Weathering and elevation (near-surface) corrections

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Problem 8.18a

Show that when the source is below the LVL, weathering and elevation corrections for a geophone at the source are given by

Figure 8.18a.  Calculation of weathering corrections.

where and are the elevations of the source point and datum, is the depth of the source, and is the uphole time.

Background

Corrections are necessary to eliminate the effect of changes in the elevation of the surface and in the thickness of and velocity in the LVL. The corrections in effect reduce the traveltimes to those that would be observed if the source and geophones were located on a reference datum, usually a horizontal plane below the base of the low-velocity layer. These corrections are called static corrections because they are the same for all reflections regardless of their arrival times.

Solution

In Figure 8.18a, the correction to the traveltime for a wave going from the source at down to the datum is


(8.18a)

The correction for travel from the datum up to a geophone at the source point is


(8.18b)

so the total correction for the traveltime for a geophone at the source point is


(8.18c)

Problem 8.18b

If the split spread in Figure 8.18a is used to find the dip, what correction must be applied to the dip moveout?

Solution

The dip moveout is obtained by subtracting traveltimes at sources and in Figure 8.18b. If traveltimes have not been corrected for weathering and elevation, the dip moveout must be corrected; this is the differential weathering correction . Using equation (8.18b) we have


(8.18d)
Figure 8.18b.  Differential weathering correction.

Problem 8.18c

Derive an expression to correct the traveltime for a geophone at in Figure 8.18b and being source points.

Solution

We use the first-break traveltimes and that correspond to the paths and . The velocity contrast at the base of the LVL is usually large enough that the paths and are so close to vertical that the distance is very small. Hence the sum is given by


(8.18e)

where is the traveltime through the LVL at , and . Therefore the correction that effectively places the geophone at on the datum is


(8.18f)

We must add to this the correction that locates the source on the datum, namely , given by equation (8.18a). Thus the total correction for a traveltime recorded at is


(8.18g)

Problem 8.18d

The weathering and elevation corrections given by equations (8.18a) to (8.18g) assume that the source is below the base of the LVL. What changes are required if the source is within the LVL?

Solution

When the source is within the LVL, the wave traveling down to the datum is in the LVL for the distance , hence equation (8.18a) is changed to


(8.18h)

where . Equation (8.18b) is unchanged provided we use the value of in equation (8.18h). Equation (8.18c) becomes


(8.18i)

Equation (8.18d) is unchanged provided we use equation (8.18h) for . Equation (8.18e) becomes

where , . Thus, equation (8.18e) becomes


(8.18j)

Equations (8.18f,g) are unchanged except that we must use the values of and from equations (8.18j) and (8.18h).

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