# Effect of migration on plotted reflector locations

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

## Problem 4.8a

Figure 4.8a shows a hand-migrated section having the same horizontal and vertical scales. The steepest dips at a depth of about 1500 m below datum are around ${\displaystyle 45^{\circ }}$ to the left of the central uplift and ${\displaystyle 55^{\circ }}$ to the right. If the velocity is 2500 m/s, what are the dip moveouts and the horizontal distances between the migrated reflection points and the points of observation?

At a depth around 2500 m, the steepest dips are about ${\displaystyle 40^{\circ }}$ to the left and about ${\displaystyle 55^{\circ }}$ to the right, the latter extending to a depth of about 4000 m. If the velocity is 3500 m/s, what are the dip moveouts and horizontal displacements of these reflections?

### Background

After reflection events have been identified on an unmigrated seismic record section and their arrival times and dip moveouts measured, they can be migrated to place them at the reflector locations. When the dip moveout is zero, reflection points are located directly below the source, but otherwise they are located updip. Numerous methods are available for migrating events. The simplest hand-migration method is to assume constant velocity (usually the average velocity${\displaystyle {\overline {V}}}$ calculate source-reflector distances, and then swing arcs centered at the sources with radii equal to these distances.

Figure 4.8a.  Hand-migrated seismic section.
Figure 4.8b.  Migrated section in Wyoming thrust belt (from Harding et al., 1983).

### Solution

Equation (4.2b) states that ${\displaystyle \sin \xi =(V/2)\Delta t_{d}/\Delta x}$, where ${\displaystyle \xi }$ is the dip and ${\displaystyle \Delta t_{d}/\Delta x}$ is the dip moveout. For ${\displaystyle V=2500}$ m/s,

{\displaystyle {\begin{aligned}\Delta t_{d}/\Delta x=2\sin \xi /2500=800\sin \xi \ \mathrm {ms/km} .\end{aligned}}}

For ${\displaystyle \xi =45^{\circ }}$, the dip moveout is 566 ms/km, and for ${\displaystyle \xi =55^{\circ }}$, it is 655 ms/km. For constant velocity, horizontal displacement is ${\displaystyle \Delta x=z\tan \xi }$. For the depth 1500 m, ${\displaystyle x=1500}$ m for ${\displaystyle \xi =45^{\circ }}$ and 2140 m for ${\displaystyle \xi =55^{\circ }}$.

For the depth 2500 m and ${\displaystyle V=3500}$ m/s, the dip moveouts are

{\displaystyle {\begin{aligned}\Delta t_{d}/\Delta x&=571\sin \xi =367\ \mathrm {ms/km} \quad \mathrm {for} \quad \xi =40^{\circ },\\&=468\ \mathrm {ms/km} \quad \mathrm {for} \quad \xi =55^{\circ }.\end{aligned}}}

The horizontal displacements are, respectively, 2100 and 3570 m.

## Problem 4.8b

How far horizontally did selected reflections migrate in Figure 4.8b? This section has been plotted so that the scale is approximately 1:1 over the depth of principal interest, 10 to 20 kft.

### Solution

Although at first glance the band of energy in the thrust sheet in the central third of the section looks like parallel events, careful examination shows apparent downdip thinning. An increase of velocity with depth can produce this effect.

Figure 4.8c.  Portion of Figure 4.8b.

From the depth scale in Figure 4.8b, we estimate the average velocity to 1 s is 10 kft/s and from 1 s to 1.8 s is 12.5 kft/s. Event ${\displaystyle A}$ has a dip moveout of 45 ms/kft, dips about ${\displaystyle 15^{\circ }}$, and extends downward from about 7 to 10 kft. Assuming straight rays, this gives a horizontal displacement of ${\displaystyle z\tan \xi =1900}$ to 2700 ft. The shallow continuation of ${\displaystyle A}$, event ${\displaystyle B}$, has dip moveout of 80 ms/kft and dips about ${\displaystyle 25^{\circ }}$; it extends from about 2 to 7 kft and has horizontal displacements of 930 to 3250 ft. If the dip change from ${\displaystyle A}$ to ${\displaystyle B}$ is abrupt, the events may overlap before migration.

Event ${\displaystyle C}$ has about the same dip moveout as event ${\displaystyle A}$ and the dip extends from about 17 to 20 kft with horizontal displacements of 4600 to 5400 ft. Event ${\displaystyle D}$ with about the same dip moveout as event ${\displaystyle B}$ extends from about 9 to 17 kft with horizontal displacements of 4200 to 7900 ft.

Allowing for raypath curvature would decrease these displacements.