WEIGHTING FACTORS IN THE CONSTRUCTION AND RECONSTRUCTION OF ACOUSTICAL WAVE FIELDS

Geophysics ◽  
1977 ◽  
Vol 42 (6) ◽  
pp. 1183-1198 ◽  
Author(s):  
Milos J. Kuhn ◽  
Khalid A. Alhilali
Keyword(s):  
Free Space ◽  
Green's Functions ◽  
Green’S Functions ◽  
Diffraction Theory ◽  
Weighting Factor ◽  
Total Response ◽  
Wave Fields ◽  
Seismic Migration ◽  
Weighting Factors ◽  
The Fourier Transform

The numerical solution of the Helmholtz equation is examined for a separated source and receiver over a model having a single planar interface. Expressions describing the construction and reconstruction of acoustical wave fields are derived in terms of Green’s functions. Their relation to the Fourier transform is briefly discussed. Three simple Green’s functions—free space, free surface, and rigid surface—are used to test the relative accuracy of the respective weighting factors by comparing the numerically calculated field for a simple model to a field obtained analytically by application of rigorous diffraction theory. The main purpose of this paper is to study the behavior of the total response (amplitude and phase) for models in which the aperture is not sufficiently sampled (e.g., close to half the wavelength). The degree of distortion in the response due to spatial undersampling is unacceptable for all three Green’s functions. A modified weighting factor relative to the free‐space Green’s function is introduced, which effectively reduces the degree of distortion in the total response under the same sampling condition. The importance of this finding to exploration geophysics in the construction of the synthetic seismograms by application of the Huygen’s principle and in seismic migration will be demonstrated.

Parabolic Representations of Scattering Green’s Functions

1999 ◽  
Author(s):  
Paul E. Barbone
Keyword(s):  
Asymptotic Expansion ◽  
Wave Equation ◽  
Green’S Function ◽  
Inhomogeneous Medium ◽  
Green's Function ◽  
Free Space ◽  
Green's Functions ◽  
Green’S Functions

Abstract We derive a one-way wave equation representation of the “free space” Green’s function for an inhomogeneous medium. Our representation results from an asymptotic expansion in inverse powers of the wavenumber. Our representation takes account of losses due to scattering in all directions, even though only one-way operators are used.

scholarly journals Seismic migration of blended shot records with surface-related multiple scattering

Geophysics ◽  
2011 ◽  
Vol 76 (1) ◽  
pp. A7-A13 ◽  
Author(s):  
D. J. (Eric) Verschuur ◽  
A. J. (Guus) Berkhout
Keyword(s):  
Multiple Scattering ◽  
Input Data ◽  
Green's Functions ◽  
Green’S Functions ◽  
Migration Process ◽  
Seismic Migration ◽  
Seismic Image ◽  
Blended Data

This paper focuses on the concept of using blended data and multiple scattering directly in the migration process, meaning that the blended input data for the proposed migration algorithm includes blended surface-related multiples. It also means that both primary and multiple scattering contribute to the seismic image of the subsurface. Essential in our approach is that multiples are not included in the Green’s functions but are part of the incident wavefields, utilizing the so-called double illumination property. We find that complex incident wavefields, such as blended primaries and/or blended multiples, require a reformulation of the imaging principle in order to provide broadband angle-dependent reflection properties.

scholarly journals MONTE CARLO-BASED DYNAMIC CALCULATIONS OF STATIONARY PERTURBATIONS

2021 ◽  
Vol 247 ◽  
pp. 21003
Author(s):  
C Demazière ◽  
A Tatidis ◽  
P Vinai
Keyword(s):  
Monte Carlo ◽  
Cross Sections ◽  
Green's Functions ◽  
Green’S Functions ◽  
Source Code ◽  
Test System ◽  
The Real ◽  
Neutron Noise ◽  
Homogeneous Test ◽  
The Fourier Transform

Capitalizing on some earlier work, this paper presents a novel Monte Carlo-based approach that allows estimating the neutron noise induced by stationary perturbations of macroscopic cross-sections in the frequency domain. This method relies on the prior computation using Monte Carlo of modified Green’s functions associated to the real part of the dynamic macroscopic cross-sections, mimicking equivalent subcritical problems driven by external neutron sources. Once such modified Green’s functions are estimated, the neutron noise induced by any type of perturbations can be recovered, by solving a linear algebra problem accounting for the interdependence between the real and imaginary parts of the governing balance equations. The newly derived method was demonstrated on a large homogeneous test system and on a small heterogeneous test system to provide results comparable to a diffusion-based solver specifically developed for neutron noise applications. The new method requires the specification by the user of the real part of the Fourier transform of the macroscopic cross-sections. This is accomplished using ACE-formatted cross-section files defined by the user. Beyond this input data preparation, no change to the Monte Carlo source code is necessary. This represents the main advantage of the proposed method as compared to similar efforts requiring extensive modifications to the Monte Carlo source code.

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