Feasibility of mapping a horizon using head waves
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?
|Depth range (km)||(km/s)||(s)||(km/s)|
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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Also in this chapter
- Salt lead time as a function of depth
- Effect of assumptions on refraction interpretation
- Effect of a hidden layer
- Proof of the ABC refraction equation
- Adachi’s method
- Refraction interpretation by stripping
- Proof of a generalized reciprocal method relation
- Delay time
- Barry’s delay-time refraction interpretation method
- Parallelism of half-intercept and delay-time curves
- Wyrobek’s refraction interpretation method
- Properties of a coincident-time curve
- Interpretation by the plus-minus method
- Comparison of refraction interpretation methods
- Feasibility of mapping a horizon using head waves
- Refraction blind spot
- Interpreting marine refraction data