# Difference between revisions of "Variation of reflectivity with angle (AVA)"

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* [[Amplitude/energy of reflections and multiples]] | * [[Amplitude/energy of reflections and multiples]] | ||

* [[Reflection/transmission coefficients at small angles and magnitude]] | * [[Reflection/transmission coefficients at small angles and magnitude]] | ||

+ | * [[Magnitude]] | ||

* [[AVO versus AVA and effect of velocity gradient]] | * [[AVO versus AVA and effect of velocity gradient]] | ||

## Latest revision as of 09:17, 25 February 2019

Series | Geophysical References Series |
---|---|

Title | Problems in Exploration Seismology and their Solutions |

Author | Lloyd P. Geldart and Robert E. Sheriff |

Chapter | 3 |

Pages | 47 - 77 |

DOI | http://dx.doi.org/10.1190/1.9781560801733 |

ISBN | ISBN 9781560801153 |

Store | SEG Online Store |

## Contents

## Problem 3.12a

The values in Table 3.12a illustrate the differences that the interstitial fluid can produce. Calculate the reflectivity for shale-brine sand and shale/gas sand interfaces at incident angles of , , , , and .

### Background

It is difficult to tell from the Zoeppritz equations how the variation of amplitude with angle of incidence is affected by changes in the various parameters involved. Shuey (1985) simplified the equations by assuming that the changes in physical properties at an interface are small, so that the raypath bending is small, resulting in Shuey’s equation:

Medium | (m/s) | (m/s) | (g/cm) | |
---|---|---|---|---|

Shale | 2742 | 1394 | 2.062 | 1.967 |

Brine sand | 2833 | 1470 | 2.078 | 1.927 |

Gas sand | 2371 | 1473 | 2.044 | 1.610 |

**(**)

where

**(**)

**(**)

and is Poisson’s ratio.

Hilterman (1989) introduced additional approximations resulting in

**(**)

### Solution

Note that 4 significant figures are required to illustrate the effect. We first calculate for the three beds using equation (10,2) in Table 2.2a:

We take the following average values and increments : , , ,

Using these values for the Shuey equation for the shale/brine-sand interface, equations (3.12a,b,c) give

At the shale-gas sand interface, averages and increments are , , , , ,

Substituting , in equation (3.12d), we get for the Hilterman equation (3.12d) for the shale/brine-interface,

For shale/brine sand | |||||

Shuey equation | 0.0202 | 0.0182 | 0.0128 | 0.0052 | –0.0022 |

Hilterman equation | 0.0202 | 0.0189 | 0.0152 | 0.0095 | 0.0026 |

For the shale/gas sand | |||||

Shuey equation | –0.0765 | –0.0881 | –0.1221 | –0.1782 | –0.2558 |

Hilterman equation | –0.0765 | –0.0837 | –0.1044 | –0.1361 | –0.1750 |

The Hilterman equation (3.12d) for the shale/gas-sand interface is

Table 3.12b compares the values given by the Shuey and Hilterman equations and the results are graphed in Figure 3.12a.

The two equations give essentially the same results for angles up to . The increase of amplitude with angle (offset) is larger with the Shuey equation. An additional term that becomes important at large angles is sometimes added to these equations.

## Continue reading

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---|---|

AVO versus AVA and effect of velocity gradient | Accuracy of normal-moveout calculations |

Previous chapter | Next chapter |

Theory of Seismic Waves | Geometry of seismic waves |

## Also in this chapter

- General form of Snell’s law
- Reflection/refraction at a solid/solid interface and displacement of a free surface
- Reflection/refraction at a liquid/solid interface
- Zoeppritz’s equations for incident SV- and SH-waves
- Reinforcement depth in marine recording
- Complex coefficient of reflection
- Reflection and transmission coefficients
- Amplitude/energy of reflections and multiples
- Reflection/transmission coefficients at small angles and magnitude
- Magnitude
- AVO versus AVA and effect of velocity gradient