Feasibility of mapping a horizon using head waves

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Problem 11.15

Construct the expected time-distance curve for the Java Sea velocity-depth relation shown in Figure 11.15a. Is it feasible to map the top of the relatively flat 4.25 km/s limestone at a depth of about 0.9 km by using head waves? What problems are likely to be encountered?


Figure 11.15a.  Java Sea velocity-depth relation.
Table 11.15a. Java Sea layering.
Depth range (km) (km/s) (s) (km/s)
0.00–0.03 1.53 0.039 0.039 0.091 0.091
0.03–0.16 1.9 0.137 0.176 0.495 0.586
0.16–0.28 1.97 0.122 0.298 0.472 1.059
0.28–0.50 2.25 0.196 0.494 0.992 2.051
0.50–0.70 2.15 0.186 0.68 0.86 2.911
0.70–0.90 2.67 0.15 0.83 1.069 3.98 2.19
0.90–0.97 4.25 0.033 0.863 0.596 4.576 2.30
0.97–1.10 5.27 0.049 0.912 1.361 5.937

Solution

The time-depth data in Figure 11.15a are listed in the first two columns of Table 11.15a. We calculated the data in columns 3 ( two-way traveltime through the layer) to 6 to determine reflection arrival times (column 4) and [using equation (4.13a)]. We take km/s (see Figure 11.15a) to plot the direct wave.

We must take into account other events that might interfere, primarily the reflection and head wave from the 5.27 km/s layer. To plot the refraction curves, we need their slopes, one point on each curve, and the critical distances—where a head wave is tangent to the reflection (see Figure 4.18a). We also calculate the intercept times as a check.

The slope of the limestone refractor (assumed to be flat) is 1/4.25 s/km; taking km, . From Figure 4.18a the critical distance km; at this point s. The intercept time given by equation (4.18a) is s. Thus the head-wave curve passes through the point with slope 1/4.25, is tangent to its reflection at km, and the intercept time s. The reflection arrives at 0.863 s at zero offset and also passes through (0.96,1.1). These curves are shown in Figure 11.15b.

Carrying out similar calculations for the 5.27 km/s layer and using km/s (estimated from Figure 11.15a), we get

The reflection arrives at zero offset at 0.912 s and also passes through (0.95, 0.94). These curves are also plotted in Figure 11.15b.

The 4.25 km/s head wave is always a second arrival. It also follows very closely the reflection from the 5.27 km/s layer. It will almost certainly not be observed as a distinctly separate arrival because later cycles of earlier events will mask it.

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