Analysis of Seismic Profiles

NUMEROUS results and formulas have been published for analyzing seismic records, but most of them apply only to large-scale phenomena such as are encountered in studying earthquakes. In a few cases,1 formulas have been published for some of the simpler structures. In the present paper, an attempt will be made to analyze several types of struc-tures without using methods more advanced than those of a first course in calculus. In, tracing a disturbance through a medium, it is almost always possible to base the analysis on Fermat's Principle of Extreme Time, which states that waves of displacement travel between points in such a manner as to make the time of travel an extremum with respect to all neighboring paths. In the simpler cases, comprising most of those used in optics or geophysical prospecting, this time is a minimum and the principle is often referred to as the Principle of Least Time. Within a homogeneous medium, having a uniform speed of transmission of the disturbance in all directions and throughout the medium, the paths are straight and are refracted at the interfaces in accordance with the Snell law of refraction, which states that the ratio of the sine of the angle, made by the ray with the normal to the interface, to the speed of trans-mission is the same on both sides of the interface. Thus, in any medium composed of homogeneous sections, this same ratio has a constant value at all points. In particular, if all interfaces are horizontal, it is apparent that the angles of incidence are the angles made by the ray with the vertical direction. Furthermore, the incident ray, the refracted ray and the normal to the interface are all in the same plane at each refraction;