Forward modelling formulas for least-squares reverse-time migration
Gang Yao 1 3 Nuno V. da Silva 1 Di Wu 2
+ Author Affiliations
- Author Affiliations
1 Department of Earth Science and Engineering, Imperial College London, London, SW7 2BP, UK.
2 The Unconventional Natural Gas Institute, China University of Petroleum (Beijing), Beijing, 102249, China.
3 Corresponding author. Email: g.yao@imperial.ac.uk
Exploration Geophysics 49(4) 506-518 https://doi.org/10.1071/EG16157
Submitted: 19 December 2016 Accepted: 5 July 2017 Published: 1 September 2017
Abstract
Reverse-time migration can be formulated in a least-squares inversion framework. This is referred to as least-squares reverse-time migration, which attempts to find an optimal model of the reflectors that fits the observed data in a least-squares sense. Based on different representations of the model, different formulas of the forward modelling for least-squares reverse-time migration can be derived. In this paper, we derive two different formulas. One formula is to recover the impedance-perturbation-related images based on Born approximation. The other is to invert the reflectivity-related images based on Kirchhoff approximation. The theoretical analysis unveils there is an iω difference between the two formulas. Consequently, the seismic image using the two formulas has different shape/phase: the one based on Born approximation produces anti-symmetric images; the other based on Kirchhoff approximation gives symmetric images. Two numerical examples demonstrate the similarities and differences between the two formulas.
Key words: Born approximation, forward modelling, Kirchhoff approximation, least-squares inversion, least-squares reverse-time migration, reverse-time migration.
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