Effect of migration on plotted reflector locations

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 4.8a

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 $45^{\circ }$ to the left of the central uplift and $55^{\circ }$ 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 $40^{\circ }$ to the left and about $55^{\circ }$ 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${\overline {V}}$ 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 $\sin \xi =(V/2)\Delta t_{d}/\Delta x$, where $\xi$ is the dip and $\Delta t_{d}/\Delta x$ is the dip moveout. For $V=2500$ m/s,

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

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

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

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

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 $A$ has a dip moveout of 45 ms/kft, dips about $15^{\circ }$, and extends downward from about 7 to 10 kft. Assuming straight rays, this gives a horizontal displacement of $z\tan \xi =1900$ to 2700 ft. The shallow continuation of $A$, event $B$, has dip moveout of 80 ms/kft and dips about $25^{\circ }$; it extends from about 2 to 7 kft and has horizontal displacements of 930 to 3250 ft. If the dip change from $A$ to $B$ is abrupt, the events may overlap before migration.

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

Allowing for raypath curvature would decrease these displacements.

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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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