scholarly journals Seismic interferometry: Reconstructing the earth’s reflection response

Geophysics ◽  
2006 ◽  
Vol 71 (4) ◽  
pp. SI61-SI70 ◽  
Author(s):  
Deyan Draganov ◽  
Kees Wapenaar ◽  
Jan Thorbecke
Keyword(s):  
Particle Velocity ◽  
Green's Functions ◽  
Green’S Functions ◽  
Reciprocity Theorem ◽  
Depth Image ◽  
Acoustic Medium ◽  
S Wave ◽  
Noise Sources ◽  
Subsurface Structures ◽  
Area Of Interest

In 1968, Jon Claerbout showed that the reflection response of a 1D acoustic medium can be reconstructed by autocorrelating the transmission response. Since then, several authors have derived relationships for reconstructing Green’s functions at the surface, using crosscorrelations of (noise) recordings that were taken at the surface and that derived from subsurface sources. For acoustic media, we review relations between the reflection response and the transmission response in 3D inhomogeneous lossless media. These relations are derived from a one-way wavefield reciprocity theorem. We use modeling results to show how to reconstruct the reflection response in the presence of transient subsurface sources with distinct excitation times, as well as in the presence of simultaneously acting noise sources in the subsurface. We show that the quality of reconstructed reflections depends on the distribution of the subsurface sources. For a situation with enough subsurface sources — that is, for a distribution that illuminates the subsurface area of interest from nearly alldirections — the reconstructed reflection responses and the migrated depth image exhibit all the reflection events and the subsurface structures of interest, respectively. With only a few subsurface sources, that is, with insufficient illumination, the reconstructed reflection responses are noisy and can even become kinematically incorrect. At the same time, however, the depth image, which was obtained from their migration, still shows clearly all the illuminated subsurface structures at their correct positions. For the elastic case, we review a relationship between the reflection Green’s functions and the transmission Green’s functions derived from a two-way wavefield reciprocity theorem. Using modeling examples, we show how to reconstruct the different components of the particle velocity observed at the surface and resulting from a surface traction source. This reconstruciton is achieved using crosscorrelations of particle velocity components measured at the surface and resulting from separate P- and S-wave sources in the subsurface.

Lithospheric structure of the Arabian Shield from joint inversion of P- and S-wave receiver functions and dispersion velocities

2015 ◽  
Vol 65 (2) ◽  
pp. 239-255 ◽  
Author(s):  
Abdullah M. Al-Amri
Keyword(s):  
Green's Functions ◽  
Velocity Structure ◽  
Green’S Functions ◽  
Joint Inversion ◽  
Receiver Functions ◽  
Gulf Of Aqaba ◽  
Arabian Shield ◽  
S Wave ◽  
Velocity Models ◽  
Seismic Networks

Abstract New velocity models of lithospheric thickness and velocity structure have been developed for the Arabian Shield by three tasks: 1) Computing P-Wave Receiver Functions (PRFs) and S-Wave Receiver Functions (SRFs) for all the broadband stations within the Saudi seismic networks. The number of receiver function waveforms depends on the recording time window and quality of the broadband station. 2) Computing ambient noise correlation Green’s functions for all available station pairs within the Saudi seismic networks to image the shear velocity in the crust and uppermost mantle beneath the Arabian Peninsula. Together they provided hundreds of additional, unique paths exclusively sampling the region of interest. Both phase and group velocities for all the resulting empirical Green’s functions have been measured and to be used in the joint inversion. 3) Jointly inverted the PRFs and SRFs obtained in task 1 with dispersion velocities measured on the Green’s functions obtained in task 2 and with fundamental-mode, Rayleigh-wave, group and phase velocities borrowed from the tomographic studies to precisely determine 1D crustal velocity structure and upper mantle. The analysis of the PRFs revealed values of 25-45 km for crustal thickness, with the thin crust next to the Red Sea and Gulf of Aqaba and the thicker crust under the platform, and Vp/Vs ratios in the 1.70-1.80 range, suggesting a range of compositions (felsic to mafic) for the shield’s crust. The migrated SRFs suggest lithospheric thicknesses in the 80-100 km range for portions of the shield close to the Red Sea and Gulf of Aqaba and near the Arabian Gulf. Generally, the novelty of the velocity models developed under this paper has consisted in the addition of SRF data to extend the velocity models down to lithospheric and sub-lithospheric depths.

scholarly journals An adapted eigenvalue-based filter for ocean ambient noise processing

Geophysics ◽  
2020 ◽  
Vol 85 (1) ◽  
pp. KS29-KS38 ◽  
Author(s):  
Guoli Wu ◽  
Hefeng Dong ◽  
Ganpan Ke ◽  
Junqiang Song
Keyword(s):  
Covariance Matrix ◽  
Ambient Noise ◽  
Green's Functions ◽  
Green’S Functions ◽  
Homogeneous Distribution ◽  
Noise Sources ◽  
Data Set ◽  
Recording Time ◽  
Receiver Array ◽  
Sample Covariance

Accurate approximations of Green’s functions retrieved from the correlations of ambient noise require a homogeneous distribution of random and uncorrelated noise sources. In the real world, the existence of highly coherent, strong directional noise generated by ships, earthquakes, and other human activities can result in biases in the ambient-noise crosscorrelations (NCCs). We have developed an adapted eigenvalue-based filter to attenuate the interference of strong directional sources. The filter is based on the statistical model of the sample covariance matrix and can separate different components of the data covariance matrix in the eigenvalue spectrum. To improve the effectiveness and make it adaptable for different data sets, a weight is introduced to the filter. Then, the NCCs can be calculated directly from the filtered data covariance matrix. This approach is applied to a 1.02 h data set of ambient noise recorded by a permanent reservoir monitoring receiver array installed on the seabed. The power spectral density indicates that the noise recordings were contaminated by strong directional noise over nearly half of the whole observation period. Beamforming and crosscorrelation results indicate that the interference still exists even after applying traditional temporal and spectral normalization techniques, whereas the adapted eigenvalue-based filter can significantly attenuate it and help to obtain improved crosscorrelations. The approach makes it possible to retrieve reliable approximations of Green’s functions over a much shorter recording time.

A Short Survey on Green’s Function for Acoustic Problems

2020 ◽  
Vol 28 (02) ◽  
pp. 1950025
Author(s):  
Augustus R. Okoyenta ◽  
Haijun Wu ◽  
Xueliang Liu ◽  
Weikang Jiang
Keyword(s):  
Integral Equation ◽  
Boundary Conditions ◽  
Green’S Function ◽  
Green's Function ◽  
Green's Functions ◽  
Green’S Functions ◽  
Acoustic Medium ◽  
Acoustic Source ◽  
Impedance Boundary ◽  
Source Method

Green’s functions for acoustic problems is the fundamental solution to the inhomogeneous Helmholtz equation for a point source, which satisfies specific boundary conditions. It is very significant for the integral equation and also serves as the impulse response of an acoustic wave equation. They are important for acoustic problems that involve the propagation of sound from the source point to the observer position. Once the Green’s function, which satisfies the necessary boundary conditions, is obtained, the sound pressure at any point away from the source can be easily calculated by the integral equation. The major problem faced by researchers is in the process of constructing these Green’s functions which satisfy a specific boundary condition. The aim of this work is to review some of these fundamental solutions available in the literature for different boundary conditions for the ease of analyzing acoustics problems. The review covers the free-space Green’s functions for stationary source and rotational source, for both when the observer and the acoustic medium are at rest and when the medium is in uniform flow. The half-space Green’s functions are also summarized for both stationary acoustic source and moving acoustic source, derived using the image source method, equivalent source method and complex equivalent method in both time domain and frequency domain. Each of these methods used depends on the different impedance boundary conditions for which the Green’s function will satisfy. Finally, enclosed spaced Green’s functions for both rectangular duct and cylindrical duct for an infinite and finite duct is also covered in the review.

Temperature field evaluation of a two-dimensional partial heat flow problem through Green's Functions

2019 ◽  
Author(s):  
Guilherme Ramalho Costa ◽  
José Aguiar santos junior ◽  
José Ricardo Ferreira Oliveira ◽  
Jefferson Gomes do Nascimento ◽  
Gilmar Guimaraes
Keyword(s):  
Temperature Field ◽  
Heat Flow ◽  
Green's Functions ◽  
Flow Problem ◽  
Green’S Functions ◽  
Field Evaluation ◽  
Two Dimensional
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