Resolving Delay Times

The delaytm.m procedure solves for the delay times, and then resolves them into two end-limit solutions. Variations in delay times are resolved totally into a variation in the refractor structure with the formula

$$\begin{array}{c} h=\frac{V_{1}}{\cos\left(\theta\right)}\cdot... ...}\\ \theta=\arcsin\left(\frac{V_{1}}{V_{2}}\right)\end{array},$$ (38)

where $T_{j}$ is the j-th delay time and “h” is the distance from the source or geophone to the refractor. This distance, h, is a radius specifying a circle, somewhere on which the refractor may be found. In delaytm.m, the refractor position is plotted a distance, h, directly below the source or geophone (unmigrated position). For the purpose of most engineering surveys, migration of the refractor point is not a significant issue (the distances are quite small).

The alternative end-limit resolution of delay times is as a variation in overburden velocity. The user provides a distance from the recording surface to the refractor (held constant), and an overburden velocity is found from the formula

$$V_{1}=\frac{V_{2}}{\sqrt{1+\left(\frac{T_{j}V_{2}}{h}\right)^{2}}},$$ (39)

where $T_{j}$ is the j-th delay time and “h” is the constant distance from the recording surface to the refractor. This assumes that the refractor velocity, $V_{2}$ , is constant, and the only variation is in $V_{1}$ , the overburden velocity. This type of solution makes sense when the water content of the overburden soil is known to vary, and the overburden thickness is relatively constant. In reality, the truth will be somewhere between these two limiting cases. See Michaels (9) for a discussion on this topic.

One should probably produce xfig scaled plots, as some CAD work is usually required to clean things up. Figure 37 shows how a final merging of the exported *.fig files will look with a little CAD effort. In this case, the structural solution, Figure 37B is preferred because of our knowledge of the geology from trenching and surface observations.

Figure 37: Line 3 solution, merged xfig plots. A). Arrival times and fit, B). Structural Solution (accepted), C). Overburden velocity solution (rejected)