Difference between revisions of "Dictionary:Nonhyperbolic normal-moveout (velocity) analysis"

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<translate>{{#category_index:N|nonhyperbolic normal-moveout (velocity) analysis}}
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Analysis that allows for typical vertical changes in velocity and anisotropy when using long offsets, that is, where the offset exceeds the reflector depth. In this case the hyperbolic equation for a reflection can often be expressed as  
 
Analysis that allows for typical vertical changes in velocity and anisotropy when using long offsets, that is, where the offset exceeds the reflector depth. In this case the hyperbolic equation for a reflection can often be expressed as  
  
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<center><math>t_x^2 = t_0^2\left[ 1+\left(\frac{x}{t_0V}\right)^2-\frac {2\eta \left(\frac{x}{t_0V}\right)^4}{1+(1+2\eta)\left(\frac{x}{t_0V}\right)^2}\right]</math>,</center>
 
<center><math>t_x^2 = t_0^2\left[ 1+\left(\frac{x}{t_0V}\right)^2-\frac {2\eta \left(\frac{x}{t_0V}\right)^4}{1+(1+2\eta)\left(\frac{x}{t_0V}\right)^2}\right]</math>,</center>
  
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where ''t''<sub>0</sub> is the zero-offset traveltime, ''x'' is offset, ''V'' is P-wave velocity, and <math>\eta=\frac{\varepsilon-\delta}{1+2\delta}
 
where ''t''<sub>0</sub> is the zero-offset traveltime, ''x'' is offset, ''V'' is P-wave velocity, and <math>\eta=\frac{\varepsilon-\delta}{1+2\delta}
 
</math> where <math>\varepsilon</math> and <math>\delta</math> are [[Special:MyLanguage/Dictionary:Thomsen_anisotropic_parameters_(tom&#x2019;_s&#x2202;n)|''Thomsen anisotropic parameters'']] (q.v.).  
 
</math> where <math>\varepsilon</math> and <math>\delta</math> are [[Special:MyLanguage/Dictionary:Thomsen_anisotropic_parameters_(tom&#x2019;_s&#x2202;n)|''Thomsen anisotropic parameters'']] (q.v.).  
  
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Use of the 4<sup>th</sup>-order term given by a Taylor expansion corrects for the undesirable "hockey-stick" effect.
 
Use of the 4<sup>th</sup>-order term given by a Taylor expansion corrects for the undesirable "hockey-stick" effect.
 
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Revision as of 20:57, 24 March 2018

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Analysis that allows for typical vertical changes in velocity and anisotropy when using long offsets, that is, where the offset exceeds the reflector depth. In this case the hyperbolic equation for a reflection can often be expressed as

,

where t0 is the zero-offset traveltime, x is offset, V is P-wave velocity, and where and are Thomsen anisotropic parameters (q.v.).

Use of the 4th-order term given by a Taylor expansion corrects for the undesirable "hockey-stick" effect.