- 63 Views
- Uploaded on
- Presentation posted in: General

“Exploring” spherical-wave reflection coefficients

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

“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.