View source for Models with horizontal layers

{{SDA publication 
 | title   = Seismic Data Analysis
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 | series  = Investigations in Geophysics
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 | author  = [[Öz Yilmaz]]
 | doi     = 10.1190/1.9781560801580
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In this section, we shall examine the accuracy of [[Dix conversion]] and [[coherency inversion]] to estimate layer velocities using two earth models with horizontal layers, but with [[lateral velocity variations]]. The near-surface layer is of constant velocity in the first model and its velocity varies laterally in the second model. Otherwise, both models are identical. Shown in Figure 9.1-1a are the velocity profiles for the six layers in the model. We shall refer to the layers by the horizon names corresponding to the base of each layer, H1 through H6. Listed in Table 9-2 are the layer velocities and depths to the base of each layer. When the layer velocity is not constant, the range is given in Table 9-1. The lateral velocity gradients in layers H3 and H4 are about 125 m/s and 200 m/s over one cable length, respectively. Figure 9.1-1b shows the velocity-depth model with the color bar on the right-hand margin.

<gallery>
file:ch09_fig1-1.png|{{figure number|9.1-1}} An earth model that comprises six flat layers: (a) the interval velocity profiles for the six horizons H1-H6; (b) true velocity-depth model created from the profiles in (a).
file:ch09_fig1-2.png|{{figure number|9.1-2}} (a) The CMP-stacked section derived from the modeled common-shot gathers using the earth model shown in Figure 9.1-1b; (b) the stacking velocity section.
file:ch09_fig1-3.png|{{figure number|9.1-3}} Horizon-consistent stacking velocity semblance spectra computed from the CMP gathers of the synthetic data as in Figure 9.1-2a along the time horizons H1-H6.
</gallery>

A total of 384 shot records was modeled using the two-way acoustic wave equation. The simulated recording geometry consists of an off-end cable with 96 receivers and offset range 25-2400 m. Shot and receiver intervals are both 25 m, and the CMP interval is 12.5 m and CMP fold is 48. Figure 9.1-2a shows the CMP-stacked section with the picked time horizons that correspond to the layer boundaries H1 through H6 in Figure 9.1-1b. Compare with the velocity-depth model (Figure 9.1-1b) and note that flat horizons in depth correspond to curved horizons in time because of the [[lateral velocity variations]] (Figure 9.1-1a). The stacking velocity section is shown in Figure 9.1-2b with the color bar on the right-hand margin. The stacking velocity section was derived from the horizon-consistent stacking velocity profiles shown in Figure 9.1-3.

{|class="wikitable" style="text-align:center; width:300px; height:200px; "border="1"
|+ '''Table 9-1.''' A set of [[inversion procedures for earth modeling]] in depth to estimate layer velocities and delineate reflector geometries.
|-
|''Layer Velocities'' ||''Reflector Geometries''
|-
|[[Dix conversion]] of rms velocities ||vertical-ray [[time-to-depth conversion]] (vertical stretch)
|-
|[[stacking velocity inversion]] ||image-ray [[time-to-depth conversion]] (map [[migration]])
|-
|[[coherency inversion]] ||poststack depth [[migration]]
|-
|image-gather analysis ||prestack depth [[migration]]
|}

{|class="wikitable" style="text-align:center; width:300px; height:200px; "border="1"
|+ '''Table 9-2.''' Parameters of the model with horizontal layers and constant-velocity near-surface layer.
|-
|Layer ||Velocity (m/s) ||Depth (m)
|-
|H1 ||1500 ||100
|-
|H2 ||2000 ||1000
|-
|H3 ||2400 – 2700 ||1500
|-
|H4 ||3000 – 3500 ||1800
|-
|H5 ||4500 ||2250
|-
|H6 ||3000 ||2700
|}

==See also==
* [[Dix conversion]]
* [[Coherency inversion]]
* [[Near-surface layer with laterally varying velocities]]

==External links==
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[[Category: Earth modeling in depth]]