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Problem 4.10a

4.10a Two intersecting spreads have bearings N10E and N140E. If the first spread shows an event at s with dip moveout of 56 ms/km down to the south and the same event on the second spread has a dip moveout of 32 ms/km down to the northwest. Assume average velocity of 3.00 km/s.

  1. Find the true dip, depth, and strike.
  2. What are the values if the dip on the second spread is southeast?


We first give numerical solutions, then graphical solutions.

i) We take the -axis in the N40W direction, the -axis in the N130W direction, and the -axis in the N170W direction (see Figure 4.10a). We now use equation (4.2j) to calculate for .

Figure 4.10a.  Dips northwest and southwest.

hence, ms/km; total dip moveout ms/km, dip ,

depth km (normal to bed).

ii) We take the -axis in the S10W direction (see Figure 4.10b) where , so

The positive -axis is toward S80E, so the minus sign means that the -component of dip is in the N80W direction.

Figure 4.10b.  Dips southeast and southwest.

The strike is measured relative to the negative direction of the -axis as shown in Figure 4.2d where both dip components are positive; when the -component of dip is negative, as it is here, the strike line goes from to a point on the negative -axis. Referring to Figure 4.10b, we see that the strike line is rotated counter-clockwise from the negative direction. Graphical solutions for (i) and (ii) are shown in Figure 4.10c.

Figure 4.10c.  Graphical solutions to cross-dip problem.

Problem 4.10b

4.10b Calculate the position of the reflecting point (migrated position) for each spread in (i) as if the cross information had not been available and each had been assumed to indicate total moveout; compare with the result of part (a). Would the errors be more or less serious if the calculations were made for the usual situation where the velocity increases with depth?


We find the coordinates of the migrated reflecting points assuming the velocity is constant at the value of the average velocity. We take the -, -, and -axes positive to the south, west, and downward, respectively, the source being at the origin.

In (i) the spread along the -axis with bearing N10E has dip moveout down to the south and west (Figure 4.10b), hence

Since the dip is mainly south and west, the reflection point is shifted north and east along the spread direction, the distance m. Resolving this along the - and -axes, we get m and m. The vertical depth is m, giving coordinates ().

For the spread bearing S140E (Figure 4.10b),

The reflecting point is m north and west of the source. Thus, m, m, m, so the coordinates are .

Taking into account cross-dip, the total dip is down to the south and west. The horizontal displacement of the reflecting point is m in the direction . Thus, m, m, m. The coordinates are now . The change in is small but the - and -coordinates vary considerably, both percentagewise and in absolute values.

The errors become more serious when the velocity increases with depth because these calculations are based on the average velocity rather than the interval velocity , which is usually greater than .

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Resolution of cross-dip Variation of reflection point with offset
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Partitioning at an interface Seismic velocity

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