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The plane-wave primary reflection response from an impedance gradient interface.

Lasse Amundsen1, Bjørn Ursin2, Martin Landrø2

  • 1Equinor Research Centre, Trondheim N-7005, Norway, and Department of Geoscience and Petroleum, The Norwegian University of Science and Technology, Trondheim N-7091, Norway.

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|August 5, 2022
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Summary
This summary is machine-generated.

This study introduces a weak scattering model for predicting acoustic plane wave reflections from impedance gradients. The model simplifies complex reflections using the Bremmer series, offering insights into seismic wave propagation.

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Area of Science:

  • Geophysics
  • Acoustics
  • Wave Propagation

Background:

  • Accurate modeling of seismic wave reflections is crucial for subsurface characterization.
  • Impedance gradients represent complex geological interfaces.
  • Existing models may struggle with weak scattering scenarios.

Purpose of the Study:

  • To develop a weak scattering model for predicting acoustic plane wave primary reflection responses.
  • To analyze reflection responses from impedance gradient interfaces.
  • To provide a simplified analytical solution for specific geophysical scenarios.

Main Methods:

  • Utilizing a smooth approximation to the Heaviside function (Fermi-Dirac distribution type) for gradient profiles.
  • Employing the Bremmer series to simplify complex reflection problems.
  • Expressing the reflection response using Appellian and Gaussian hypergeometric functions.

Main Results:

  • The model accurately predicts primary reflection responses for small impedance contrasts.
  • Appellian hypergeometric functions simplify to Gaussian hypergeometric functions at larger distances.
  • The Born approximation offers a further simplification of the reflection response.

Conclusions:

  • The developed weak scattering model provides a robust method for analyzing acoustic reflections from impedance gradients.
  • The mathematical framework offers insights into wave behavior in layered media.
  • The model's results align with established coefficients in limiting cases, validating its approach.