676 EXPLORATION GEOPHYSICS 



the two seismometers. If the seismic wave velocity in layer 1 is represented 

 by the symbol Vi, then the time difference dT is 



_ dx sin Ox 

 dT - — ^;— (18) 



since by geometry di = ai, we may write 



sinai = Fx£ (19) 



From Figure 418 it is seen that the angle of dip 6 of the reflecting 

 interface is the same as the vertical angle of the reflected ray at the point 

 of reflection, a fact which is true only of the reflected ray which reverses 

 its path. 



Using Equation 17 we may write for this particular situation: 



V 

 sin 6 = — sin ai (20) 



hence sin ^ = V~ (21) 



where V is the wave velocity at the reflecting point. 



Because of the fact that the reflecting interface is at a finite depth, the 

 wave surface is curved, and therefore the quantity dT/dx is a function of 

 the distance from the shot-point. In the region around the shot-point the 

 wave front is very nearly spherical. The slope of the wave at the shot- 

 point may be obtained in practice by measuring the time-difference, dT, 

 as the amount of time required for the reflected wave front to pass from 

 one end seismometer to the seismometer at the other end of a spread of 

 instruments spaced so that the shot-point is centrally located. This quantity 

 dT, often referred to in practice as the step-out time of a reflection, is not 

 taken directly from the outside pair of seismometers alone. Its numerical 

 value, usually in milliseconds, is estimated from a consideration of the 

 reflection arrival-times of the wave at each of the instruments in the seis- 

 mometer spread. Where a straight line of uniform slope cannot be drawn 

 through the arrival-times on the record, the greatest weight generally is 

 given to those arrival-times farthest from the center. 



It is to be noted that this so-called step-out time determined for a 

 reflection in this manner gives the direction of the dip, the down-dip being 

 in the direction of the latest arrival-time. If the shot-point is placed at 

 any other position than the center of the spread, the direction of the dip 

 may be computed from the step-out time only by the use of the velocities 

 within the media between the surface and the reflecting interface. Another 

 practical advantage of this method of shooting (with the shot-point cen- 

 trally located with respect to the seismometer spread) is that theoretically 

 the reflected amplitude is greater in the vicinity of the shot-point. 



