SEISMIC METHODS 



677 



Dip Shooting — Three Dimensional Case 



In the foregoing discussion it was tacitly assumed that the seismometers 

 were placed in a line of direction of the true dip. Thus in Figure 419, the 

 plane of the paper represents the plane of incidence and the reflecting 

 interface is perpendicular to it. The slope of the reflected wave is a vector, 

 and its direction does not in general coincide with the direction of the line 

 of seismometers in field practice. Furthermore, being a vector in two 

 dimensions, it requires the measurement of two components to determine 

 its direction and magnitude. To do this, two lines of instruments are set up, 

 intersecting at the shot-point. The most accurate and easily computed 

 arrangement of the seismometers is a right-angled cross, with the shot- 

 point directly below the crossing point of the two spreads. 



Let the lines of the cross of seismom- 

 eters be the x and the y axes, and let the 

 s axis represent depth. The origin of the 

 coordinates then represents the shot- 

 point. 



In Figure 419 is illustrated a small 

 triangular section of the wave surface 

 an instant before arriving at the origin. 

 A small pyramid is formed with its apex 

 at the origin, its base representing a 

 small area of the surface and the lengths 

 of its edges being equal to the increments 

 dx, dy, and dz. Let dp be a perpendicu- 

 lar to the wave surface from the origin. 



The wave normal dp forms three angles with the coordinate axes. The 

 cosines of these angles are known as directional cosines in analytical geom- 

 etry and are customarily given the notation /, m, and n. 



Fig. 419. — Triangular section of reflected 

 wave front near origin. 



Thus, dp = I dx = m dy = nds 



The wave moves forward a distance dp in time dT, where 



dp = VidT 

 Equating (22) and (23) and solving for / and w, 



dT 



(22) 

 (23) 



m = V\ 



dx 



dT 

 dy 



(24) 



Since T is a function of both x and y, partial derivative notation must 

 be used. 



