Papers - Seismic Methods - Comparison of Two Methods for Interpretation of Seismic Time-distance Graphs Which Are Smooth Curves

The most important quantitative method in seismic prospecting by refraction shooting is the method of profiles. A profile is established by firing a series of charges at various points along a straight line which terminates at the seismograph. The same data are obtained by repeatedly firing charges at one place and recording at a series of stations along the line of the profile. The quantities which are measured are the distance x from each firing position to the seismograph and the time t required for the first disturbance from each explosion to travel to the seismograph. These data are used in plotting the familiar time-distance graph. The only time-distance graphs that will be considered here are those obtained in localities where the velocity of propagation depends solely on the depth beneath the surface; that is, where there is no slope in the subsurface. The essential calculation to be made from such a time-distance graph is the determination of P(x), the maximum depth of penetration of a disturbance coming to the seismograph from a firing point at the distance x from the instrument. If the time-distance graph consists of a series of straight lines, as is often the case, the penetration P(x) can be calculated by means of formulas which appear in almost every description of seismic prospecting.' Until the present, however, the only formula that has been available for calculating P(x) for time-distance graphs which are smooth curves is one which requires an arbitrary assumption regarding the law of velocity increase with depth.2 The practice in these cases has been to approximate the curve by means of a number of straight lines and then to apply the ordinary straight-line formulas. This method clearly can yield accurate results only when a sufficiently large number of straight lines is used. The labor of computation increases rapidly when the number of lines is increased, so too few lines often are used. Further than that, there is a strong tendency to overlook the approximate nature