Calculation of reflector depths and dips

Problems in Exploration Seismology and their Solutions

Series	Geophysical References Series
Title	Problems in Exploration Seismology and their Solutions
Author	Lloyd P. Geldart and Robert E. Sheriff
Chapter	4
Pages	79 - 140
DOI	http://dx.doi.org/10.1190/1.9781560801733
ISBN	ISBN 9781560801153
Store	SEG Online Store

Problem 4.6

In Figure 4.6a assume that the depth to 1.0 s is 1500 m and that the interval velocity between 1.0 and 1.4 s is 3300 m/s, and the trace spacing is 100 m. Calculate the depths and dips of the four picked reflectors.

Figure 4.6a.  Portion of a reflection section (from Fitch, 1976).

Solution

There are 126 trace intervals corresponding to 12.6 km between the end traces. We have timed four reflections (on an enlargement) at the end traces to the nearest millisecond, giving the depths:

${\begin{aligned}A&=1.075\ \mathrm {s} \to 1500+(3300/2)\times 0.075=1624\ \mathrm {m} ;\quad A'=1.045\ \mathrm {s} \to 1574\ \mathrm {m} ;\\B&=1.200\ \mathrm {s} \to 1830\ \mathrm {m} ;\quad B'=1.184\ \mathrm {s} \to 1804\ \mathrm {m} ;\\C&=1.308\ \mathrm {s} \to 2008\ \mathrm {m} ;\quad C'=1.302\ \mathrm {s} \to 1998\ \mathrm {m} ;\\D&=1.347\ \mathrm {s} \to 2073\ \mathrm {m} ;\quad D'=1.347\ \mathrm {s} \to 2074\ \mathrm {m} .\end{aligned}}$

The dips of the four reflections are given by tan $\xi =\Delta z/\Delta x$:

${\begin{aligned}\tan \xi _{\rm {A}}&=(1624-1574)/12.60=3.97\ \mathrm {m/km} ,\qquad \xi _{\rm {A}}=0^{\circ }14';\\\tan \xi _{\rm {B}}&=2.06\ \mathrm {m/km} ,\qquad \xi _{\rm {B}}=0^{\circ }7';\\\tan \xi _{\rm {C}}&=0.79\ \mathrm {m/km} ,\qquad \xi _{\rm {C}}=0^{\circ }3';\\\tan \xi _{\rm {D}}&=-0.08\ \mathrm {m/km} ,\qquad \xi _{\rm {D}}=0^{\circ }0'.\end{aligned}}$

The section is thickening to the right. Although the seismic reflections are nearly flat, the small dip can be measured.

Note that all four reflections have slight bending and changes in character about one-third of the way from the left end, suggesting that something unresolvable is happening here, perhaps a very small fault.

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Partitioning at an interface	Seismic velocity
Table of Contents (book)

Also in this chapter

• Accuracy of normal-moveout calculations
• Dip, cross-dip, and angle of approach
• Relationship for a dipping bed
• Reflector dip in terms of traveltimes squared
• Second approximation for dip moveout
• Calculation of reflector depths and dips
• Plotting raypaths for primary and multiple reflections
• Effect of migration on plotted reflector locations
• Resolution of cross-dip
• Cross-dip
• Variation of reflection point with offset
• Functional fits for velocity-depth data
• Relation between average and rms velocities
• Vertical depth calculations using velocity functions
• Depth and dip calculations using velocity functions
• Weathering corrections and dip/depth calculations
• Using a velocity function linear with depth
• Head waves (refractions) and effect of hidden layer
• Interpretation of sonobuoy data
• Diving waves
• Linear increase in velocity above a refractor
• Time-distance curves for various situations
• Locating the bottom of a borehole
• Two-layer refraction problem

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