Papers - Seismic Methods - Seismic Propagation Paths (With Discussion)

Assuming that wave velocities in seismic prospecting increase as a continuous linear function of the depth, the authors have derived formulas for computing, from two time-distance observations, the amount of velocity increase, depth of penetration and a graphical determination of the path of the vibrations, and have discussed the ground, reflected and refracted waves. The application of the formulas is illustrated numerically. Earlier Investigations Observations of the energy propagated from the center of an earthquake disturbance have been used to give information about the velocities and paths of elastic waves in the interior of the earth. One method of accomplishing this depends on the use of the times of transmission. Herglotz(7) § and Bateman(3) obtained a solution of the integral equation involved, which determines the velocity of propagation at any point as a function of the distance from the center of the earth, with no assumption as to the manner in which the velocity of the disturbance varies with depth below the earth's surface. The expressions on which the value of the time and the form of the ray of propagation depend contain an unintegrable definite integral, involving the velocity as an unknown function of the distance from the center of the earth. Wiechert and Zoppritz(15) obtained a manageable form for this function by assuming a law of variation which required a constant curvature form for the path within each of a succession of concentric spherical layers of the earth. C. G. Knott(9) worked out the problem for the first time by an absolutely rigorous method from the data of observation (Zoppritz-Turner tables), without making any assumptions as to the functional relationship connecting the speed of propagation and the distance from the earth's center. His method is a numerical solution of an integral equation, giving each velocity and the corresponding distance from the center of the earth in figures.