View source for Velocity analysis using common-reflection-point gathers

{{SDA publication 
 | title   = Seismic Data Analysis
 | image   = [[File:Seismic-data-analysis.jpg|frameless|180px]]
 | width   = 120px
 | series  = Investigations in Geophysics
 | part    = 
 | chapter = 
 | frompg  =
 | topg    =
 | author  = [[Öz Yilmaz]]
 | doi     = 10.1190/1.9781560801580
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 | store   = http://shop.seg.org/OnlineStore/ProductDetail/tabid/177/Default.aspx?ProductId=847
 | isbn    = ISBN 978-1-56080-094-1
}}

The next [[field data example]] demonstrates the use of constant-velocity prestack time [[migration]] to generate selected CMP gathers in their migrated positions to determine [[migration velocities]]. Figure 5.4-12 shows a CMP stack without DMO correction; the exploration objective requires delineation of fault blocks which manifest themselves with phantom diffractions. These diffractions conflict with the gently dipping reflections associated with the surrounding strata. Poststack time [[migration]] of the CMP stack without DMO correction falls short of providing a crisp image of the fault blocks (Figure 5.4-13).

[[Dip-moveout correction]] preserves the phantom diffractions and [[fault-plane reflections]] on stacked data as shown in Figure 5.4-14. As a result, [[migration]] of the DMO stack (Figure 5.4-15) enables a better delineation of the [[fault planes]] as compared with the [[migration]] of the conventional CMP stack without DMO correction (Figure 5.4-13).

{|class="wikitable" style="text-align:center; width:300px; height:200px; "border="1"
|+ '''Table 5-4.''' Velocity function derived from the constant-velocity [[migration]] panel of Figure 5.4-16.
|-
|Two-way Zero-Offset time, ms ||RMS Velocity Picked, m/s
|-
|0 ||1500
|-
|450 ||1500
|-
|700 ||1600
|-
|900 ||1750
|-
|1050 ||1900
|-
|1200 ||2200
|-
|1500 ||2500
|-
|2000 ||2800
|-
|2350 ||3000
|-
|2500 ||3000
|}

{|class="wikitable" style="text-align:center; width:300px; height:200px; "border="1"
|+ '''Table 5-5.''' Velocity function derived from the constant-velocity [[migration]] panel of Figure 5.4-17.
|-
|Two-way Zero-Offset time, ms ||RMS Velocity Picked, m/s
|-
|0 ||1500
|-
|400 ||1500
|-
|750 ||1700
|-
|900 ||1800
|-
|1050 ||2000
|-
|1350 ||2300
|-
|1500 ||2600
|-
|2050 ||2900
|-
|2500 ||3000
|}

To derive a [[migration]] velocity field, we perform prestack time [[migration]] using a range of constant velocities and generate selected gathers at their migrated positions. The interval for output gathers is specified in accordance with the degree of [[lateral velocity variations]] that can be accommodated by time [[migration]]. An interval equal to a cable length is a reasonable rule to follow. Figures 5.4-16 through 5.4-19 show [[migration]] velocity panels at four midpoint locations. The way to use these panels to pick rms velocity functions at analysis locations is similar to the use of a CMP gather that has been normal-moveout corrected using a range of constant velocities (Figure 3.2-11). In both cases, a velocity function is picked based on the criterion of flatness of events. The flatness of an event on a moveout-corrected gather means that the moveout velocity associated with that event is optimum. Similarly, the flatness of an event on a CMP gather created by prestack time [[migration]] means that the image below the midpoint location associated with that gather is the same irrespective of offset, and thus [[migration]] velocity is correct. Erroneously too low velocity yields a moveout on a gather from prestack time [[migration]] similar to the moveout of an event on a CMP gather which has been overcorrected. Similarly, erroneously too high velocity yields a moveout on a gather from prestack time [[migration]] much like to the moveout of an event on a CMP gather which has been undercorrected. Observe flat, over- and undercorrected events in the velocity panels shown in Figures 5.4-16 through 5.4-19, and pick for each CMP location rms velocity functions. Tables 5-4 through 5-7 list the picked rms velocity functions.

{|class="wikitable" style="text-align:center; width:300px; height:200px; "border="1"
|+ '''Table 5-6.''' Velocity function derived from the constant-velocity [[migration]] panel of Figure 5.4-18.
|-
|Two-way Zero-Offset time, ms ||RMS Velocity Picked, m/s
|-
|0 ||1500
|-
|375 ||1500
|-
|700 ||1700
|-
|950 ||2000
|-
|1100 ||2200
|-
|1350 ||2350
|-
|1500 ||2450
|-
|2500 ||3000
|}

{|class="wikitable" style="text-align:center; width:300px; height:200px; "border="1"
|+ '''Table 5-7.''' Velocity function derived from the constant-velocity [[migration]] panel of Figure 5.4-19.
|-
|Two-way Zero-Offset time, ms ||RMS Velocity Picked, m/s
|-
|0 ||1500
|-
|350 ||1500
|-
|650 ||1750
|-
|750 ||1800
|-
|950 ||2000
|-
|1250 ||2500
|-
|1750 ||2700
|-
|2500 ||3000
|}

There is one very important aspect of the constant-velocity [[migration]] panel as in Figure 5.4-19 and the constant-velocity moveout panel as in Figure 3.2-11. When picking a moveout velocity function from the latter, you are tracking the same event at the same reflection point from gather to gather in the same panel — overcorrected at low velocities, flat at optimum velocity value and undercorrected at high velocities. Whereas, when picking an rms velocity function from the former, you are not tracking the event at the same reflection point because of the lateral positioning effect of [[migration]].

<gallery>file:ch05_fig4-12.png|{{figure number|5.4-12}} A portion of a CMP stack from an area with fault blocks. (Data courtesy BHP Petroleum.)
file:ch05_fig4-13.png|{{figure number|5.4-13}} Poststack time [[migration]] of the CMP stack shown in Figure 5.4-12. Note the undermigration caused by the 2-D [[migration]] of 3-D behavior of the fault-plane diffractions and reflections ([[introduction to 3-D seismic exploration|3-D seismic exploration]]).
file:ch05_fig4-14.png|{{figure number|5.4-14}} DMO stack associated with the data set as in Figure 5.4-12.
file:ch05_fig4-15.png|{{figure number|5.4-15}} Poststack time [[migration]] of the DMO stack shown in Figure 5.4-14. Note the undermigration caused by the 2-D [[migration]] of 3-D behavior of the fault-plane diffractions and reflections ([[introduction to 3-D seismic exploration|3-D seismic exploration]]).
file:ch05_fig4-16.png|{{figure number|5.4-16}} [[Migration]] [[velocity analysis]] panel for CMP 1161 of the data set as in Figure 5.4-12. The panel is created by performing prestack time [[migration]] using a range of constant velocities and displaying the results at CMP location 1161.
file:ch05_fig4-17.png|{{figure number|5.4-17}} [[Migration]] [[velocity analysis]] panel for CMP 1561 of the data set as in Figure 5.4-12. The panel is created by performing prestack time [[migration]] using a range of constant velocities and displaying the results at CMP location 1561.
file:ch05_fig4-18.png|{{figure number|5.4-18}} [[Migration]] [[velocity analysis]] panel for CMP 1961 of the data set as in Figure 5.4-12. The panel is created by performing prestack time [[migration]] using a range of constant velocities and displaying the results at CMP location 1961.
file:ch05_fig4-19.png|{{figure number|5.4-19}} [[Migration]] [[velocity analysis]] panel for CMP 2361 of the data set as in Figure 5.4-12. The panel is created by performing prestack time [[migration]] using a range of constant velocities and displaying the results at CMP location 2361.
file:ch05_fig4-20.png|{{figure number|5.4-20}} Time [[migration]] velocity field computed from the vertical velocity functions picked from the [[migration]] [[velocity analysis]] panels as in Figures 5.4-16 through 5.4-19.
file:ch05_fig4-21.png|{{figure number|5.4-21}} Selected image gathers from prestack time [[migration]] using the velocity field shown in Figure 5.4-20. These gathers were obtained from data which were subjected to [[multiple attenuation]] prior to prestack time [[migration]]. Compare with the gathers shown in Figure 6.0-39.
file:ch05_fig4-22.png|{{figure number|5.4-22}} The stack of image gathers as in Figure 5.4-21 derived from prestack time [[migration]]. Compare with Figure 6.0-40.
file:ch03_fig2-11.png|{{figure number|3.2-11}} Stacked amplitude along a hyperbolic trajectory. Amplitudes ''f<sub>i,t(i)</sub>'' along the best-fit hyperbola (equation {{EquationNote|17}}) defined by optimum stacking velocity ''v<sub>stk</sub>'' are summed to get the stacked amplitude ''S'' (equation {{EquationNote|16}}).
</gallery>

By interpolating between the picked rms velocity functions as listed in Tables 5-4 through 5-7, a velocity field for time [[migration]] can be created (Figure 5.4-20). By using this velocity field, data are migrated before stack. The common-reflection-point (CRP) gathers in Figure 5.4-21 exhibit flatness of events — a way to check the accuracy of the [[migration]] velocity field. Stacking the CRP gathers yields the image from prestack time [[migration]] as shown in Figure 5.4-22. Admittedly, there is some undermigration caused by the 3-D geometry of the [[fault planes]] which can be adequately imaged only by [[3-D migration]]. Nevertheless, compare with [[migration|migrations]] of the conventional stack (Figure 5.4-13) and DMO stack (Figure 5.4-15), and note that the faults have been delineated much more distinctively. Such differences — conflicting dips with different stacking velocities associated with fault blocks and salt diapirs where vertical velocity variations may be beyond the accuracy of DMO correction, are one motivation for doing time [[migration]] before stack.

Limitations in picking reliable velocity functions are the same as those associated with constant-velocity moveout panels (Figure 3.2-11). Shortening of effective cable length at shallow times because of muting, interference of linear noise and multiples all impose a limit on the picking accuracy ([[introduction to noise and multiple attenuation|noise and multiple attenuation]]).

==See also==
*[[Prestack Stolt migration]]
*[[Common-offset migration of DMO-corrected data]]
*[[Prestack Kirchhoff migration]]
*[[Focusing analysis]]
*[[Fowler’s velocity-independent prestack migration]]

==External links==
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[[Category: Dip-moveout correction and prestack migration]]
[[Category: Migration velocity analysis]]