Element-free precise integration method and its applications in seismic modelling and imaging

Abstract

SUMMARY In this paper the theory of the element-free precise integration method (EFPIM) is presented as well as its applications in seismic modelling and imaging. The key point of this method is the absence of elements, which makes nodes free from the elemental restraint. Due to the moving least-squares (MLS) fitting instead of interpolation, the EFPIM results in high accuracy for both the dependent variable and its gradient. The EFPIM improves the implicit element-free method (EFM) by cutting the computational cost significantly. At the same time, the accuracy of this method keeps as good as that of the implicit EFM. The scheme of EFPIM is shown for the full scalar wave equation. Numerical stability is examined for the scheme subsequently. Based on the theory, a simple example of vibrant film is discussed in details to indicate the effectivity of the EFPIM. Main factors affecting the accuracy of the method are illustrated. Furthermore, we show some synthetic examples to demonstrate good performance of the EFPIM in seismic modelling and imaging problems. Both post-stack and pre-stack cases are considered. Combined with appropriate absorbing boundary conditions, the EFPIM can generate sections with accurate traveltimes and amplitudes. Complex structures can be imaged clearly such as high-angle dip and embedded high-velocity anomalies.