3D spectral reverse time migration with no‐wraparound absorbing conditions

Abstract

Comparative studies of methods of reverse time migration (RTM) show that spectral methods for calculating the Laplacian impose the least stringent demands on discretization stepsize; thus with spectral methods, the grid re nements often required by other methods can be avoided. Implemented with absorbing boundary conditions, which are energy-tuned to give good absorption at the boundaries, these spectral methods can be used e ectively for migration, without su ering the problems of wraparound which have traditionally plagued them (Furumyra and Takenaka, 1995).

Time evolution of the first‐order linear acoustic/elastic wave equation using Lie product formula and Taylor expansion

“…Chen (2009), Bonomi et al . (1998) and Araujo et al . (2014) used the Hamiltonian formulation to rewrite the wave equation as a system of equations in the time domain and presented several integration schemes that are known in the literature as symplectic schemes.…”

“…For instance, Tal-Ezer et al (1987) presented a time integration scheme based on the Chebyshev polynomial expansion. Chen (2009), Bonomi et al (1998) and Araujo et al (2014) used the Hamiltonian formulation to rewrite the wave equation as a system of equations in the time domain and presented several integration schemes that are known in the literature as symplectic schemes. Xu et al (2015), Gao et al (2015), Zhou (2001) and Hu (1996) expressed the acoustic wave equation as a system of first-order differential equations in terms of particle velocity and pressure field and presented numerical solutions using finite-differences, staggered grids and others numerical schemes.…”

Seismic Reverse Time Migration Using A New Wave-Field Extrapolator and a New Imaging Condition

“…According to Skell et al (1997), symplectic methods preserve a certain invariant of the Hamiltonian system and are stable for systems in which the linear extrapolation step size is sufficiently small. Bonomi et al (1998) performed a time integration (Eq. 5) using a third order symplectic scheme presented by Sexton and Weingarten (1992).…”

“…5) using a third order symplectic scheme presented by Sexton and Weingarten (1992). The numerical solution to the wave equation of Bonomi et al (1998), called leapfrog, that is given by the following expressions:…”

“…According to Bonomi et al (1998), Eq. 14 allows an improvement in the accuracy, without increasing the memory requirement in relation to the method of central finite differences of the second order and preserves the time reversibility of the wave equation.…”