Sarva Jit Singh

The Simulation of Ground Motions Using Envelope Summations

Abstractu200a—u200aThe technique of Midorikawa (1993) has been modified to obtain a resultant envelope function at the observation point by placing the rupture causing an earthquake in a layered earth model. The method and its dependency on various modelling parameters are studied in detail. The complete study shows that the generated resultant envelope follows important strong motion characteristics such as directivity and attenuation effects. The simulated resultant envelope is further used for generating synthetic accelerograms by multiplying filtered white noise with the envelope of accelerogram at a particular observation point. Filters through which white noise passes include the effects of geometrical spreading, anelastic attenuation and near-site attenuation at high frequencies.¶Uttarkashi earthquake is among few Indian earthquakes for which strong motion data are available at thirteen different stations. Using the technique presented in this work, envelope function as well as complete acceleration time history during Uttarkashi earthquake has been simulated at these observation points. Comparison of peak acceleration, duration and acceleration response spectra confirms the utility and efficacy of the approach.

Deformation of a homogeneous gravitating sphere by internal dislocations

SummaryAn explicit solution is obtained for the system of equations describing the spheroidal motion in a homogeneous, isotropic, gravitating, elastic medium possessing spherical symmetry. This solution is used to derive the Greens dyad for a homogeneous gravitating sphere. The Greens dyad is then employed to obtain the displacement field induced by tangential and tensile dislocations of arbitrary orientation and depth within the sphere.

Deformation of a Spherical Earth Model by Finite Dislocations

Numerical results are obtained for the static surface displacements, strains and tilts of a homogeneous, isotropic, non-gravitating, elastic sphere due to finite dip-slip and strike-slip faults. The theory is applied to strain observations from the Alaska earthquake of March 28, 1964. It is shown that the theoretical values are within an order of magnitude of the observed values and are of the correct sign. The method can be extended to derive the displacements everywhere within the sphere. These are required for the determination of the changes in the components of the inertia tensor in the earth due to major earthquakes which lead to a spherical theory for the calculation of the contribution of earthquakes to the excitation of the Chandler wobble and the secular polar shift. During the preceding few years, elasticity theory of dislocations has been developed and applied by several investigators, e.g. Steketee (I958a, b), Chinnery (1961, 1963), Maruyama (1964), Press (1965), Savage and Hastie (1966). Mansinha and Smylie (1967), computed the changes in the products of inertia of the earth due to rearrangexad ment of masses associated with major earthquakes. As a mathematical model, they used vertical, rectangular, strike-slip and dip-slip faults in a half-space. They then calculated the contribution to the excitation of the Chandler wobble and the secular polar shift from the above changes in the products of inertia. However, there is no justification for using a half space model in problems with intrinsic spherical geometry. Ben-Menahem and Singh (1968), obtained explicit exxad pressions for the deformation of a uniform non-gravitating sphere due to internal dislocations of arbitrary orientation and depth. These results constitute the theoretical nucleus of a fundamental study by Ben-Menahem et al. (1969). Therein displacexad ments and strains are calculated everywhere on a spherical earth model and the numerical results are displayed in various forms. Some important results of this study are summarized below. (I) The field components are practically insensitive to changes in the Poisson ratio in the range O.25~CT~O.33. (2) By using the results of this paper it is possible to calculate the displacements, strains, stresses and tilts at any point on the surface of a sphere induced by a tangenxad tial dislocation of arbitrary depth and dip and slip angles. (3) The ratio of the displacement at the free surface of a sphere to the corresponding

On the disturbance due to a point source in an inhomogeneous medium

SummaryThe problem of a point source in an isotropic, inhomogeneous fluid medium is discussed. It is assumed that the density of the fluid is constant and the acoustic velocity varies with depth asc=c0(1 +m z) wherem is a constant andc0 is, the velocity at the level of the origin. An approximate expression for the field due to a point source in such a medium is obtained when the medium is infinite as well as when it is semi-infinite. It is found that the results obtained agree with the WKB solution of the problem.

Comments on the paper ‘propagation of surface waves on a nonhomogeneous spherically aelotrophic shell' by Verma and Srivastava

SummaryIn a recent paper,Verma andSrivastava [1] discussed the vibrations of an inhomogeneous, transradially isotropic, spherical shell. An assumption made by these authors at the very outset appears to be incorrect. Consequently, most of the equations and results obtained by them are either wrong or irrelevant. The purpose of this note is to point out these mistakes and give the corresponding correct results.The notation of Verma and Srivastava is used throughout.