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.

/pdf/surface-deformation-due-to-shear-and-tensile-faults-in-a-2vckanzx6g.pdf

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

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.

http://arrowsmith510.asu.edu/TheLectures/Lecture18/Okada_1992.pdf

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

The conventional magnitude scale M suffers saturation when the rupture dimension of the earthquake exceeds the wavelength of the seismic waves used for the magnitude determination (usually 5–50 km). This saturation leads to an inaccurate estimate of energy released in great earthquakes. To circumvent this problem the strain energy drop W (difference in strain energy before and after an earthquake) in great earthquakes is estimated from the seismic moment M_0. If the stress drop Δσ is complete, W = W_0 = (Δσ/2μ)M_0 ∼ M_0/(2×10^4), where μ is the rigidity; if it is partial, W_0 gives the minimum estimate of the strain energy drop. Furthermore, if Orowan's condition, i.e., that frictional stress equal final stress, is met, W_0 represents the seismic wave energy. A new magnitude scale M_w is defined in terms of W_0 through the standard energy-magnitude relation log W_0 = 1.5M_w + 11.8. M_w is as large as 9.5 for the 1960 Chilean earthquake and connects smoothly to M_s (surface wave magnitude) for earthquakes with a rupture dimension of about 100 km or less. The M_w scale does not suffer saturation and is a more adequate magnitude scale for great earthquakes. The seismic energy release curve defined by W_0 is entirely different from that previously estimated from Ms. During the 15-year period from 1950 to 1965 the annual average of W_0 is more than 1 order of magnitude larger than that during the periods from 1920 to 1950 and from 1965 to 1976. The temporal variation of the amplitude of the Chandler wobble correlates very well with the variation of W_0, with a slight indication of the former preceding the latter. In contrast, the number N of moderate to large earthquakes increased very sharply as the Chandler wobble amplitude increased but decreased very sharply during the period from 1945 to 1965, when W_0 was largest. One possible explanation for these correlations is that the increase in the wobble amplitude triggers worldwide seismic activity and accelerates plate motion which eventually leads to great decoupling earthquakes. This decoupling causes the decline of moderate to large earthquake activity. Changes in the rotation rate of the earth may be an important element in this mechanism.

/pdf/the-energy-release-in-great-earthquakes-27rg7m8mky.pdf

The energy release in great earthquakes

A Viking Lander 1 image was modeled as mixtures of reflectance spectra of palagonite dust, gray andesitelike rock, and a coarse rocklike soil. The rocks are covered to varying degrees by dust but otherwise appear unweathered. Rocklike soil occurs as lag deposits in deflation zones around stones and on top of a drift and as a layer in a trench dug by the lander. This soil probably is derived from the rocks by wind abrasion and/or spallation. Dust is the major component of the soil and covers most of the surface. The dust is unrelated spectrally to the rock but is equivalent to the global-scale dust observed telescopically. A new method was developed to model a multispectral image as mixtures of end-member spectra and to compare image spectra directly with laboratory reference spectra. The method for the first time uses shade and secondary illumination effects as spectral end-members; thus the effects of topography and illumination on all scales can be isolated or removed. The image was calibrated absolutely from the laboratory spectra, in close agreement with direct calibrations. The method has broad applications to interpreting multispectral images, including satellite images.

Spectral mixture modeling - A new analysis of rock and soil types at the Viking Lander 1 site. [on Mars]

Preface 1. Origin and history of the Solar System 2. Composition of the Earth 3. Radioactivity, isotopes and dating 4. Isotopic clues to the age and origin of the Solar System 5. Evidence of the Earth's evolutionary history 6. Rotation, figure of the Earth and gravity 7. Precession, wobble and rotational irregularities 8. Tides and the evolution of the lunar orbit 9. The satellite geoid, isostasy and post-glacial rebound 10. Elastic and inelastic properties 11. Deformation of the crust: rock mechanics 12. Tectonics 13. Convective and tectonic stresses 14. Kinematics of the earthquake process 15. Earthquake dynamics 16. Seismic wave propagation 17. Seismological determination of Earth structure 18. Finite strain and high pressure equations of state 19. Thermal properties 20. The surface heat flux 21. The global energy budget 22. Thermodynamics of convection 23. Thermal history 24. The geomagnetic field 25. Rock magnetism and paleomagnetism 26. Alternative energy sources and natural climate variations: some geophysical background Appendix A. General reference data Appendix B. Orbital dynamics (Kepler's laws) Appendix C. Spherical harmonic functions Appendix D. Relationships between elastic moduli of an isotropic solid Appendix E. Thermodynamic parameters and derivative properties Appendix F. An Earth model: mechanical properties Appendix G. A thermal model of the Earth Appendix H. Radioactive isotopes Appendix I. A geological time scale 2004 Appendix J. Problems References Index.

Physics of the Earth

Two dimensional local spectral information can be obtained from an image using Instantaneous Wavevector (the extension of instantaneous frequency to two dimensions). This 2 dimensional function is a vector quantity found by taking the gradient of the phase of the Analytic Image. Several synthetic images will be presented to illustrate the utility of Instantaneous Wavenumber Analysis, and its application to OH airglow images will be discussed. The IW of an image gives us the dominant wavevector present at any point in the image. The amplitude of the analytic image gives us the magnitude of this component, and the phase differences of the Analytic Image between successive images allow us to infer the velocity of these waves. This method is used to determine phase velocities of internal waves from Hydroxyl airglow data. The instrument used, UWOSCR, is a scanning radiometer in the near infra-red, taking an 256 pixel image of the OH airglow every minute.

Instantaneous wavevector analysis

In this paper we analyse the gravimetric records obtained with tidal instruments, during the solar eclipse on August 11, 1999, when the shadow crossed Europe. Measurements recorded with spring and super-conducting gravimeters set up in Annelles, Uccle, Walferdange and Bondy are discussed. Comparisons between super-conducting gravimeters and spring gravimeters are made, in order to fix the limits of the magnitude of abnormal effects in relation to the possibility of a shielding effect by the Moon on the Sun's gravitational attraction. The results from the LCR and Askania gravimeters will also be discussed in the paper. Our conclusions are that significant effects during an eclipse, if indeed they do exist, may be below the noise level of the gravimeters which is ±1 nm/s² (0.1µGal) for super-conducting gravimeters. Our findings confirm that in these situations both spring and super-conducting gravimeters are working at the limits of their precision, with a risk that abnormal environmental features induced by the eclipse could significantly modify the signals. Keyword: gravity, gravitational shield, gravimeter, solar eclipse, Earth-tide

Search for the Gravitational Absorption Effect Using Spring and Super-conducting Gravimeters during the Total Solar Eclipse of August 11, 1999

Review of Applications of 1- and 2-D S-transforms

Most earthquake ruptures propagate with speeds smaller than the Rayleigh wave velocity of the medium. These are called sub- Rayleigh ruptures. However, under suitable conditions, segments of otherwise sub- Rayleigh seismogenic ruptures can occasionally accelerate to speeds higher than the local shear wave velocity, giving rise to so-called supershear ruptures. The occurrence of supershear ruptures is usually associated with a locally higher value of pre-stress on the fault segment compared to the sub-Rayleigh segments of the same fault. Additionally, shear stress changes generated by the supershear rupture are radiated out unattenuated to distances comparable to the depth of rupture instead of rapidly decaying at much smaller distances from the rupture. This leads to aftershocks being distributed away from the fault on the supershear segment. This study attempts to verify whether these pre- and postseismic stress conditions and the resultant spatial aftershock distributions lead to discernible features in the statistical properties of the aftershock sequences of the earthquakes known to be associated with supershear ruptures. We analyze the Gutenberg-Richter scaling, the modified Omori law and Bath’s law for the aftershock sequences of two supershear mainshocks: the 1979 M W 6.5 Imperial Valley (California) and 2002 M W 7.9 Denali (Alaska) earthquakes. We observe that the b -value is always higher in the supershear zone than the rest of the sequence. We also observe that there is no systematic trend in the exponent of the modified Omori law when comparing the aftershocks in the supershear zone with the rest of the aftershocks. We argue that the b -value anomaly can be explained in terms of the off-fault distribution of aftershocks around the supershear segment of the rupture.

/pdf/anomalous-statistics-of-aftershock-sequences-generated-by-3a3hsvenbq.pdf

Lalu Mansinha

Papers

Instantaneous wavevector analysis

Search for the Gravitational Absorption Effect Using Spring and Super-conducting Gravimeters during the Total Solar Eclipse of August 11, 1999

Review of Applications of 1- and 2-D S-transforms

Anomalous statistics of aftershock sequences generated by supershear ruptures

On the double exponential frequency-magnitude relation of earthquakes