# Feasibility of mapping a horizon using head waves

Series | Geophysical References Series |
---|---|

Title | Problems in Exploration Seismology and their Solutions |

Author | Lloyd P. Geldart and Robert E. Sheriff |

Chapter | 11 |

Pages | 415 - 468 |

DOI | http://dx.doi.org/10.1190/1.9781560801733 |

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## 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?

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.

## Continue reading

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Comparison of refraction interpretation methods | Refraction blind spot |

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Geologic interpretation of reflection data | 3D methods |

## 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