Implementation of marine seismic source wavefields in finite-difference methods using wavefield injection

Geophysics ◽  
2016 ◽  
Vol 81 (5) ◽  
pp. T211-T219 ◽  
Author(s):  
Kjetil E. Haavik ◽  
Espen Birger Raknes ◽  
Martin Landrø
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Waveform Inversion ◽  
Seismic Source ◽  
Injection Technique ◽  
Surface Reflection ◽  
Air Gun ◽  
True Source ◽  
Grid Points ◽  
Marine Seismic

We have developed a method for implementing source wavefields in finite-difference (FD) schemes for marine seismic modeling, migration, and inversion. By using the wavefield injection technique, it is possible to inject arbitrary source wavefields into an FD grid. We have assumed that the notional source signatures from each gun in an air-gun array and their positions are known. The source wavefield is extrapolated to a specified surface below the true source positions using analytical Green’s functions. On this surface, the pressure and its vertical derivative are inserted into the FD grid. The wavefield propagating from this surface will then propagate downward and appear as if it came from the true source position. The source positions do not need to coincide with the FD grid points, and the free-surface reflection coefficient for the source ghost can be specified; i.e., it can deviate from [Formula: see text], and it can be frequency dependent. These features are possible because of the analytical extrapolation step. The presented method allows modeling of any kind of marine seismic source as long as the notional source signature and radiation pattern from each individual source element is known. A simple full-waveform inversion example shows that it is important to honor the source geometry in forward modeling of seismic data.

Implementing measured source signatures in a coarse‐grid, finite‐difference modeling scheme

Geophysics ◽  
1993 ◽  
Vol 58 (12) ◽  
pp. 1852-1860 ◽  
Author(s):  
Martin Landrø ◽  
Rune Mittet ◽  
Roger Sollie
Keyword(s):  
Finite Difference ◽  
Pressure Field ◽  
Coarse Grid ◽  
Dipole Source ◽  
Difference Grid ◽  
Air Gun ◽  
Error Energy ◽  
Grid Points ◽  
Grid Nodes ◽  
Marine Seismic

In a marine seismic air‐gun array, each gun location does not necessarily coincide with a node in a finite‐difference grid. Especially for coarse‐grid, finite‐difference modeling, this problem must be handled with care since there might be up to three or four air guns between adjacent grid points. The real sources are represented by fictitious monopole‐ and dipole source functions located at grid nodes. The effective sources are estimated from the extrapolated pressure field at a horizontal surface located below the sources. We find that an array consisting of eight guns separated by a distance of 3 m and located at 7.5 m depth can be approximated by six monopole‐ and dipole source functions distributed on a finite‐difference grid with 10 m spatial sampling. The residual error energy norm between the actual wavefield and the corresponding finite‐difference wavefield observed on a fictitious streamer placed at 95 m depth is less than 0.5 percent.

Some notes on air-gun development as a marine seismic source

2009 ◽  
Vol 28 (11) ◽  
pp. 1334-1335 ◽  
Author(s):  
Ben F. Giles
Keyword(s):  
Seismic Source ◽  
Air Gun ◽  
Marine Seismic

Design of Near-orthogonal Air-gun Sequences for Marine Seismic Source Encoding

2016 ◽  
Author(s):  
M.B. Mueller ◽  
D.F. Halliday ◽  
D.J. van Manen ◽  
J.O.A. Robertsson
Keyword(s):  
Seismic Source ◽  
Air Gun ◽  
Marine Seismic ◽  
Source Encoding

An optimal frequency-domain finite-difference operator with a flexible stencil and its application in discontinuous-grid modeling

Geophysics ◽  
2021 ◽  
pp. 1-41
Author(s):  
Na Fan ◽  
Xiao-Bi Xie ◽  
Lian-Feng Zhao ◽  
Xin-Gong Tang ◽  
Zhen-Xing Yao
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Waveform Inversion ◽  
Uniform Grid ◽  
Optimal Method ◽  
Velocity Models ◽  
Full Waveform ◽  
Rotationally Symmetric ◽  
Grid Points ◽  
Coarse To Fine

We develop an optimal method to determine expansion parameters for flexible stencils in 2D scalar wave finite-difference frequency-domain (FDFD) simulation. The proposed stencil only requires the involved grid points to be paired and rotationally symmetric around the central point. We apply this method to the transition zone in discontinuous-grid modeling, where the key issue is designing particular FDFD stencils to correctly propagate the wavefield passing through the discontinuous interface. The proposed method can work in FDFD discontinuous-grid with arbitrary integer coarse-to-fine gird spacing ratios. Numerical examples are presented to demonstrate how to apply this optimal method for the discontinuous-grid FDFD schemes with spacing ratios 3 and 5. The synthetic wavefields are highly consistent to those calculated using the conventional dense uniform grid, while the memory requirement and computational costs are greatly reduced. For velocity models with large contrasts, the proposed discontinuous-grid FDFD method can significantly improve the computational efficiency in forward modeling, imaging and full waveform inversion.

Viscoacoustic waveform inversion of velocity structures in the time domain

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. R103-R119 ◽  
Author(s):  
Jianyong Bai ◽  
David Yingst ◽  
Robert Bloor ◽  
Jacques Leveille
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Field Data ◽  
Wave Equations ◽  
Finite Difference Methods ◽  
Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Difference Methods ◽  
The Time Domain

Because of the conversion of elastic energy into heat, seismic waves are attenuated and dispersed as they propagate. The attenuation effects can reduce the resolution of velocity models obtained from waveform inversion or even cause the inversion to produce incorrect results. Using a viscoacoustic model consisting of a single standard linear solid, we discovered a theoretical framework of viscoacoustic waveform inversion in the time domain for velocity estimation. We derived and found the viscoacoustic wave equations for forward modeling and their adjoint to compensate for the attenuation effects in viscoacoustic waveform inversion. The wave equations were numerically solved by high-order finite-difference methods on centered grids to extrapolate seismic wavefields. The finite-difference methods were implemented satisfying stability conditions, which are also presented. Numerical examples proved that the forward viscoacoustic wave equation can simulate attenuative behaviors very well in amplitude attenuation and phase dispersion. We tested acoustic and viscoacoustic waveform inversions with a modified Marmousi model and a 3D field data set from the deep-water Gulf of Mexico for comparison. The tests with the modified Marmousi model illustrated that the seismic attenuation can have large effects on waveform inversion and that choosing the most suitable inversion method was important to obtain the best inversion results for a specific seismic data volume. The tests with the field data set indicated that the inverted velocity models determined from the acoustic and viscoacoustic inversions were helpful to improve images and offset gathers obtained from migration. Compared to the acoustic inversion, viscoacoustic inversion is a realistic approach for real earth materials because the attenuation effects are compensated.

Arbitrary source and receiver positioning in finite‐difference schemes using Kaiser windowed sinc functions

Geophysics ◽  
2002 ◽  
Vol 67 (1) ◽  
pp. 156-165 ◽  
Author(s):  
Graham. J. Hicks
Keyword(s):  
Free Surface ◽  
Finite Difference ◽  
Finite Difference Methods ◽  
Source Region ◽  
Seismic Source ◽  
Point Sources ◽  
Finite Difference Schemes ◽  
Surface Source ◽  
Body Forces ◽  
Sinc Functions

In finite‐difference methods a seismic source can be implemented using either initial wavefield values or body forces. However, body forces can only be specified at finite‐difference nodes, and, if using initial values, a source cannot be located close to a reflecting boundary or interface in the model. Hence, difficulties can exist with these schemes when the region surrounding a source is heterogeneous or when a source either is positioned between nodes or is arbitrarily close to a free surface. A completely general solution to these problems can be obtained by using Kaiser windowed sinc functions to define a small region around the true source location that contains several nodal body forces. Both monopole and dipole point sources can be defined, enabling many source types to be implemented in either acoustic or elastic media. Such a function can also be used to arbitrarily locate receivers. If the number of finite‐difference nodes per wavelength is four or more (and with a source region half‐width of only four nodes) this scheme results in insignificant phase errors and in amplitude errors of no more than 0.1%. Numerical examples for sources located less than one node from either a free surface or an image source demonstrate that the scheme can be used successfully for any surface‐source or multisource configuration.

Source signature encoding of a vertical source array to separate the emitted direct wave from its ghost

Geophysics ◽  
2018 ◽  
Vol 83 (4) ◽  
pp. P9-P18
Author(s):  
Moritz B. Mueller ◽  
David F. Halliday ◽  
Dirk-Jan van Manen ◽  
Johan O. A. Robertsson
Keyword(s):  
Seismic Source ◽  
Opposite Polarity ◽  
Direct Wave ◽  
Air Gun ◽  
Short Period ◽  
Separate Source ◽  
Marine Seismic ◽  
Separation Feature ◽  
Marine Air ◽  
Simultaneous Source

Marine air-gun sources can be sequence-encoded by firing their individual elements independently over a short period of time. Using near-orthogonal firing sequences, whose crosscorrelation is minimal, as encoding sequences for multiple sets of air-gun sources, enables us to exploit their orthogonality as a separation feature. We find that, by distributing air guns over depths from 5 to 30 m, firing sequences can be designed whose direct, down-going wavefield is close to orthogonal to its source-ghost wavefield. The fundamentally new aspect of this approach is that the source-ghost signal is no longer just a time-delayed, opposite-polarity version of the down-going wavefield, but due to the different air-gun depths results in a different source sequence. This enables the consideration of the ghost wavefield as a separate source. We generate a set of such firing sequences by minimizing the crosscorrelation of these wavefields and optimizing their respective autocorrelations to achieve sharp peaks. The obtained, optimized firing sequences are then used for marine seismic source encoding. By adapting a multifrequency algorithm originally developed for simultaneous source separation, we determine that the ghost-source wavefield can be separated as a separate source from the direct, down-going wavefield.

scholarly journals Estimating source signatures from source-over-spread marine seismic data

Geophysics ◽  
2018 ◽  
Vol 83 (6) ◽  
pp. P39-P48
Author(s):  
Kristian Svarva Helgebostad ◽  
Martin Landrø ◽  
Vetle Vinje ◽  
Carl-Inge Nilsen
Keyword(s):  
Field Data ◽  
Forward Modeling ◽  
Inversion Algorithm ◽  
Surface Reflection ◽  
Air Gun ◽  
Recent Developments ◽  
Seismic Acquisition ◽  
The Difference ◽  
Marine Seismic ◽  
Bubble Oscillations

Recent developments in marine seismic acquisition include deploying a source vessel above a towed-streamer spread. We have developed an inversion algorithm to estimate source signatures for such acquisition configurations, by minimizing the difference between the recorded and a modeled direct wave. The forward modeling is based upon a physical modeling of the air bubble created by each air gun in the source array, and a damped Gauss-Newton approach is used for the optimization. Typical inversion parameters are empirical damping factors for the bubble oscillations and firing time delays for each air gun. Variations in streamer depth are taken into account, and a constant sea-surface reflection coefficient is also estimated as a by-product of the inversion. For data acquired in shallow waters, we have developed an extension of the forward modeling to include reflections from the water bottom to stabilize the inversion. The algorithm is tested on synthetic- and field-data examples, and the estimated source signature for the field-data example is used in a designature processing flow.

Delaying the source ghost to improve the ultralow-frequency response of a marine air-gun source

Geophysics ◽  
2020 ◽  
Vol 85 (5) ◽  
pp. P45-P51
Author(s):  
Honglei Shen ◽  
Thomas Elboth ◽  
Chunhui Tao ◽  
Gang Tian ◽  
Hanchuang Wang ◽  
...  
Keyword(s):  
Seismic Data ◽  
Waveform Inversion ◽  
Low Frequency ◽  
Ultralow Frequency ◽  
Full Waveform ◽  
Air Gun ◽  
Marine Source ◽  
Frequency Output ◽  
Marine Seismic ◽  
Marine Air

The competing effect between the fundamental bubble and its source-ghost response results in a strong attenuation of the lowest frequencies (below 7 Hz). This loss cannot be compensated easily by adjusting the source depth. Consequently, the low-frequency content in marine seismic data is not optimal, degrading the performance of low-frequency dependent processing approaches, such as full-waveform inversion. To overcome this, we have developed an additional source to counteract the ghost from the main source. In this situation, the fundamental bubble is characterized by the depth of the main source, whereas the ghost response is characterized by the summed depth of the main and additional sources. This source setup mitigates the competing effect and reduces the suppression of ultralow frequencies. Compared with a conventional horizontal source, our source design will reduce the mid- to high-frequency output, which may be beneficial in situations in which environmental constraints limit the maximum allowed output of a marine source.

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