Implicit staggered-grid finite difference elastic wave numerical simulation method and device
A staggered grid and finite difference technology, applied in the field of seismic wave exploration, can solve problems such as poor accuracy
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Embodiment 1
[0075] This embodiment provides an implicit staggered grid finite difference elastic wave numerical simulation method, Figure 4 is a flow chart of an implicit staggered grid finite difference elastic wave numerical simulation method according to an embodiment of the present invention, as shown in Figure 4 As shown, the method includes the following steps (step S401-step S405):
[0076] Step S401, based on the implicit staggered grid finite difference scheme (ie the above formula 2) and the plane wave theoretical formula (ie the above formula 5), the dispersion relation expression (ie the above formula 8) is obtained:
[0077] [ 1 - 2 b + 2 b cos ( 2 β ) ] β ≈ Σ m = 1 M ...
Embodiment approach
[0087] In the first step, the implicit staggered grid finite difference coefficient a m and the constant b are substituted into the implicit staggered grid finite difference scheme to solve the spatial partial derivatives in the elastic wave equation;
[0088] This step specifically includes: the implicit staggered grid finite difference coefficient a m and the constant b are substituted into the implicit staggered grid finite difference scheme, and the implicit staggered grid finite difference scheme is applied to each grid point, and the difference equations on all grid points are simultaneously established (the implicit staggered grid finite difference equation is obtained through the above-mentioned implicit staggered grid finite-difference format conversion), and the tridiagonal matrix equation is obtained; the spatial partial derivatives in the elastic wave equation are obtained by solving the tridiagonal matrix equation.
[0089] In the second step, the spatial partial...
Embodiment 2
[0094] This embodiment introduces the complete flow of the implicit staggered grid finite-difference elastic wave numerical simulation method.
[0095] In a homogeneous isotropic medium, the two-dimensional elastic wave equation (Equation 1) is expressed as:
[0096] ρ ∂ v x ∂ t = ∂ τ x x ∂ x + ...
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