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In an ideal world, there is an obvious agreement between the seismic line trace and the synthetic seismogram. A formation top or other correlation marker on the well log can then be tied to the corresponding seismic horizon with relative ease. In the real world, however, the interpreter may be, and often is, confronted with a synthetic trace and seismic data trace that bear little resemblance to each other. Variations in the quality of the well log data can have a major impact on the final synthetic display. A sonic log that was generated from a borehole containing numerous washed out zones will contain areas of unrealistic velocities. Careful editing of the well log data can help to smooth spurious data readings and generate a more realistic synthetic. Care should be taken, however, whenever well log data are edited. For more details about synthetic seismograms, the interested reader can refer to ''Seismic Exploration Fundamentals'' (Coffen, 1978).
 
In an ideal world, there is an obvious agreement between the seismic line trace and the synthetic seismogram. A formation top or other correlation marker on the well log can then be tied to the corresponding seismic horizon with relative ease. In the real world, however, the interpreter may be, and often is, confronted with a synthetic trace and seismic data trace that bear little resemblance to each other. Variations in the quality of the well log data can have a major impact on the final synthetic display. A sonic log that was generated from a borehole containing numerous washed out zones will contain areas of unrealistic velocities. Careful editing of the well log data can help to smooth spurious data readings and generate a more realistic synthetic. Care should be taken, however, whenever well log data are edited. For more details about synthetic seismograms, the interested reader can refer to ''Seismic Exploration Fundamentals'' (Coffen, 1978).
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==Creating a synthetic seismogram==
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Once a stratigraphic model has been built using velocities and densities, a synthetic seismogram (or synthetic) can be constructed to identify seismic reflections. A synthetic seismogram is the fundamental link between well data and seismic data, and it is the main tool (along with a VSP, if available) that allows geological picks to be associated with reflections in the seismic data. As discussed, if a VSP is available for a particular well, a synthetic is not needed. The VSP directly measures both time and depth to a formation of interest. Usually synthetic seismograms are created using specialized software. The user may be unaware of the process that creates them. The table below lists the steps necessary to create a synthetic seismogram manually.
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{| class = "wikitable"
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|-
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! Step
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! Action
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|-
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| 1
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| Edit the sonic and density logs for bad intervals.
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|-
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| 2
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| Calculate vertical reflection times.
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|-
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| 3
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| Calculate reflection coefficients, R<sub>o</sub> .
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|-
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| 4
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| Combine the last two items to create a reflection coefficient time series.
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|-
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| 5
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| Convolve the reflection coefficient series with the wavelet.
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|}
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==Reflection coefficient==
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The normal-incidence reflection coefficient for a rock contact is an important quantity. Sheriff (1984) defines it as “the ratio of the amplitude of the displacement of a reflected wave to that of the incident wave.” Mathematically, reflection coefficient can be expressed as
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:<math>R_{0} = \frac{(\rho_{2} \upsilon_{2} - \rho_{1} \upsilon_{1})}{(\rho_{2} \upsilon_{2} + \rho_{1} \upsilon_{1})}</math>
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where:
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* ρ = rock density
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* ''υ'' = rock velocity
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* 1 = parameters above the interface
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* 2 = parameters below the interface
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==Convolutional model==
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The final simulated seismic trace can be summarized by the convolutional model:
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:<math>T(t) = R_{0}(t) * w(t) + n(t)</math>
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where:
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* ''T''(''t'') = seismic trace
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* ''R''<sub>0</sub>(''t'') = reflection coefficient series (spikes)
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* * = convolution
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* ''w''(''t'') = wavelet
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* ''n''(''t'') = noise
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This model of the seismic trace assumes many things, including removal of all amplitude effects except R<sub>0</sub>. The job of seismic data processors is to deliver data to the interpreter in a form consistent with the convolutional model, but it is hard to get it right.
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==Example synthetic seismogram==
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[[file:interpreting-seismic-data_fig12-7.png|thumb|{{figure number|12-7}}From software by S. Hill, Conoco.]]
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The figure below shows a simple synthetic seismogram. We can see most of the components that go into the creation of a synthetic seismogram—the velocity model, reflection coefficient series, individual wavelets, synthetic trace, and simulated stack section (lower plot). The velocity model is from north-central Oklahoma. The density model is not shown.
    
==See also==
 
==See also==
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* [[Building a stratigraphic model]]
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* [[Matching synthetics to data]]
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* [[Identifying reflectors]]
 
* [[Seismic interpretation]]
 
* [[Seismic interpretation]]
 
* [[Vertical and lateral seismic resolution and attenuation]]
 
* [[Vertical and lateral seismic resolution and attenuation]]
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* [http://store.aapg.org/detail.aspx?id=612 Find the book in the AAPG Store]
 
* [http://store.aapg.org/detail.aspx?id=612 Find the book in the AAPG Store]
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[[Category:Geophysical methods]]
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[[Category:Geophysical methods]][[Category:Interpreting seismic data]]

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