Weathering corrections and dip/depth calculations

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 4.16a

Figure 4.16a shows part of a seismic record where the geophone group spacing is 50 m and the offset to the nearest group is 50 m and that to the far group 600 m. What is the apparent velocity of the first breaks?

Background

The weathered layer or low-velocity layer (LVL) is a shallow layer that usually extends from the surface downward for 4 to 50 m and is characterized by low velocity of the order of 250 to 1000 m/s. Often the base of the LVL is near to or coincident with the water table, and many of the pore spaces in the LVL are filled with air. The LVL is important because of the high absorption in it and because its low (and frequently quite variable) velocity has considerable effect on the traveltime. The velocity change at the base of the LVL is usually large, making it a good reflector and therefore important in the generation of multiples (see problem 3.8) and in P- to S-wave conversion. The large velocity change at its base also bends raypaths from below the LVL so that they are nearly vertical within the LVL regardless of their direction below the LVL.

Figure 4.16a.  Seismic record (courtesy Chevron).

The first energy from a source to arrive at the geophone groups is called the first break. When the source is below the base of the LVL, as in Figure 4.16b, first-break raypaths are almost parallel to the base of the LVL until they are refracted upwards at approximately the critical angle $\theta _{c}$ (see problem 4.18).Writing $V_{W}$ and $V_{H}$ for the velocities in the LVL and just below it, $\sin \theta _{c}=V_{W}/V_{H}$.

Figure 4.16b.  Refraction weathering profile.

Solution

The slope of the first breaks is about 0.200 s/600 m, or a velocity of 3000 m/s.

Problem 4.16b

Assuming that the source is just below the base of the LVL and that the LVL velocity is 500 m/s, how thick is the LVL?

Solution

The uphole time is about 31 ms, so the depth of the base of the LVL is $D_{w}=500\times 0.031=16$ m.

Problem 4.16c

Arrival times at the sourcepoint for two reflections are given as 0.475 and 0.778 s; what is the average velocity to these reflectors?

Solution

The normal moveout equation [see equation (4.1c)] is $\Delta t_{\rm {NMO}}=x^{2}/2V^{2}t_{0}$, so $V=(x^{2}/2t_{0}\Delta t_{\rm {NMO}})^{1/2}$. The NMO measure gives about 0.040 ms/600m = 0.067 ms/km for the 0.475 s reflection and about 0.037 ms/600m = 0.062 ms/km for the 0.778 s reflection; this gives velocities of 2.4 km/s and 1.9 km/s, respectively.

Problem 4.16d

For these reflections, the arrival-time differences between the far traces in opposite directions from the source point are given as $+0.005$ s for both reflections. What are the reflector dips?

Solution

For dip moveouts of 0.005 s/600m = 0.0083 s/km, equation (4.2b) gives for the 0.475 s reflection, $\sin \xi =(2.4/2)\times 0.0083=0.010$, $\xi =0.6^{\circ }$. For the deeper reflection we get $\sin \xi =(1.9/2)\times 0.0083$, $\xi =0.5^{\circ }$.

Problem 4.16e

What is the dominant frequency of these reflections (approximately)?

Solution

Counting the number of cycles in 0.1 s at the arrival times of the two reflections, we get approximately 80 and 60 Hz.

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Depth and dip calculations using velocity functions	Using a velocity function linear with depth
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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

External links

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