Correction to: Green’s functions and integral representation of generalized continua: the case of orthogonal pantographic lattices

Abstract A method is presented for the accurate and efficient calculation of the dynamic Green's functions for a layered viscoelastic solid under plane strain conditions. The method is based on the classical wavenumber integral representation and a delta matrix formulation of the elastodynamic field. The high efficiency is achieved through the introduction of a new quadrature scheme in which the kernels of the wavenumber integrals are represented by means of polynomials in finite and semi-infinite panels, and the resulting oscillatory integrals are evaluated analytically. The accuracy of the results are controlled through the use of an adaptive procedure whereby the number of panels are increased successively until the desired accuracy is reached, with no previous function evaluations wasted. The computer program currently runs on IBM PCs for all multi-layered structures at all finite frequencies.

Download Full-text

Generalized generating functional for mixed-representation Green’s functions: Coherent-state path integral representation

Journal of Physics Conference Series ◽

10.1088/1742-6596/965/1/012008 ◽

2018 ◽

Vol 965 ◽

pp. 012008

Author(s):

M Blasone ◽

P Jizba ◽

L Smaldone

Keyword(s):

Integral Representation ◽

Coherent State ◽

Path Integral ◽

Green's Functions ◽

Green’S Functions ◽

Generating Functional ◽

Path Integral Representation ◽

Mixed Representation ◽

State Path

Download Full-text

On seismic deghosting using integral representation for the wave equation: Use of Green’s functions with Neumann or Dirichlet boundary conditions

Geophysics ◽

10.1190/geo2012-0305.1 ◽

2013 ◽

Vol 78 (4) ◽

pp. T89-T98 ◽

Cited By ~ 8

Author(s):

Lasse Amundsen ◽

Arthur B. Weglein ◽

Arne Reitan

Keyword(s):

Wave Equation ◽

Integral Representation ◽

Boundary Conditions ◽

Representation Theorem ◽

Green's Functions ◽

Dirichlet Boundary ◽

Green’S Functions ◽

Dirichlet Boundary Conditions ◽

Sea Surface ◽

Receiver Side

The recent interest in broadband seismic technology has spurred research into new and improved seismic deghosting solutions. One starting point for deriving deghosting methods is the representation theorem, which is an integral representation for the wave equation. Recent research results show that by using Green’s functions with Dirichlet boundary conditions in the representation theorem, source-side deghosting of already receiver-side deghosted wavefields can be achieved. We found that the choice of Green’s functions with Neumann boundary conditions on the sea surface and the plane that contains the sources leads to an identical but simpler solution with fewer processing steps. In addition, we found that pressure data can be receiver-side deghosted by introducing Green’s functions with Dirichlet boundary conditions on the sea surface and the plane containing the receivers into a modified representation theorem. The deghosting methods derived from the representation theorem are wave-theoretic algorithms defined in the frequency-space domain and can accommodate streamers of any shape (e.g., slanted). Our theoretical analysis of deghosting is performed in the frequency-wavenumber domain where analytical deghosting solutions are well known and thus are available for verifying the solutions. A simple numerical example can be used to show how source-side deghosting can be performed in the space domain by convolving data with Green’s functions.

Download Full-text