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“Exploring” spherical-wave reflection coefficientsPowerPoint Presentation

“Exploring” spherical-wave reflection coefficients

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“Exploring” spherical-wave reflection coefficients

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“Exploring” spherical-wave reflection coefficients

Chuck Ursenbach

Arnim Haase

Research Report: Ursenbach & Haase, “An efficient method for calculating spherical-wave reflection coefficients”

- Motivation: Why spherical waves?
- Theory: How to calculate efficiently
- Application: Testing exponential wavelet
- Analysis: What does the calculation “look” like?
- Deliverable: The Explorer
- Future Work: Possible directions

- Spherical wave effects have been shown to be significant near critical angles, even at considerable depth

See poster: Haase & Ursenbach, “Spherical wave AVO-modelling in elastic isotropic media”

- Spherical-wave AVO is thus important for long-offset AVO, and for extraction of density information

- Motivation: Why spherical waves?
- Theory: How to calculate efficiently
- Application: Testing exponential wavelet
- Analysis: What does the calculation “look” like?
- Deliverable: The Explorer
- Future Work: Possible directions

- One obtains the potential from integral over all p:

- Computing the gradient yields displacements

- Integrate over all frequencies to obtain trace

- Extract AVO information: RPPspherical

Hilbert transform → envelope; Max. amplitude; Normalize

- Motivation: Why spherical waves?
- Theory: How to calculate efficiently
- Application: Testing exponential wavelet
- Analysis: What does the calculation “look” like?
- Deliverable: The Explorer
- Future Work: Possible directions

- Values given by Haase (CSEG, 2004; SEG, 2004)
- Possesses critical point at ~ 43

- Motivation: Why spherical waves?
- Theory: How to calculate efficiently
- Application: Testing exponential wavelet
- Analysis: What does the calculation “look” like?
- Deliverable: The Explorer
- Future Work: Possible directions

qi = 15

qi = 0

qi = 45

qi = 85

- Motivation: Why spherical waves?
- Theory: How to calculate efficiently
- Application: Testing exponential wavelet
- Analysis: What does the calculation “look” like?
- Deliverable: The Explorer
- Future Work: Possible directions

Spherical effects

Waveform inversion

Joint inversion

EO gathers

Pseudo-linear methods

- RPPsph can be calculated semi-analytically with appropriate choice of wavelet
- Spherical effects are qualitatively similar for wavelets with similar lower bounds
- New method emphasizes that RPPsph is a weighted integral of nearby RPPpw
- Calculations are efficient enough for incorporation into interactive explorer
- May help to extract density information from AVO

- Include n > 4
- Use multi-term wavelet: Sn An wn exp(-|snw|)
- Layered overburden (effective depth, non-sphericity)
- Include cylindrical wave reflection coefficients
- Extend to PS reflections

The authors wish to thank the sponsors of CREWES for financial support of this research, and Dr. E. Krebes for careful review of the manuscript.