Abstract
Reflection full-waveform inversion (RFWI) can reduce the nonlinearity of inversion providing an accurate initial velocity model for full-waveform inversion (FWI) through the tomographic components (low-wavenumber). However, elastic-wave reflection full-waveform inversion (ERFWI) is more vulnerable to the problem of local minimum due to the complicated multi-component wavefield. Our algorithm first divides kernels of ERFWI into four subkernels based on the theory of decoupled elastic-wave equations. Then we try to construct the tomographic components of ERFWI with only single-component wavefields, similarly to acoustic inversions. However, the S-wave velocity is still vulnerable to the coupling effects because of P-wave components contained in the S-wavefield in an inhomogeneous medium. Therefore we develop a method for decoupling elastic- wave equations in an inhomogeneous medium, which is applied to the decomposition of kernels in ERFWI. The new decoupled system can improve the accuracy of S-wavefield and hence further reduces the high-wavenumber crosstalk in the subkernel of S-wave velocity after kernels are decomposed. The numerical examples of Sigsbee2A model demonstrate that our ERFWI method with decoupled elastic-wave equations can efficiently recover the low-wavenumber components of the model and improve the precision of the S-wave velocity.
Highlights
The traditional theory of velocity recovery is divided into two parts: background velocity construction and amplitude projection
We propose a set of decoupled elastic-wave equations in an inhomogeneous medium to reduce the crosstalk artifact in the elastic-wave reflection full waveform inversion (ERFWI) after kernels are decomposed
We propose a set of elastic vector decoupled equations for inhomogeneous medium to improve the accuracy of S-wavefield for the elastic-wave reflection full-waveform inversion (ERFWI) of low-wavenumber V
Summary
The traditional theory of velocity recovery is divided into two parts: background velocity construction and amplitude projection. In order to update velocity of different scales of wavelength simultaneously, Lailly [1983] and Tarantola [1984] proposed the full waveform inversion (FWI) theory that matches all the wavefield information without any approximation between the calculated data and the observed data in model parameter inversion In practice, this method is highly non-linear, suffering from many local minima (cycle-skipping) [Bunks et al, 1995]. As the initial velocity model of FWI is smooth, there are only the downgoing waves in the wavefield rather than the upgoing waves To address this issue, Xu et al [2012a, 2012b] proposed a reflection FWI (RFWI) method with a migration/demigration [Symes and Kern, 1994] process to generate the upgoing waves and recover the background velocity along the tomographic components. In the numerical example session, we apply ERFWI with the conjugation gradient method to the Sigsbee2A model to demonstrate the effectiveness of our proposed method
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