Stationary-phase analysis of time-shift extended imaging in a constant-velocity model

To estimate the depth errors in a subsurface model obtained from the inversion of seismic data, the stationary-phase approximation in a two-dimensional constant-velocity model with a dipped reflector is applied to migration with a time-shift extension. This produces two asymptotic solutions: one is a straight line, and the other is a curve....

Performance of old and new mass-lumped triangular finite elements for wavefield modelling

Finite elements with mass lumping allow for explicit time stepping when modelling wave propagation and can be more efficient than finite differences in complex geological settings. In two dimensions on quadrilaterals, spectral elements are the obvious choice. Triangles offer more flexibility for meshing, but the construction of polynomial...

Temporal dispersion correction for wave-propagation modelling with a series approach

Temporal dispersion correction of second-order finite-difference time stepping for numerical wave propagation modelling exploits the fact that the discrete operator is exact but for the wrong frequencies. Mapping recorded traces to the correct frequencies removes the numerical error. Most of the implementations employ forward and inverse...

Research note: Inverse propagation in 1.5-dimensional amplitude-versus-offset joint migration inversion

The state-of-the-art joint migration inversion faces the so-called amplitude-versus-offset challenge, due to adopting over-simplified one-way propagation, reflection and transmission operators to avoid over-parameterization in the inversion process. To overcome this challenge, we apply joint migration inversion to horizontally layered media ...

Research Note: A workaround for the corner problem in numerically exact non-reflecting boundary conditions

Simulations of wave propagation in the Earth usually require truncation of a larger domain to the region of interest to keep computational cost acceptable. This introduces artificial boundaries that should not generate reflected waves. Most existing boundary conditions are not able to completely suppress all the reflected energy, but suffice...

Research Note: On the error behaviour of force and moment sources in simplicial spectral finite elements

The representation of a force or moment point source in a spectral finite-element code for modelling elastic wave propagation becomes fundamentally different in degenerate cases where the source is located on the boundary of an element. This difference is related to the fact that the finite-element basis functions are continuous across...