The Effect Asymptotically Varying Density on Oblique Shock Wave Parameters: The Theory of Earthquake

The CCW Method has been used in study the propagation of strong spherical oblique stock in rotating medium. Assuming the initial density distribution region Law as   = '  r, where '  is the density at centre and  is density paramenter taken as constant, the expressions for shock velocity shock strength, non-dimensional particle velocity and nondimensional pressure have been obtained, the effect of propagation distance, adiabatic heat index, wedge angle, density parameter and angular velocity, on shock velocity and shock strength have been discussed through tables. INTRODUCTION An earthquake is a sudden vibration or trembling in the earth. Earthquake motion is caused by the quick release of strong potential energy into kinetic energy of motion. Earthquake generates oblique strong spherical shock waves. The study of strong spherical converging oblique shock in non-uniform rotating medium is of interest to many researchers. The study of propagation of oblique shock waves is immense important for production of very high pressure and other flow variables. Using several approximate techniques. Many authors Chaturani (1970), Kumar (1978), Yadav (1992) taken the propagation of diverging shock waves through a rotating gas have been studied. The motion of converging cylindrical and spherical shock waves in perfect gas with constant specific heats has been studied by Stanyukovich (1960) using similarity method. The propagation of spherical converging shock in various metals has been studied by Yadav and Singh (1982) by Whitham method. Yadav et al (2001) have studied the propagation of spherical converging strong shock in uniform medium by CCW method. Afaimovich. E.L. et al. (2001) studied the shock acoustic waves generated by earthquakes. It was found that in spite of the difference of earthquake characteristics, the local time, the season and the level of geomagnetic disturbance, for the four earthquakes, the time period of the ionosphere response is 180-390s and the amplitude exceeds, by a factor of two as a minimum, the standard vibration of back ground fluctuations in total electron content in this range of periods under quite and moderate geomagnetic conditions. Wu, Y.K. et al. (1998) studied the propagation characteristic of blast-induced shock waves in a jointed rock mass. And he conclude that the amplitude and principal frequency of shock waves attenuate with increase of distance from the charge centre and the increase of incident angle between, the joint strike and the wave propagation path. Recently Singh (2004) has co-related, the shock wave with earthquake and obtained the variation of normal shock in the medium having asymptotically varying density region. In the present paper the propagation of strong spherical oblique shock wave through asymptotically varying density medium has been studied by Chisnell-Chester-Whitham method. The medium becomes inhomogeous on account of solid body rotation. Assuming an initial density distribution Law as , 0= '  r-, where '  is the density at the centre and  is a constant. The analytical relations for shock velocity, shock strength non-dimensional particle velocity and non-dimensional pressure for freely propagation and in the influence of overtaking disturbances are obtained. The variation of shock velocity and shock strength with propagation distance (r), adiabatic heat index (). wedge angle (), density parameter () and angular velocity (0) have been discussed through tables. Finally the result obtained here are compared with Singh (2004). Basic Equations and Boundary Conditions Under the assumption that the gas is in viscid and non-conducting of heat the basic equations governing the spherically symmetrical flow enclosed by the shock front are