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Summary We propose to apply the Bojarski equation for the Green's function and T-matrix reconstruction using surface data, in which only the background Green's function is assumed to be known. With this reconstruction, no weak-scattering assumption is needed, and direct nonlinear inversion can be applied to the reconstructed new data sets. The key problem is the removal of anti-causal scattered waves. We discussed several approaches to solve this problem. Introduction Green's function retrieval has been a powerful method to reconstruct Green's function for imaging, tomography and inversion (see, Schuster, 2009; Wapenaar et al., 2008). However, the method needs to put receivers inside the medium. There are new proposed methods of wavefield reconstruction using surface data only, but some extra information such as the first arrival data, is needed (Wapenaar et al., 2011). Wu et al (2014) proposed a direct nonlinear inversion using inverse thin-slab propagator for a tomographic problem. However the method assumed the Tmatrix is known. The traditional approach to obtain full Tmatrix is by an iterative linearized inversion, in which scattering potential and T-matrix are updated alternatively order-by-order (Moses, 1956; Razavy, 1975; Weglein, 1981; Weglein et al, 2006, Jakobsen and Ursin, 2015). The approach is based on the weak perturbation assumptionmay not converge for strong scattering. Therefore, it is desirable to have a Green's function or T-matrix reconstruction method which is not based on the weak perturbation assumption, so that it can be applied to the nonlinear direction inversion. In this work we propose to use a non-perturbative method of Green's function and T-matrix reconstruction based on causal backpropagation integral which uses the background Green's function to recover the scattered wavefield. We notice that the interference from the anti-causal scattered waves is the key problem and needs to be further studied.
Summary We report from the development of a T-matrix representation of the De Wolf series for seismic waveform modeling and inversion based on the scalar wave equation in the frequency domain. We show that the renormalized DWS has a much large convergence radius and speed than the naive Born series. We have not renormalized the inverse problem, but we have used the DWS to develop a Gauss-Newton consistent method for FWI that does not require a full forward simulation at each iteration. Since the DWS accounts for multiple backscattering as well as the phase-accumulation in the forward direction, the forward model can be accurately updated after each iteration via simple matrix multiplication independent of the sourcereceiver geometry. The excellent convergence properties of the DWS are illustrated with numerical examples dealing with seismic modeling and FWI in strongly scattering media. Introduction Seismic modeling and inversion are essentially scattering and inverse scattering problems similar to the ones that have been studied in other parts of physics and engineering for many years (Newton, 1992; Pike and Sabatier, 2002). Therefore, it may be a good idea to modify the highly developed multiple scattering and renormalization methods that have been developed to solve scattering and inverse scattering problems in physics for use in seismics (Jakobsen and Ursin, 2015). In this paper, we report from the development of a renormalized multiple scattering theory that can be used for both modeling and inversion. By renormalized, we mean that the different terms in the well-known Born series have been reorganized and partially summed, so that their order better reflect the physics of seismic wave propagation, especially related with reflection seismology (Wu et al., 2007, 2014a,b). The Born series may not converge in the presence of large contrast volumes (Innanen, 2009). This is a problem since the (distorted) Born approximation is used to calculate the sensitivity matrix in standard full waveform inversion (Virieux and Operto, 2009). The De Wolf series has much better convergence properties, since it accounts for all multiple scattering in the forward direction and as many back-scattering terms as required (Wu et al., 2007, 2014a,b). However, only the first term of the De Wolf series, the so-called De Wolf approximation has so far been implemented in the context of reflection seismology (Wu et al., 2007). On the basis of the works ofWu et al. (2007) and Jakobsen (2012), we have developed an efficient T-matrix representation of the De Wolf series that can be useful for both modeling and inversion. The T-matrix representation of the DeWolf series represents a renormalization of the direct forward scattering problem, that can also be used to eliminate the need to perform a full forward simulation at each iteration in scattering-based FWI (Jakobsen and Ursin, 2015).
Summary Full Waveform Inversion (FWI) has been regarded as an effective tool to build the velocity model for the following pre-stack depth migration. While traditional methods, which are built on the Born approximation, are initial model dependent. Introducing Transmission matrix (Tmatrix), which includes all orders of scattering effects, can avoid the initial model dependence. From the T-matrix to estimate the velocity perturbation, it requires matrix inversion which is always time consuming. In order to achieve that efficiently, previously we have proposed Inverse Thin-Slab Propagator (ITSP) which is suitable for smooth media, and we study domain decomposition strategy to estimate the velocity perturbation efficiently in this abstract. Numerical examples demonstrate the validity of the proposed method. Introduction As the development of seismic exploration and exploitation, it requires more and more accurate seismic processing technologies. Full waveform inversion (FWI) can provide accurate parameter distributions of the sub-surface media, while it is always time consuming and initial model dependent (Virieux and Operto, 2009). In order to improve the inversion efficiency, the GPU, phase encoding and source encoding technologies are adopted (Ben-Hadj-Ali et al., 2009; Luo et al., 2012). In order to weaken the initial model dependence, many authors have done much work. Bunks et al. (Bunks et al., 1995) proposed a multi-scale seismic waveform inversion strategy: the result from long scale seismic data is regarded as the initial model for the short scale seismic data which can weaken the initial model dependence. Shin and Cha (Shin and Cha, 2008; Shin and Cha, 2009) proposed Laplace domain and Laplace-Fourier domain waveform inversion strategy to provide initial model for the following FWI. Wu et al (Luo and Wu, 2015; Wu et al., 2014) proposed envelope inversion strategy, which can use the ultra low frequency components compared with source frequency band, to provide initial model for FWI. While these methods are all built on born approximation and the differences lie in the objective functions.
- Geophysics > Seismic Surveying > Seismic Processing (1.00)
- Geophysics > Seismic Surveying > Seismic Modeling > Velocity Modeling > Seismic Inversion (0.91)