Abstract
Abstract Scattering theory is the basis for various seismic modeling and inversion methods. Conventionally, the Born series suffers from an assumption of a weak scattering and may face a convergence problem. We present an application of a modified Born series, referred to as the convergent Born series (CBS), to frequency-domain seismic wave modeling. The renormalization interpretation of the CBS from the renormalization group prospective is described. Further, we present comparisons of frequency-domain wavefields using the reference full integral equation method with that using the convergent Born series, proving that both of the convergent Born series can converge absolutely in strongly scattering media. Another attractive feature is that the Fast Fourier Transform is employed for efficient implementations of matrix–vector multiplication, which is practical for large-scale seismic problems. By comparing it with the full integral equation method, we have verified that the CBS can provide reliable and accurate results in strongly scattering media.
Highlights
1.1 Seismic modelingSeismic forward modeling plays an important role in seismic survey design, imaging, inversion and interpretation
From the perspective of applicability to inversion, the integral equation approach has several advantages compared with the differential equation approach: (1) it is naturally target oriented (Huang et al, 2018), (2) it gives the sensitivity matrix directly in terms of Green’s functions (Jakobsen and Ursin, 2015) which is convenient for uncertainty estimation (Eikrem et al, 2019) and (3) it is compatible with the use of domain decomposition and renormalization methods from modern physics (Jakobsen and Wu, 2016; Jakobsen et al, 2018)
This thesis analyzed the convergence properties of both the scattering series by comparing them with the full integral equation. This analysis builds a connection between the convergent Born series and conventional Born series
Summary
1.1 Seismic modelingSeismic forward modeling plays an important role in seismic survey design, imaging, inversion and interpretation. Convergence issues may occur in strongly scattering areas, such as salt structures It is important for seismic imaging in such strong-contrast regions to address the weak-scattering assumption. Efficient implementations of the integral equations approach are typically based on the use of iterative methods and /or scattering series solutions (Jakobsen and Wu, 2016, Malovichko et al, 2018; Jakobsen et al, 2019, Huang et al, 2019b,c). Renormalization can be performed on a term-by-term basis or more generally on the basis of the renormalization group (RG) (Hollowood, 2013). Jakobsen and Wu (2016) derived a renormalized scattering series by considering a T-matrix representation of the De Wolf series (Wu et al, 2007). Wu et al (2016) has described applications of renormalization group theory in the context of seismic envelope inversion in the time domain. Jakobsen et al (2018) derived a renormalized Born series using the RG theory
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