WO2016155771A1 - Procédé de déparasitage - Google Patents

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Publication number
WO2016155771A1
WO2016155771A1 PCT/EP2015/056884 EP2015056884W WO2016155771A1 WO 2016155771 A1 WO2016155771 A1 WO 2016155771A1 EP 2015056884 W EP2015056884 W EP 2015056884W WO 2016155771 A1 WO2016155771 A1 WO 2016155771A1
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seismic data
data
deghosted
seismic
wavefield
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PCT/EP2015/056884
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English (en)
Inventor
Lasse Amundsen
Johan Olof Anders Robertsson
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Statoil Petroleum As
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Priority to PCT/EP2015/056884 priority Critical patent/WO2016155771A1/fr
Publication of WO2016155771A1 publication Critical patent/WO2016155771A1/fr

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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. for interpretation or for event detection
    • G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/38—Seismology; Seismic or acoustic prospecting or detecting specially adapted for water-covered areas
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/50—Corrections or adjustments related to wave propagation
    • G01V2210/56—De-ghosting; Reverberation compensation
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/60—Analysis
    • G01V2210/67—Wave propagation modeling
    • G01V2210/673—Finite-element; Finite-difference
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V2210/00—Details of seismic processing or analysis
    • G01V2210/60—Analysis
    • G01V2210/67—Wave propagation modeling
    • G01V2210/679—Reverse-time modeling or coalescence modelling, i.e. starting from receivers

Definitions

  • the present invention relates to methods of deghosting seismic data and to methods of reducing the noise in deghosted seismic data.
  • Seismic ghosts are a long-standing issue in the marine seismic exploration industry.
  • a source ghost is an event starting its propagation upward from the seismic source, and a receiver ghost ends its propagation moving downward at the receiver. They both have a reflection at the sea surface, which leads to a reduction of the useful frequency bandwidth and therefore damages seismic resolution.
  • ghosts have traditionally proved difficult to eliminate through data processing, leading to attempts to eliminate them in data acquisition through methods, such as hydrophone-geophone streamers, dual-streamer or slanted- streamer towing (e.g., Ozdemir et al., 2008; Day et al., 2013; Soubaras and Lafet, 2013). Although significant progress has been made over the last several years, the problem is still not fully solved.
  • the ghost removal process is known as deghosting.
  • Deghosting can be applied both at the receiver side and on the source side.
  • the inventors have described a new method for deghosting and other applications of wavefield separation and prediction that relies on multicomponent recordings (Amundsen and Robertsson, 2014).
  • multicomponent recordings require special consideration when they are recorded. It is therefore desirable to have a method of deghosting that does not rely upon multicomponent recordings, such as a method that uses pressure data.
  • Receiver-side wave equation based deghosting techniques for conventional pressure recorded data are described in, e.g., Amundsen (1993), Fokkema and van den Berg (1993), Robertsson and Kragh (2002), Amundsen et al. (2005), and Weglein et al. (2002).
  • the invention provides a method of deghosting seismic data using a model, the seismic data having been captured at a location below the sea surface, and the model comprising a wave-propagation space having the wave propagation properties of sea- water, the method comprising: a. injecting into the model a seismic wavefield based on the seismic data at an injection location in the model corresponding to the location at which the seismic data was captured, and allowing the injected seismic wavefield to propagate through the wave-propagation space; b.
  • the recording location being located at a distance from the injection location of twice the depth of the location below the sea surface at which the seismic data was captured; c. scaling or convolving the recorded seismic wavefield with a reflection coefficient, R; d. adding the scaled or convolved seismic wavefield to a subsequent seismic wavefield, which is based on a corresponding subsequent portion of the seismic data, the subsequent seismic wavefield being the seismic wavefield that is to be injected at the injection location at the same time as the propagating seismic wavefield passes the recording location.
  • the method is advantageous as there is no need for multi-component seismic data to be used. Further, the method is stable for all frequencies of the seismic data, i.e. there are no frequencies that cannot be handled due to, for example, notching. Further still, the method can be used both for receiver-side deghosting and source-side deghosting (receiver- side deghosting takes place in the common shot domain, whereas source-side deghosting operates in the common receiver domain). Further still, the method can handle seismic data which has been captured at varying depths (i.e. not constant depth). In the method it is merely required that the depth of the captured seismic data is known, however this depth can vary over time. Further still, the model of the present invention is simple and robust. For instance, there is no need for a free surface to be present in the model.
  • the method assumes causality to predict the down-going wavefield from the up- going wavefield, and may use a wave-equation propagator in the wave-propagation space, preferably a two-way wave equation finite-difference propagator.
  • the seismic data may relate to primary wavefields or multiples.
  • the seismic data may be marine seismic hydrophone data.
  • the method works for conventional hydrophone streamer data, even when the streamer is towed at arbitrary and variable depths. Apart from the captured seismic data, only the depth profile of the streamer recording the data beneath a sea surface with a known reflection coefficient as well as the propagation velocity in water above the streamer need be known.
  • the method may comprise the step of capturing the seismic data.
  • the seismic data may consist of pressure data.
  • the seismic data may consist of velocity data.
  • the velocity data may be single component velocity data.
  • the velocity data may be particle velocity data.
  • the single component may the vertical velocity component (v z ).
  • the method does not require multi-component seismic data, thus mere single-component seismic data can be used. This allows the method to be used for more seismic data sets and eases the capturing of the seismic data.
  • the wave-propagation space may be rectangular.
  • the rectangle may be orientated such that it has a horizontal lower and upper edges and vertical side edges.
  • the horizontal and vertical edges correspond to the horizontal and vertical directions of the sea in which the seismic data was captured.
  • the model may be a 2D model (e.g. rectangular).
  • the model may be a 3D model (e.g. cuboid).
  • the "rectangle” may also refer to cuboid-shaped models, and an "edge” of the model may refer to a surface of the 3D model.
  • the recording location may be vertically above or vertically below the injection location in the model. This is advantageous because this location of the recording location best correlates the geometry of the model to the real subsea geometry.
  • the wave-propagation space may comprise edges, at least some of which have absorbing boundary conditions. All of the edges may have absorbing boundary conditions.
  • the injected seismic wavefield will be a multi-component wavefield (e.g. it will consist of both pressure and velocity seismic data).
  • single-component, preferably directionless, seismic data may be used (e.g. pressure data, or vertical component velocity data)
  • the injected wavefield normally propagates in all directions.
  • the seismic data actually captured is mostly up-going seismic data (with down-going ghosts).
  • this is injected into the wave-propagating model, an inaccurate wavefield solution will be found. It is therefore important to compensate for the directionless nature of the captured seismic data.
  • the first solution is that the injection location may be located at an edge portion of the wave-propagation space.
  • the edge portion of the model may comprise rigid or free boundary conditions.
  • the boundary conditions of the edge portion may be Neumann or Dirichlet boundary conditions.
  • single-component velocity seismic data e.g. v z data
  • the boundary condition is preferably Dirichlet
  • pressure data when pressure data is used the boundary condition is preferably Neumann.
  • the rigid or free boundary provides the correct propagation of the injected wavefield.
  • the rigid or free boundary condition forces the seismic wavefield injected at the location to propagate away from the boundary and hence toward the recording location.
  • At least some of the remaining edges of the wave- propagation space may have absorbing boundary conditions, for example convolutional perfectly matched layers (PML). This reduces reflections within the wave-propagation space.
  • PML convolutional perfectly matched layers
  • the edge portion may be the lower edge of the rectangle.
  • the remaining edges of the rectangle may form the remaining edges of the wave-propagation space.
  • the edge portion may extend in a substantially rectilinear direction.
  • the wavefield is injected at an edge portion as described above, the wavefield propagates only away from the edge portion, and hence in one direction away from the injection location.
  • the wavefield propagates generally perpendicularly away from the edge portion.
  • the edge portion is the lower edge of the rectangle, the wavefield generally propagates upwards.
  • all of the injected seismic wavefield may propagate in one direction, for example the direction in which it is known for it generally to have been propagating when it was captured, i.e. upwards.
  • the injection location may be at any location within the wave-propagation space (i.e. within the space itself, or at or near the edges).
  • at least two edges of the wave-propagation space e.g. the upper and lower edges, or the entire perimeter
  • the recorded wavefield has an amplitude of approximately one half of the "correct" value.
  • a reflection coefficient of 0 ⁇ R ⁇ 2, preferably 2, preferably 1 .95, preferably 1 .9, preferably 1.8 may be used. By using a larger reflection coefficient, the reduction in amplitude can be compensated for.
  • the absorbing boundary conditions may be Perfectly Matched Layers (PML), for example convolutional PMLs.
  • PML Perfectly Matched Layers
  • the injected seismic data may drive the model.
  • steps of a to d may be occurring continuously, i.e. seismic data may be injected as the wavefield propagates through the model. Steps a to d may therefore be considered to be repeated for every time sample of seismic data injected into the model.
  • continuous may include sequential discrete data separated in time (which is typically how the seismic data is captured and processed). A subsequent piece of seismic data may be injected into the model prior to the wavefield from the preceding piece of seismic data being recorded.
  • the complete deghosted seismic data produced by performing the method for all of a seismic data set captured over a period of time may be referred to as a solution.
  • the wave-propagation space may comprise two side edge portions opposite one another.
  • the method may comprise performing steps a to d with at least one side edge portion of the model comprising a first boundary condition to provide first deghosted seismic data; performing steps a to d with the at least one side edge portion of the model comprising a second complimentary boundary condition to provide second deghosted seismic data; and summing the first and second deghosted seismic data.
  • the steps a to d may be effectively run through twice, with one of the side edge portions of the model having a first boundary condition on the first run and a second boundary condition on the second run, the second boundary condition being complimentary to the first boundary condition.
  • the same boundary conditions may be applied to the other side edge portion during the first and second runs.
  • Complimentary boundary conditions may be Neumann and Dirichlet boundary conditions.
  • the same seismic data may be used to calculate the first and second deghosted seismic data.
  • the first and second boundary conditions may be complimentary.
  • the first and second deghosted seismic data calculated in such a way can be used to remove all of the reflections from the side edge portions of the wave-propagation space. This is at least true for wavefield energy that interacts once with the side edge portions.
  • the first order reflection vanishes once the first and second deghosted seismic data is summed because of the complimentary boundary conditions used. This method of removing reflections is particularly useful when the seismic data has been captured close to the source of seismic energy.
  • the side edge portions may be vertically orientated.
  • the side edge portions may join the edge portion.
  • the edge portion may be horizontally orientated.
  • the wave-propagation space may comprise a fourth edge portion, opposite the edge portion and joining the two side edge portions.
  • the fourth edge portion may have absorbing boundary conditions, e.g. PML.
  • the side edge portions may be joined by a third and a fourth edge portion, the third and fourth edge portions being opposite one another.
  • the third and fourth edge portions may be parallel to one another.
  • the side edge portions and the third and fourth edge portions may form the edges of the rectangle space (or the faces of the cuboid space).
  • the third and fourth edges may have absorbing boundary conditions, e.g. PML.
  • the wave-propagation space may comprise fifth and sixth surfaces closing the cuboid (i.e. joining to the first, second, third and fourth surfaces, at opposite ends thereof).
  • the fifth and sixth surfaces may have absorbing boundary conditions (e.g. PML), or complimentary boundary conditions (e.g. Neumann and Dirichlet).
  • the model may be a finite-difference model, a finite-element model, a spectral element model, or a pseudo-spectral model.
  • the wave-propagation space may be a grid, e.g. a finite-difference wave-propagation grid.
  • the method may be a finite-difference method, a finite-element method, a spectral element method, or a pseudo-spectral method.
  • the model may be in the space-time domain.
  • the axes of the wave-propagation space may be spatial, i.e. depicting distances.
  • the seismic data may be injected at a location corresponding to the location at which they were captured.
  • the seismic data may be injected over a time and at a rate corresponding to the time period over and the rate at which the seismic data were captured.
  • the location at which the seismic wavefield is injected into the model corresponds to the location beneath the sea at which the seismic wavefield data were captured.
  • the seismic wavefield may be injected at a point source or a plurality of point sources.
  • the point source(s) may be monopole(s).
  • the plurality of point sources may correspond to the location at which the seismic data was captured using a streamer.
  • the respective point sources may be at the same depth as one another.
  • the respective point sources may be spaced horizontally from one another.
  • the depth may be constant over time.
  • the depth of all of the point sources may vary together over time.
  • the depth of the point sources may vary with respect to each other and the sea surface over time.
  • the respective point sources may be at varying depths with respect to one another.
  • the respective depths may be constant over time. However, the respective depths may vary over time.
  • the configuration of the point sources merely depends on the configuration of the equipment used to capture the data, e.g. the streamer.
  • the propagating seismic wave may be recorded at a plurality of locations.
  • the recording locations may comprise a plurality of point recording data corresponding to the plurality of point sources.
  • the configuration of the recording datum merely depends on the configuration of the source(s) and/or the varying depth of the data-capturing locations, which may be due to a varying depth of the streamer and/or having a rough sea surface.
  • the recorded wavefield at a recording datum may be added to the subsequent seismic wavefield being injected at the corresponding source location.
  • the recording datum/data may be spaced at a distance of twice the depth of the captured seismic data substantially vertically away from the corresponding source.
  • the recording datum/data may be spaced at a distance of twice the depth of the captured seismic data substantially perpendicularly to the edge portion.
  • the model may not include any free surface.
  • a free surface is not required. This simplifies the method in comparison to the methods of the prior art.
  • the direct wave may have been removed from the seismic data.
  • the seismic data may comprise captured seismic data, the captured seismic data missing near offset seismic data, and reconstructed near offset seismic data, the method may comprise reconstructing the reconstructed near offset seismic data. It is common to have missing near offset seismic data, however it is best to have complete data sets. Thus, it is useful to reconstruct the missing near offset data. Such reconstruction can be performed by normal moveout (NMO).
  • NMO normal moveout
  • the seismic data may comprise captured seismic data and reconstructed negative offset seismic data, the method comprising reconstructing the reconstructed negative offset seismic data.
  • the use of negative offset seismic data is particularly important in regions of dipping geology. Negative seismic data can be reconstructed by mirroring positive offset seismic data.
  • a value of 0 ⁇ R ⁇ 1 may be used in the method.
  • R of less than 1 is advantageous since it helps to stabilise the deghosting method, and is closer to the actual reflection coefficient of the sea-air interface.
  • R of 0.95 or 0.9 is used. As mentioned above, this value may be used when the wavefield is injected at the edge portion of the model.
  • a value of 0 ⁇ R ⁇ 2 may be used in the method.
  • R of less than 2 is advantageous since it helps to stabilise the deghosting method, and is closer to the actual reflection coefficient of the sea-air interface.
  • an R of 1.95 or 1.9 or 1 .8 may be used. As mentioned above, this value may be used when the injection location is not at the edge of the model and/or all of the edges of wave model are absorbing boundaries.
  • the reflection coefficient of the sea surface is approximately -1 .
  • the reflection coefficient used in the present method should be of opposite polarity and should best match the amplitude of the scaled/convolved seismic wavefield to the amplitude of the ghost wavefield.
  • an R of approximately 1 or approximately 2, in the case where the amplitude of the recorded wavefield is one half of the "correct value", as discussed above
  • Using an R of 0.95 or 0.9 (or 1 .95, 1.9, or 1.8) can help to stabilise the solution.
  • the reflection coefficient, R may be a function that may vary with time. Such a reflection coefficient may allow for changing surface reflection coefficients that vary in time.
  • Conformal mapping may be used to model the effects of a rough sea surface and/or a depth varying recording streamer. Specific examples of using conformal mapping for such a purpose are given in Fornberg (1988).
  • the method may comprise performing steps a to d using forward time extrapolation (FTE) to produce forward time extrapolated seismic data.
  • FTE forward time extrapolation
  • the method may comprise performing steps a to d using reverse time extrapolation (RTE) to produce reverse time extrapolated seismic data.
  • RTE reverse time extrapolation
  • the down-going wavefield may be calculated which can then be, at the end, subtracted from the total recorded wavefield to estimate the up-going (deghosted) wavefield.
  • the invention provides a method of reconstructing a multicomponent wavefield from seismic data using a model, the seismic data having been captured at a location below the sea surface, and the model comprising a wave-propagation space having the wave propagation properties of sea-water and a reflecting surface at a location corresponding to the location of the sea surface, the method comprising: a. injecting into the model a seismic wavefield based on the seismic data at an injection location in the model corresponding to the location at which the seismic data was captured; b. introducing a boundary condition at the injection location; and c. allowing the wavefield to propagate through the wave-propagation space and reflect off the reflecting surface, thus
  • Such a reconstructed multicomponent wavefield can be used, for instance, to calibrate multicomponent seismic data or can be used in performing deghosting.
  • the method is advantageous as there is no need for multi-component seismic data to be used in order to produce a reconstruction of a multicomponent seismic wavefield.
  • the method is stable for all frequencies of the seismic data, i.e. there are no frequencies that cannot be handled due to, for example, notching. Further still, the method can be used both for receiver-side deghosting and source-side deghosting (receiver-side deghosting takes place in the common shot domain, whereas source-side deghosting operates in the common receiver domain). Further still, the method can handle seismic data which has been captured at varying depths (i.e. not constant depth). In the method it is merely required that the depth of the captured seismic data is known, however this depth can vary over time. Further still, the model of the present invention is simple and robust. For instance, there is no need for a free surface to be present in the model.
  • the method assumes causality to predict the down-going wavefield from the up- going wavefield, and may use a wave-equation propagator in the wave-propagation space, preferably a two-way wave equation finite-difference propagator.
  • the seismic data may relate to primary wavefields or multiples.
  • the seismic data may be marine seismic hydrophone data.
  • the method works for conventional hydrophone streamer data, even when the streamer is towed at arbitrary and variable depths. Apart from the captured seismic data, only the depth profile of the streamer recording the data beneath a sea surface with a known reflection coefficient as well as the propagation velocity in water above the streamer need be known.
  • the method may comprise the step of capturing the seismic data.
  • the seismic data may consist of velocity data.
  • the velocity data may be single component velocity data.
  • the velocity data may be particle velocity data.
  • the single component may the vertical velocity component (v z ).
  • the boundary condition at the injection location may preferably be Dirichlet boundary conditions.
  • the seismic data may consist of pressure data.
  • the boundary condition at the injection location may preferably be Neumann boundary conditions.
  • the method does not require multi-component seismic data, thus mere single-component seismic data can be used. This allows the method to be used for more seismic data sets and eases the capturing of the seismic data.
  • the reconstructed seismic wavefield may be used to calibrate seismic data as follows. It is usually the case that the captured pressure data are of much higher quality than the captured single component velocity (e.g. v z ) data and there is therefore a need to calibrate the single component velocity data, particularly at low frequencies.
  • the method of this aspect can be used to generate total seismic wavefield data from single component velocity data.
  • the total seismic wavefield data includes seismic pressure data.
  • This reconstructed seismic pressure data can then be compared to captured pressure data corresponding to the captured velocity data. Any differences may indicate a need to (and can be used to) calibrate the captured velocity data.
  • the wave-propagation space may be rectangular.
  • the rectangle may be orientated such that it has a horizontal lower and upper edges and vertical side edges.
  • the horizontal and vertical edges correspond to the horizontal and vertical directions of the sea in which the seismic data was captured.
  • the reflecting surface may be orientated horizontally and may be vertically above (or below) the injection location. In the case where there are more than one injection locations, the reflecting surface may be orientated generally parallel to the direction between adjacent injection locations.
  • the purpose of the reflecting surface is to model the sea surface in the model.
  • the wave-propagation space may comprise edges that have absorbing boundary conditions.
  • the injected seismic wavefield will be a multi-component wavefield (e.g. it will consist of both pressure and velocity seismic data).
  • the model may be a finite-difference model, a finite-element model, a spectral element model, or a pseudo-spectral model.
  • the wave-propagation space may be a grid, e.g. a finite-difference wave-propagation grid.
  • the method may be a finite-difference method, a finite-element method, a spectral element method, or a pseudo-spectral method.
  • the present aspect includes the step of introducing a boundary condition at the injection location.
  • the boundary condition may be a boundary condition such that the injected seismic wavefield generally only propagates toward the reflecting surface (e.g. upwards in the model, when the reflecting surface is above the injection location). Thus, the injected seismic wavefield does not propagate away from the reflecting surface.
  • the boundary condition may be an artificial free-surface boundary condition.
  • the boundary condition may have a reflection coefficient of -1 .
  • the boundary condition may be a Dirichlet boundary condition.
  • the boundary condition may be a Neumann boundary condition.
  • the model may comprise one or more sources where the seismic wavefield is injected.
  • the sources may be superimposed on top of the boundary condition.
  • the boundary condition may be superimposed on top of the sources.
  • the boundary condition may form a second reflecting surface in the model at the injection location(s).
  • the second reflecting surface may be parallel to the reflecting surface.
  • the method may comprise: d. allowing the propagating seismic wave that has reflected off the reflecting surface in step c to propagate back to the injection location where it is again reflected back towards the reflecting surface.
  • the resulting injected wavefield is effectively given a direction of propagation by the boundary condition at the injection location.
  • the direction may be generally towards the reflecting surface.
  • all of the injected wavefield may propagate towards the reflecting surface.
  • this method also relies on the assumption that, when using FTE, the first captured seismic data corresponds to a purely up-going wavefield and, when using RTE, the last captured seismic data corresponds to a purely down-going wavefield.
  • the boundary condition may force the wavefield to propagate toward the reflecting surface (e.g. upwards). This is acceptable for the initial seismic data, since the initial seismic data is upwards only (in FTE) or downwards only (in RTE). However, subsequent seismic data can have both upward and downward components. Forcing all of the subsequent injected wavefields towards the reflecting surface is therefore not itself accurate. However, due to the reflecting surface, the reflected wavefield in the propagating space of the model interferes with subsequently injected wavefields, thus cancelling out the portion of the injected wavefield that in the real situation (i.e. in the real sub-sea situation) was actually propagating downwards.
  • the only wavefields are those corresponding to the upward propagating wavefields in the real situation, and their downward propagating reflections.
  • the full wavefield present in reality between the capturing location (e.g. the streamer location, which corresponds to the injection location in the model) and the sea surface (which corresponds to the reflecting surface in the model) is reconstructed by repeating steps a to c for all the seismic data. From the full wavefield, deghosting can be performed using any known technique of deghosting using a full reconstructed wavefield.
  • the reflected wavefield will arrive at the injection location at the time that the corresponding down-going seismic data is injected upwards.
  • the reflected wavefield interferes with this injected wavefield so that no wavefields that are down-going in the real sub-sea situation propagate upwards in the model. (Whilst "up” and “down” are used here, it is clear that in relation to the model these can be any two opposite directions.)
  • this method can construct the full multi-component wavefield between the injection location and the reflecting surface in the model by simply injecting single- component seismic data.
  • the injection location may be located at an edge portion of the wave-propagation space.
  • the boundary condition may be introduced at the edge portion.
  • At least some of the remaining edges of the wave-propagation space may have absorbing boundary conditions, for example convolutional perfectly matched layers (PML). This reduces reflections within the wave-propagation space.
  • PML convolutional perfectly matched layers
  • the edge portion may be the lower edge of the rectangle.
  • the remaining edges of the rectangle may form the remaining edges of the wave-propagation space.
  • the edge portion may extend in a substantially rectilinear direction.
  • the wavefield is injected at an edge portion as described above, and because an appropriate boundary condition is introduced at the injection location, the wavefield propagates only away from the edge portion, and hence in one direction away from the injection location. For example, when the edge portion is the edge of the rectangle, the wavefield propagates generally perpendicularly away from the edge portion. For example, when the edge portion is the lower edge of the rectangle, the wavefield generally propagates upwards. Thus, all of the injected seismic wavefield may propagate in one direction, for example the direction in which it is known for it generally to have been propagating when it was captured, i.e. upwards.
  • the reflecting surface may be a free surface in the model.
  • the reflection coefficient of the reflecting surface may be -1 ⁇ R ⁇ 0, preferably -1 , preferably -0.95.
  • the absorbing boundary conditions may be Perfectly Matched Layers (PML), for example convolutional PMLs.
  • PML Perfectly Matched Layers
  • the model may be a 2D model (e.g. rectangular).
  • the model may be a 3D model (e.g. cuboid).
  • the "rectangle” may also refer to cuboid-shaped models, and the "edge” may refer to a surface.
  • the injected seismic data may drive the model.
  • steps of a to c may be occurring continuously, i.e. seismic data may be injected as the wavefield propagates through the model. Steps a to c may therefore be considered to be repeated for every time sample of seismic data injected into the model.
  • continuous may include sequential discrete data separated in time (which is typically how the seismic data is captured and processed). A subsequent piece of seismic data may be injected into the model prior to the wavefield from the preceding piece of seismic data being reflected.
  • the complete deghosted seismic data produced by performing the method for all of a seismic data set captured over a period of time may be referred to as a solution.
  • the wave-propagation space may comprise two side edge portions opposite one another.
  • the method may comprise performing steps a to c with at least one side edge portion of the model comprising a first boundary condition to provide a first reconstructed wavefield; performing steps a to c with the at least one side edge portion of the model comprising a second complimentary boundary condition to provide a second reconstructed wavefield; and summing the first and second reconstructed wavefields.
  • Complimentary boundary conditions may be Neumann and Dirichlet boundary conditions.
  • the same seismic data may be used to calculate the first and second reconstructed wavefields.
  • the first and second boundary conditions may be complimentary.
  • the same boundary conditions applied to the side edge portion above may also be applied to the other side edge portion during the first and second runs through steps a to c.
  • the first and second reconstructed wavefields calculated in such a way can be used to remove all of the reflections from the side edge portions of the wave-propagation space. This is at least true for wavefield energy that interacts once with the side edge portions.
  • the first order reflection vanishes once the first and second reconstructed wavefields are summed because of the complimentary boundary conditions used. This method of removing reflections is particularly useful when the seismic data has been captured close to the source of seismic energy.
  • the reconstructed wavefields with removed reflections can be then be used to produce more accurate deghosted seismic data.
  • the side edge portions may be vertically orientated.
  • the side edge portions may be joined by a third and a fourth edge portion, the third and fourth edge portions being opposite one another.
  • the third and fourth edge portions may be parallel to one another.
  • the side edge portions and the third and fourth edge portions may form the edges of the rectangle space (or the faces of the cuboid space).
  • the third and fourth edges may have absorbing boundary conditions, e.g. PML.
  • the wave-propagation space may comprise fifth and sixth surfaces closing the cuboid (i.e. joining to the first, second, third and fourth surfaces, at opposite ends thereof).
  • the fifth and sixth surfaces may have absorbing boundary conditions (e.g. PML), or complimentary boundary conditions (e.g. Neumann and Dirichlet).
  • the model may be in the space-time domain.
  • the axes of the wave-propagation space may be spatial, i.e. depicting distances.
  • the seismic data may be injected at a location corresponding to the location at which they were captured in the real subsea situation.
  • the seismic data may be injected over a time and at a rate corresponding to the time period over and the rate at which the seismic data were captured.
  • the location at which the seismic wavefield is injected into the model corresponds to the location beneath the sea at which the seismic wavefield data were captured.
  • the seismic wavefield may be injected at a point source or a plurality of point sources.
  • the point source(s) may be monopole(s).
  • the plurality of point sources may correspond to the location at which the seismic data was captured using a streamer.
  • the respective point sources may be at the same depth as one another.
  • the respective point sources may be spaced horizontally from one another.
  • the depth may be constant over time.
  • the depth of all of the point sources may vary together over time.
  • the depth of the point sources may vary with respect to each other and the sea surface over time.
  • the respective point sources may be at varying depths with respect to one another.
  • the respective depths may be constant over time. However, the respective depths may vary over time.
  • the configuration of the point sources merely depends on the configuration of the equipment used to capture the data, e.g. the streamer.
  • the distance between the injection location(s) and the reflecting surface merely depends on the depth of the equipment used to capture the data, e.g. the streamer.
  • the direct wave may have been removed from the seismic data.
  • the seismic data may comprise captured seismic data, the captured seismic data missing near offset seismic data, and reconstructed near offset seismic data, the method may comprise reconstructing the reconstructed near offset seismic data. It is common to have missing near offset seismic data, however it is best to have complete data sets. Thus, it is useful to reconstruct the missing near offset data. Such reconstruction can be performed by normal moveout (NMO).
  • NMO normal moveout
  • the seismic data may comprise captured seismic data and reconstructed negative offset seismic data, the method comprising reconstructing the reconstructed negative offset seismic data.
  • the use of negative offset seismic data is particularly important in regions of dipping geology. Negative seismic data can be reconstructed by mirroring positive offset seismic data.
  • a value of -1 ⁇ R ⁇ 0 for the reflection coefficient of the reflecting surface may be used in the method.
  • R of greater than -1 is advantageous since it helps to stabilise the reconstructing method, and is closer to the actual reflection coefficient of the sea-air interface.
  • an R of -0.95 or -0.9 is used.
  • the reflection coefficient of the real sea surface is approximately -1.
  • the wavefield that is reflected off the boundary condition at the injection location and hence is upwardly propagating in the model i.e. the wave that is injected upwards, then reflected downwards off the reflecting surface and reflected upwards again due to the boundary condition at the injection location
  • the wavefield that is injected upwards, then reflected downwards off the reflecting surface and reflected upwards again due to the boundary condition at the injection location has opposite polarity compared to the injected data and will therefore destructively interfere to remove the erroneously upwards injected downgoing wavefield.
  • the reflection coefficient, R may be a function that may vary with time. Such a reflection coefficient may allow for changing sea surface reflection coefficients that vary in time.
  • Conformal mapping may be used to model the effects of a rough sea surface and/or a depth varying recording streamer. Specific examples of using conformal mapping for such a purpose are given in Fornberg (1988).
  • the method may comprise performing steps a to c using forward time extrapolation (FTE) to produce forward time extrapolated seismic data.
  • FTE forward time extrapolation
  • the method may comprise performing steps a to c using reverse time extrapolation (RTE) to produce reverse time extrapolated seismic data.
  • RTE reverse time extrapolation
  • the inventors have found that the FTE and the RTE solutions have identical reconstructed wavefield signals but different noise. Thus, a combination of the FTE and RTE can be used to calculate the noise, as is discussed further below.
  • the method may also be a method of deghosting seismic data further comprising: d. deghosting the seismic data using the total reconstructed wave-field. Deghosting may be carried out when the seismic data is velocity seismic data, such as v z , or pressure seismic data.
  • the invention provides a method of deghosting single-component seismic data comprising using a reverse time extrapolator.
  • the single-component seismic data may be pressure data or single component velocity data.
  • the velocity data may be particle velocity data.
  • the single component may the vertical velocity component (v z ).
  • the down-going wavefield may be calculated which can then be at the end subtracted from the total recorded wavefield to estimate the up-going (deghosted) wavefield.
  • the method may comprise calculating a down-going wavefield from the single- component seismic data using the reverse time extrapolator and subtracting the down-going wavefield from the total wavefield. This produces a deghosted wavefield.
  • the method may comprise using a model having at least one edge, the at least one edge having absorbing boundary conditions.
  • the method may comprise using a model having at least two edges.
  • the method may comprise producing first deghosted seismic data using the single-component seismic data and a first set of boundary conditions for at least one of the two edges; producing second deghosted seismic data using the same single-component seismic data and a second set of boundary conditions for the at least one of the edges, the first and second sets of boundary conditions being complimentary to each other; and summing the first and second deghosted seismic data.
  • the same boundary conditions that are applied to the side edge portion above may also be applied to the other side edge portion during the production of the first and second deghosted seismic data.
  • the direct wave may have been removed from the single-component seismic data.
  • the single-component seismic data may comprise captured seismic data, the captured seismic data missing near offset seismic data, and reconstructed near offset seismic data, the method comprising reconstructing the reconstructed near offset seismic data.
  • the single-component seismic data may comprise captured seismic data and reconstructed negative offset seismic data, the method may comprise reconstructing the reconstructed negative offset seismic data.
  • the reconstructed negative offset seismic data may be reconstructed by mirroring positive offset seismic data.
  • the inventors have found that the FTE and the RTE solutions have identical deghosted signal but different noise. Thus, a combination of the FTE and RTE can be used to calculate the noise, as is discussed further below.
  • the invention provides a method comprising subtracting forward time extrapolated deghosted seismic data from reverse time extrapolated deghosted seismic data, or subtracting the reverse time extrapolated deghosted seismic data from the forward time extrapolated deghosted seismic data.
  • the method may be a method of reducing the noise in deghosted seismic data.
  • the method may be a method of identifying the noise in deghosted seismic data.
  • the forward time extrapolated deghosted seismic data may have been deghosted using a forward time extrapolator and the reverse time extrapolated seismic data has been deghosted using a reverse time extrapolator.
  • the seismic data used for both extrapolations should be the same.
  • the method may comprise producing the forward and reverse extrapolated deghosted seismic data. Any of the appropriate methods disclosed in this application may be used to produce the deghosted seismic data.
  • This method allows for the noise in the deghosted seismic data to be identified, and hence suppressed.
  • the inventors have found that the deghosted seismic data (i.e. the purely up-going seismic wavefield) produced by RTE and FTE for the same input seismic data is identical, but that each produces different noise signals.
  • RTE and FTE solution for the same seismic data is produced which only contains noise.
  • the invention provides a method of reducing noise in deghosted seismic data, comprising: constructing a gather of deghosted seismic data by producing forward time extrapolated deghosted seismic data for a first set of locations and producing reverse time extrapolated seismic data for a second set of locations, wherein the first and second set of locations are interleaving locations; performing a transform on the gather; muting the noise signal on the transform; and performing the inverse transform on the transform.
  • the "locations" may be temporal or spatial.
  • the interleaved gather may comprise interleaving traces from adjacent spatial locations, such that every second trace comes from the FTE solution and every other trace comes from the RTE solution.
  • the interleaved gather may comprise interleaving seismic data from different subsequent times, such that every second sample in a trace may come from an RTE solution and every other sample may come from an FTE solution.
  • the noise signal on the transform can be identified because its location(s) will be different from the location(s) of the remainder of the signal.
  • this signal will be continuous across the gather.
  • adjacent noise data in the gather will be at least partially uncorrelated.
  • a Fourier transform was suggested. This can be applied both in time and space (FK transform).
  • FK transform a tau-p (e.g., Radon) transform can also be used.
  • the forward/reverse time extrapolated deghosted seismic data may be produced by performing any of the appropriate methods of the other aspects of the invention.
  • the invention provides a method of reducing noise in deghosted seismic data, comprising: producing first deghosted seismic data using a model requiring one or more input parameters and seismic data; producing second deghosted seismic data using the same model and seismic data used to produce the first deghosted seismic data but using a different value of at least one of the one or more different input parameter(s);
  • first impulse response data using the same model and same value(s) of the one or more input parameters as for the first deghosted seismic data
  • second impulse response data using the same model and same value(s) of the one or more input parameters as for the second deghosted seismic data
  • using the first deghosted seismic data, the second deghosted seismic data, the first impulse response and the second impulse response to calculate the noise in at least one of the first and second deghosted seismic data.
  • Deghosted seismic data can contain noise.
  • the present aspect reduces this noise by considering the recorded noise as originating from secondary sources in the model in accordance with Huygens' Principle. It is important to note that, because the first and second deghosted solutions and the first and second impulse responses are produced in the same model, they all have data points at the same locations in the model.
  • the one or more input parameter may be any parameter of the model that the user of the model can input and hence vary. It may preferably be the reflection coefficient, as discussed below.
  • the first/second deghosted seismic data may be produced by any of the appropriate methods disclosed in the various aspects of this application.
  • An impulse response of the deghosted seismic data is a synthetic simulation of the response of the model due to an input of a spike (such as a delta function).
  • the impulse response data may be calculated by inputting a spike into the model at a location.
  • an impulse response may be calculated at each location in the model, by inputting a spike of appropriate amplitude into the model at each location.
  • one impulse response can be calculated by inputting a spike at a given location in the model (can be any location in the model).
  • the amplitude of this spike may be any amplitude, but preferably 1.
  • the values/amplitude of this impulse response can then be scaled by an appropriate factor for each location in the model, as described further below.
  • the impulse response may be a function of the depth at which the seismic data was captured, the water velocity, the sea surface reflection coefficient and the distance from the spike input location.
  • the model may advantageously comprise a constant separation between the recording location and the seismic data injection location, a constant water velocity and/or a constant reflection coefficient.
  • the first and second deghosted seismic data may be calculated separately.
  • the up- going wavefield is identical in each.
  • only the noise differs between the first and second deghosted seismic data.
  • taking the difference between the first and second deghosted seismic data results in a gather that contains no desired signal (i.e. the up-going wavefield); but rather only noise.
  • the objective is now to identify which part of this noise came from the first deghosted solution and which part came from the second deghosted solution.
  • a first impulse response may be calculated by using the same model and same value(s) of the one or more input parameters as were used for calculating the first deghosted seismic data, by inputting at that location a spike with an amplitude corresponding to the first deghosted seismic data's contribution to the difference seismic data at that location.
  • a second impulse response may be calculated by using the same model and same value(s) of the one or more input parameters as were used for calculating the second deghosted seismic data inputting, by inputting at that location a spike with an amplitude corresponding to the second deghosted seismic data's contribution to the difference seismic data at that location.
  • the first impulse response may be calculated by using the same model and same value(s) of the one or more input parameters as were used for calculating the first deghosted seismic data, by inputting a spike at any location in the model.
  • the amplitude of this spike may preferably be 1 .
  • the first impulse response can be scaled as if it were caused by a spike with an amplitude corresponding to the first deghosted seismic data's contribution to the difference seismic data at that location.
  • the scaled first impulse response can then be treated as if it originated from the given location (i.e.
  • the scaled first impulse response is treated as if its spike input location is at the given location, and so the value/amplitude of the input response becomes a function of distance and time away the given location).
  • the second impulse response may be calculated by using the same model and same value(s) of the one or more input parameters as were used for calculating the second deghosted seismic data, by inputting a spike at any location in the model.
  • the second impulse response can be scaled as if it were caused by a spike with an amplitude corresponding to the second deghosted seismic data's contribution to the difference seismic data at that location.
  • the scaled second impulse response can then be treated as if it originated from the given location (i.e. since the value/amplitude of the impulse response is known as a function of distance and time from the spike input location, when calculating the impact of the noise at a given location on all subsequent locations, the scaled impulse response is treated as if its spike input location is at the given location, and so the value/amplitude of the input response becomes a function of distance and time away from the given location).
  • the first and second impulse responses are calculated only once, but the scaled first and second impulse responses are calculated for each location.
  • values of the impulse response are known as a function of offset (distance and time) from the spike injection location. These values can be stored in a look-up table. Thus, if these values are scaled appropriately, and subtracted from the corresponding data samples in the first/second deghosted seismic data set (the "corresponding" data samples being those of the
  • noise can be removed from the first/second deghosted seismic data set by having calculated only one impulse response for the model.
  • the first/second impulse response can therefore be calculated by inputting a spike, preferably of amplitude 1 , into the model at any particular location since it is only the value of the impulse response as a function of offset from the input location that is important.
  • the impulse responses give estimates for the impact of the noise present in the sample at the given location on all subsequent locations.
  • the (scaled) first impulse response may be subtracted from first deghosted seismic data at subsequent locations.
  • the (scaled) second impulse response may be subtracted from the second seismic data at subsequent locations. This (scaling and) subtraction may occur at each subsequent location in the seismic data. Because the (scaled) first/second impulse response gives an estimate of the impact of the noise present at the current location on all subsequent locations in the first/second deghosted seismic data, when the (scaled) first/second impulse response is subtracted from the deghosted seismic data the impact of the noise from the current location is removed from the first/second deghosted seismic data. If this method is then repeated for all locations subsequent to the given location, then the impact of the noise present in all locations in the first/second deghosted seismic data set is removed. Thus, the noise can be removed from the first/second deghosted seismic data set.
  • a new difference seismic data set may need to be calculated from the new first and second deghosted seismic data sets (i.e. where the impact of noise from the current sample has been removed) before calculating the impact of noise due to noise at a subsequent sample. Doing so ensures that the noise is iteratively removed from the first and second deghosted seismic data sets.
  • the noise caused by noise in a sample of the first deghosted seismic data at that location can be removed from the first deghosted seismic data.
  • the noise caused by noise in a sample of the second deghosted seismic data at that location can be removed from the second deghosted seismic data.
  • the calculation of the difference seismic data set, the calculation of (scaled) impulse responses, and the subtraction of the impulse response from the deghosted seismic data, can then be repeated for all other locations in the seismic data.
  • the method may comprise iteratively subtracting the (scaled) first and/or second impulse response data from the respective first and/or second deghosted seismic data.
  • noise-reduced first and/or second deghosted seismic data can be produced.
  • This noise-reduced first and/or second deghosted seismic data can then be scaled using any appropriate factor.
  • This scaling may be advantageous since it may return the noise-reduced deghosted seismic data to its "correct" value (e.g. correct amplitude).
  • the deghosted seismic data may not be at its "correct” value at this stage because of the prior input parameter manipulation required by the method.
  • the first and second deghosted seismic data sets may be calculated.
  • the first and second impulse responses may be calculated.
  • the first and second impulse responses are generated by inputting a spike, preferably with an amplitude 1 , into the model and any particular location.
  • the difference seismic data set may be calculated, as mentioned above. This is done, for instance, by subtracting the first/second deghosted seismic data set from the second/first deghosted seismic data set.
  • this difference seismic data set is pure noise, or may possibly also include residual ghosts that have not been successfully removed from the deghosted seismic data.
  • the difference seismic data set thus comprises numerous data at particular time and space locations. For each sample in the difference seismic data set, a known fraction of the amplitude has come from the first deghosted solution and a known fraction of the amplitude has come from the second deghosted solution. The fractions are known, or can be calculated, from the one or more input parameters that were varied between producing the first and second deghosted seismic data.
  • a data sample of the difference seismic data set may be taken at a first time and space location, preferably the earliest location.
  • a known fraction of the amplitude of this data sample came from the first deghosted solution.
  • a known fraction of the amplitude of this data sample came from the second deghosted solution.
  • the first impulse response may be scaled such that the input spike has an amplitude equal to the known fraction of the data sample that came from the first deghosted solution.
  • the second impulse response may be scaled such that the input spike has an amplitude equal to the known fraction of the data sample that came from the second deghosted solution.
  • the scaled first impulse response can be subtracted from the first deghosted seismic data at all locations including and subsequent to the first location (the spike injection location being aligned with the first location).
  • the scaled second impulse response can be subtracted from the second deghosted seismic data at all locations including and
  • steps can be repeated for all time and space locations. For example, first the steps may be performed over all subsequent spatial locations at the same time location, and then over all subsequent time locations. Alternatively, first the steps may be performed over all subsequent time location at the same spatial location, and then over all subsequent spatial locations. It should be appreciated that once the impact of the noise in the first sample has been removed from the first and second deghosted seismic data sets, then the difference seismic data set should preferably be recalculated using the new first and second deghosted seismic data sets. In this way, when the method is repeated over all subsequent locations, the method iteratively removes the impact of noise from the first and second deghosted seismic data sets.
  • the noise will have been removed from (or at least reduced in) the first and second deghosted data sets.
  • the above method may repeat for each spatial location and then for each time interval for which deghosted seismic data has been calculated.
  • the input parameter may be a reflection coefficient, R, and the first deghosted seismic data may be calculated using R-i and the second deghosted seismic data may be calculated using R 2 .
  • the reflection coefficient may be the reflection coefficient applied in step c of the first aspect or the reflection coefficient of the reflecting surface in the second aspect.
  • the amplitude of the spike inputted at a given location to calculate the impulse response for the noise present in the first deghosted seismic data, or the amplitude of the spike for the scaled first impulse response is ⁇ Ri (Ri+ R 2 ) times the amplitude of the difference seismic data sample at the given location ⁇
  • corresponding resulting data may be calculated for all other time and space locations and then subtracted from the first deghosted seismic data.
  • the amplitude of the spike inputted at a given location to calculate the impulse response for the noise present in the second deghosted data, or the amplitude of the spike of for the scaled second impulse response is ⁇ R2 (Ri+ R2) times the amplitude of the difference seismic data sample at the given location ⁇ .
  • the method may further comprise producing noise-reduced seismic data by subtracting the calculated noise (i.e. the impulse response(s)) from the first/second deghosted seismic data.
  • the method may further comprise rescaling the noise-reduced seismic data using a different reflection coefficient, R 3 .
  • the first/second deghosted seismic data may be produced by performing any of the appropriate methods from the other aspects of the invention.
  • Figure 1 shows an example of the model used in the method of the present invention
  • Figure 2 shows an exemplary captured data set used to test the present methods
  • Figure 3 shows reconstructed data based on the data of Figure 2;
  • Figure 4 shows a portion of the reconstructed data of Figure 3
  • Figure 5 shows deghosted reference data for comparison with the deghosted data to be produced by the present method
  • Figure 6 shows deghosted data produced by an embodiment of the present invention
  • Figure 7 shows deghosted data produced by another embodiment of the present invention.
  • Figure 8 shows deghosted data produced by an embodiment of the present invention where the noise has been attenuated.
  • marine seismic hydrophone data is deghosted by letting the data drive a finite-difference simulation. Similar to Amundsen and Robertsson (2014), by injecting (e.g., Robertsson and Chapman, 2000) seismic data on a finite-difference model it is possible to separate the wavefield into various constituents such as up- and down-going wavefields, the direct wave, multiples, etc. However, whereas Amundsen and Robertsson (2014) require multicomponent seismic data, the present method only requires hydrophone data as well as the knowledge of where the sea surface is relative to the recording locations.
  • Figure 1 illustrates the basic principles behind the model used in this finite-difference simulation to deghost the data.
  • the model in Figure 1 has the wave propagation properties of seawater.
  • the top, left and right edges of the model have absorbing boundaries attenuating all waves incident on them.
  • the wavefield emitted from the monopole point sources has two superimposed parts:
  • the deghosting method is based on injecting acquired conventional hydrophone streamer data into finite-difference (FD) grids.
  • the method is implemented using a forward time extrapolator (FTE) method.
  • FTE forward time extrapolator
  • the deghosting start with the weakest arrivals.
  • Signal-to-noise is better in the RTE implementation compared to the FTE implementation as any noise generated from weaker (deeper) arrivals will interfere with stronger shallower arrivals (deghosting is started using the weakest energy first).
  • the data are injected on a lower boundary in the FD grid onto a Dirichlet boundary condition.
  • the remaining boundaries on the FD grid should be absorbing boundaries so that all energy incident on them vanishes.
  • excellent absorbing boundaries e.g., convolutional PML boundaries
  • the deghosting method predicts down-going energy (i.e. ghosts) from energy that first is up-going. It is therefore essential that the energy producing the ghost has been captured. For the near offsets this can be problematic as data are never recorded down to zero offset in practice (apart from in OBC geometries). In addition, if geology is dipping it may be necessary to also acquired negative offset data. Methods to fill in the missing near offsets are important to mitigate significant noise problems at the near offsets.
  • Reconstructing missing near offset data prior to deghosting can for instance be done by simple NMO interpolation (although other techniques may be preferred as NMO interpolation may not be accurate enough due to NMO stretching issues).
  • Reconstructing missing negative offset data prior to deghosting can for instance be done through the method of mirroring positive offset data to the corresponding negative offset locations.
  • the method relies on the knowledge of the streamer depth profile, the propagation velocity in the water between the streamer and the sea surface as well as the sea surface reflection coefficient.
  • the method tends to be somewhat robust to small errors in these parameters.
  • any noise tends to be amplified significantly if a sea surface reflection coefficient with a magnitude close to 1 is used. It is preferable in practice to use a sea surface reflection coefficient magnitudes of 0.95 or 0.9. This is not only to stabilize the deghosting method but also because practical experience shows that such values of the reflection coefficient are more realistic on real data.
  • the inventors have found that the predicted up-going energy in the FTE and RTE embodiments of the method is identical.
  • the noise is different.
  • by subtracting the RTE solution from the FTE solution we obtain a gather that contains noise only.
  • Several methods exist to separate the noise corresponding to the RTE and FTE solutions in such a gather In the following we give one example.
  • a method for removing noise from the FTE and RTE solutions is based on constructing a gather where every second trace comes from the FTE solution and every second trace comes from the RTE solution.
  • the signal is continuous but the noise (if it is uncorrelated) will be unpredictable from trace to trace.
  • the noise will appear close to Nyquist as only every second trace is repeatable from the other.
  • the signal on the other hand will map at positive and negative wavenumbers around zero wave number.
  • an FTE or RTE solution can be used.
  • the difference between these two solutions results in a pure noise gather since the up-going energy will be identical.
  • What is left is a combination of residual ghosts that have not been successfully removed in the two deghosting solutions plus the recursive impact that this noise has as it propagates and gets fed back through the deghosting method.
  • the impulse response from the two deghosting solutions are computed (a synthetic simulation where the input is all zeros except for one spike at a location in the input data).
  • the output will be a data set that contains up-going waves only of deghosting solution 1 . Since it is up-going waves only, the data can be rescaled so that the result due to any desired sea surface reflection coefficient is obtained, even though for instance a smaller reflection coefficient was used in the deghosting process for stabilization processes.
  • the resulting gather now includes data down to zero offset.
  • the first embodiment outlined above assumes that the first arrival is up-going (referred to as the FTE implementation of the deghosting method). For typical towed marine seismic data this is not necessarily the case as the direct wave will be coming from the side or will be down-going.
  • the method assumes that all data are consistent with the wave equation and that up-going waves generate down-going waves. Some care must therefore be taken if muting the data.
  • the inventors have found that in deep water environments it will generally be much easier to identify and remove the direct wave as it separates well in time from the sea bottom reflection and refractions.
  • Figure 6 shows a result of applying the FTE deghosting method to the data in Figure
  • the method can naturally accommodate for streamers with a spatially varying shape.
  • the streamer can be flattened at the expense of an irregular ghost recording location.
  • Precise ghost recording locations are less problematic in the modelling methodology as output data at precise depth locations can be generated using accurate interpolators.
  • Such an approach would allow for the use of sparse finite-difference grids where the grid-spacing is governed by the tolerance of numerical dispersion and not the ability to model the streamer shape.
  • the method can also be used for source side deghosting.
  • source locations become receivers where data are acquired.
  • the wavefield will be injected at source locations that now coincide with the Dirichlet boundary.
  • Seismic data are often less well spatially sampled on the source side so care must be taken to ensure that the wavefield is appropriately densely sampled for the finite- difference computation (e.g., by interpolating the wavefield on the source side prior to deghosting).
  • Mariner data set is a very challenging data set for the proposed deghosting methods. If such a data set had variable streamer depth that might also help in producing better results due to notch diversity in the data.
  • Moldoveanu, N., 2000 Vertical source array in marine seismic exploration: 70th Annual International Meeting, SEG, Expanded Abstracts, 53-56.
  • Moldoveanu, N., 2001 A seismic source, a marine seismic surveying arrangement, a method of operating a marine seismic source, and a method of deghosting seismic data: Australian Patent WO 01/75481 .
  • Robertsson, J. O. A. and C. H. Chapman, 2000 An efficient method for calculating finite- difference seismograms after model alterations: Geophysics, 65, 907 - 918.
  • Robertsson, J. O. A., and E. Kragh, 2002 Rough sea deghosting using a single streamer and a pressure gradient approximation: Geophysics, 67, 2005-201 1 .

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Abstract

L'invention concerne un procédé de déparasitage de données sismiques à l'aide d'un modèle, les données sismiques ayant été capturées à un emplacement au-dessous de la surface de la mer et le modèle comprenant un espace de propagation d'ondes ayant les propriétés de propagation d'ondes de l'eau de mer, le procédé comprenant les étapes consistant : a. à injecter dans le modèle un champ d'ondes sismiques sur la base des données sismiques à un emplacement d'injection dans le modèle correspondant à l'emplacement auquel les données sismiques ont été capturées, et à permettre au champ d'ondes sismiques injecté de se propager à travers l'espace de propagation d'onde; b. à enregistrer le champ d'ondes sismiques se propageant à un emplacement d'enregistrement dans le modèle, l'emplacement d'enregistrement étant situé à une certaine distance de l'emplacement d'injection de deux fois la profondeur de l'emplacement au-dessous de la surface de la mer auquel les données sismiques ont été capturées; c. à mettre à l'échelle ou à convolutionner le champ d'ondes sismiques enregistré avec un coefficient de réflexion, R; et d. à ajouter le champ d'ondes sismiques mis à l'échelle ou convolutionné à un champ d'ondes sismique suivant, qui est basé sur une partie suivante correspondante des données sismiques, le champ d'ondes sismique suivant étant le champ d'ondes sismique qui doit être injecté à l'emplacement d'injection à l'instant auquel le champ d'ondes sismiques se propageant passe par l'emplacement d'enregistrement.
PCT/EP2015/056884 2015-03-30 2015-03-30 Procédé de déparasitage WO2016155771A1 (fr)

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