# Bortfeld equation

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Yet Another Linear Approximation to the Zoeppritz equation, from Bortfeld (1961).^{[1]}

## Contents

## Original formulation

[Find the paper and add this]

## Basic formulation

This formulation is from the Stanford Exploration Project, dated 6/8/2002.^{[2]}

where

## Stack-contrained form

Again, from SEP.^{[3]} Due to Fred Herkenhoff of Chevron. The stack amplitude is given by:

where and are the averages of sin^{2}*θ* and tan^{2}*θ* over the range of input angles to the stack.

According to SEP, "this form can now be inverted for the zero-offset reflectivity (RO) and the P-wave reflectivity (RP) without needing the interval velocities."

## Implementation in Modelr

Main article: Modelr reflectivity calculation

## Implementation in Python

Bortfled's formula is implemented in **bruges**.

## References

- ↑ Bortfeld, R., 1961, Approximations to the reflection and transmission coefficients of plane longitudinal and transverse waves, Geophysical Prospecting, v.9 no. 4, 485-503.
- ↑ Bortfeld's 3 term reflectivity equation
- ↑ The Stack-Constrained form