasticity equations for a homogeneous isotropic solid is given for the case of a concentrated force acting in the interior of a semi-infinite solid.
Abstract: A solution of the three‐dimensional elasticity equations for a homogeneous isotropic solid is given for the case of a concentrated force acting in the interior of a semi‐infinite solid. This represents the fundamental solution having a singular point in a solid bounded by a plane. From it may be derived, by a known method of synthesis, the solutions for the semi‐infinite solid which correspond to the solutions known as nuclei of strain in the solid of indefinite extent.

1,181 citations


"Internal deformation due to shear a..." refers methods in this paper

  • ...If we take the Cartesian coordinate system, as shown in Figure 1, uJ(xl, x 2, xa; }1, }2, }3), the ith component of the displacement at ( x 1, x 2, x 3) due to the jth direction point force of magnitude F at (~1, ~2, 43) can be rewritten from the formula by Mindlin (1936) or Press...

    [...]

Journal ArticleDOI
TL;DR: In this article, closed analytical expressions for the displacement fields of inclined, finite strike-slip and dip-slink faults are given, and they may be readily used in the numerical computation of displacements, and by differentiation, strain and stress fields may be derived.
Abstract: Closed analytical expressions for the displacement fields of inclined, finite strike-slip and dip-slip faults are given. They may be readily used in the numerical computation of displacements, and, by differentiation, strain and stress fields may be derived. The expressions are valid both at the surface and at depth.

785 citations