WO2015106879A1

WO2015106879A1 - Full wave reverse time migration

Info

Publication number: WO2015106879A1
Application number: PCT/EP2014/076396
Authority: WO
Inventors: Lasse Amundsen; Johan Olof Anders Robertsson
Original assignee: Statoil Petroleum ASA
Current assignee: Equinor Energy AS
Priority date: 2014-01-14
Filing date: 2014-12-03
Publication date: 2015-07-23
Anticipated expiration: 2016-07-14
Also published as: GB201400594D0; GB2522073A

Abstract

A method of imaging of marine seismic data recorded by receivers on a recording surface below an ocean surface, said seismic data being recordings, at said recording surface, of at least two data quantities of a seismic wavefield, which comprises the steps of: injecting the recorded data quantities on a first velocity model using a forward propagator to generate a forward propagating down-going wavefield; injecting the recorded data quantities on a second velocity model using a backward propagator so that an up-going wavefield is back propagated from said recording surface, thus producing a backward propagating up-going wavefield; and comparing said backward propagating up-going wavefield with said forward propagating down-going wavefield to produce an image of at least one scatterer or reflecting boundary in the earth's interior.

Description

Full Wave Reverse Time Migration

FIELD OF THE INVENTION

The invention relates to methods for imaging of seismic data which we refer to as Full Wave Reverse Time Migration (FWRTM).

BACKGROUND OF THE INVENTION

Seismic migration is a set of data processing techniques for transforming recorded seismic reflection data into an image of reflecting boundaries in the earth's interior. Reverse time migration, RTM, is a particular method of migration that uses the full two- way wave equation. It takes the source and receiver wavefields at the recording surface and extrapolates them in the time domain into the earth by treating them as boundary values for the wave equation, computing wavefields inside the earth at each time step. The source wavefield is computed forwards in time, so successive wavefield snapshots show an expanding wavefront moving into the earth and interacting with reflectors and diffractors. The receiver wavefield is computed backwards in time (beginning with the final time sample on each trace of the recorded data), so successive snapshots show reflection events moving generally downward. Imaging is performed using an imaging condition.

SUMMARY OF THE INVENTION

The invention provides methods as set out in the accompanying claims.

BRIEF DESCRIPTION OF THE FIGURES Figure 1 shows the use of a recording surface in the acquisition of real data to be imaged using methods described herein;

Figure 2 shows the forward propagation of the down-going wavefield D from the recording surface; Figure 3 shows the backwards propagation of the up-going wavefield U;

Figure 4 shows the backwards propagation of the down-going wavefield D from a rectangular boundary on which the forward propagated down-going wavefield D is first recorded; and

Figures 5 to 19 show snapshots of pressure wavefields at different times, each figure comprising an upper snapshot of the total recorded wavefield, and middle snapshot showing back propagation of the up-going wavefield U, and a lower snapshot showing back propagation of the down-going wavefield D.

DESCRIPTION OF PREFERRED EMBODIMENTS

We describe methods for imaging of seismic data that we refer to as Full Wave Reverse Time Migration (FWRTM). FWRTM relies on the acquisition of multicomponent seismic recordings and is therefore particularly applicable to novel multicomponent streamer data, VSP data or seabed cable/node acquired data. By multicomponent data we mean pressure data combined with 1 , 2, or 3 components of the particle velocity field.

The FWRTM method is expected to provide substantially better images than previous Reverse Time Migration (RTM) methods since it intrinsically performs and solves two of the long-standing tasks in marine seismic data processing: 1 . Wavefield decomposition (or deghosting)

2. Simultaneous imaging of primaries (ie waves diffracted or reflected directly from a scatterer) and surface-related multiples (ie waves involving at least one reflection from the ocean surface). In a marine seismic survey, seismic waves reflected from the sea surface are known as ghost waves. Deghosting refers to the removal of the effects of ghost waves.

Figure 1 illustrates the acquisition of one shot-gather that we will use FWRTM on. The model of Figure 1 is simplistic and contains a seismic source 2, a scatterer 4 that we wish to image, a free surface (ocean surface) 6 and a line 7 of receivers 8 (which may comprise hydrophones and geophones). It is also possible to use the method in 3D, in which case the receivers 8 are arranged to from a surface or plane 7.

The source wavefield 10 from seismic source 2 generates a primary diffraction 12 from the scatterer 4 which is recorded at for instance receiver A. (We consider here a simple version of the model in which no reflections will be generated from planar interfaces. The methodology is substantially identical whether we describe it for a scatterer or a reflector). In conventional RTM this type of event (ie the primary wavefield 12) is the only part of the data contributing to the image. All other events such as the receiver ghost 14 and surface related multiples are considered noise that ideally must be removed before imaging. A ghost event 14 is illustrated in the figure as the primary diffraction 12 continues up and reflects off the sea surface 6 to be recorded at receiver B (for instance) as a down-going wavefield. Note that this ghost wavefield 14 provides a secondary illumination of the sub surface. In contrast to conventional RTM, FWRTM benefits from this secondary illumination and makes use of this secondary illumination to generate an enhanced image.

FWRTM uses extrapolation of multicomponent recordings from the recording surface, ie the surface or line 7 where the sensors 8 are distributed. When this is done forward in time it is referred to as Forward Time Extrapolation (FTE), backwards in time it is referred to as Reverse Time Extrapolation (RTE). Amundsen et al. (1993) and Mittet (2002) show how FTE and RTE can be achieved by means of Green's second identity (or the Kirchhoff integral) which also will be referred to as the method of multiple point sources in the following:

(1 )

For details about variables in this equation see Amundsen et al. (1993) and Mittet (2002). In finite-difference (FD) modelling FTE and RTE can also be achieved by using the FD-injection method (Robertson and Chapman, 2000). By injecting recorded pressure data and particle velocity data normal to the injection surface a wavefield can be forward propagated or back propagated in time. A few words about FD-injection (Finite Difference Injection) and how it works are necessary. In the original implementation by Robertsson and Chapman (2000), an initial (ie first) simulation is carried out on an unperturbed model. The first simulation mimics the actual recorded data. The simulated wavefield is recorded on a closed boundary around a target of interest. The closed boundary is for example a box in 2D or a cube in 3D. In a second simulation, the wavefield from the first simulation is injected on the boundary (ie injection surface). On the injection surface wavefield constituents are injected inwards to generate an exact replica of the original wavefield. If the model has not been altered we will see an exact replica of the wavefield from the first simulation propagating inwardly from the injection surface in the interior of the injection surface. Outside the injection surface the wavefield will be substantially zero. This is because wavefield constituents from the original (ie first) simulation will also be injected outwards from the injection surface with opposite polarity compared to the outgoing propagating waves of the second simulation to achieve destructive interference.

The method described here, FWRTM, relies on a sequence of four steps. The first step has two options. The first option is to forward propagate the full down-going wavefield from the recording surface, including all down-going sea surface multiples. The second option is to forward propagate only the direct down-going source wavefield from the recording surface, excluding all down-going sea surface multiples but including the source ghost. In the following we describe these in some detail.

Step 1 a: Forward propagation of the full down-going wavefield D from recording surface to a recording boundary

Step 1 a involves reconstructing the downgoing wavefield D shown in Figure 2.

In step 1 a the acquired data are forward propagated in time by means of FD-injection from the recording surface 7 defined by the receivers 8 illustrated in Figure 2. In this case, in contrast to the FD-injection method described above, the FD-injection surface 20 is not closed but is instead approximated by the surface (3D) or line (2D) 7 defined by the sensors 8 where the data were recorded. This recording surface 7 is therefore the surface where the receivers 8 are distributed. If we are modelling in 2-D, the receivers 8 are distributed along a line whereas if we are modelling in 3-D the receivers 8 are distributed over a surface, which may or may not be planar. The model used here (in step 1 a) is the background model without the free (sea) surface 6 and the scatterer 4 shown in Figure 1 and we will be forward propagating the entire down-going recorded wavefield D, that is, the wavefield components that pass the recording surface 7 in the downward direction (including multiples). In conventional RTM only an estimated source pulse is forward propagated from the source level as the downgoing wavefield. Note that we do not have a closed surface but apply FD- injection on the open surface 20 where we recorded data only, ie the surface 7 defined by the receivers 8 in Figures 1 and 2. This will strictly speaking not be correct but as we shall see it will achieve the wavefield decomposition of the recorded data that we are after.

FD-injection will automatically radiate all up-going waves upwards (but with the wrong polarity or sign relative to the true up-going wavefield), and radiate all down-going waves downwards (with the correct polarity). The upward radiating up-going waves are generated to destructively interfere with up-going waves propagating from below. However, since there will be differences in the actual sub-surface and the used background model, the destructive interference will no longer be perfect, but since we have replaced the free surface 6 above the injection surface 20 with an absorbing boundary 22 (see Figure 2) all up-going waves will disappear (the absorbing boundary acts as a "trash can"). Note that even though we do not have a free surface 6 in the numerical background model of Figure 2, FD-injection will automatically inject all down- going wavefields from the acquired data correctly without suffering from unknown differences in the background and actual velocity models. This will also work independent of knowing the exact depth of the streamer or the shape of the sea surface (in case it is rough).

We will forward propagate the downgoing wavefield D to the last time in which we are interested so that we can later step the downgoing wavefield D backwards in time just as can be done by playing a movie backwards. This is done so that we can correlate the snapshot at each time step with the back propagated up-going wavefield U to form the FWRTM image. This will be covered in detail later. There are several existing methods for "exactly" recovering snapshots at arbitrary time steps for the downgoing, illuminating wavefield. Symes (2007) describes the method of check-pointing. Clapp (2009) and Fletcher and Robertsson (201 1 ) use random boundaries. We will again use the method of FD-injection for this purpose. We therefore place a rectangular boundary 24 around the entire model (see Figure 2) where we record the downgoing wavefield D during the forward propagation of the downgoing wavefield D from the recording surface 7.

After having recorded all the forward propagated data on the rectangular injection boundary 24 we time reverse it and flip polarity on the particle velocity recordings (only the component perpendicular to the injection boundary 24 is needed). When (in step 3) this wavefield later is injected from the rectangular injection surface 24 in a separate simulation it will exactly "play the movie backwards" of the forward propagation of the down-going wavefield D from the recording surface 20.

Step 1 b: Forward propagation of the down-going source wavefield D from recording surface to a recording boundary

In step 1 a we applied FTE of the recorded wavefield in a model that has absorbing boundary conditions above the receiver surface. That option includes all down-going sea surface multiples in the time extrapolation of the down-going wavefield. Another option is to apply FTE to the down-going source wavefield including the source ghost. The down-going source wavefield including the source ghost can be modelled by injecting the data measurements into a homogeneous model bounded above the sea surface. The modelled output is recorded at a depth just beneath the receiver depth. Then this recording is used in FTE as described in step 1 a. This option will exclude all down-going sea surface multiples in the time extrapolation.

Step 2: Back propagation of up-going wavefield U

The second step is illustrated in Figure 3 where we go back to the recording surface 7 (where the original data were recorded). We reverse the recorded data in time and flip polarity on the particle velocity recordings. We then inject this wavefield along the recording surface 7 on a background model that lacks the free surface 6 and the scatterer 4. This time we will see RTE of the up-going wavefield U only. The down- going wavefield will be injected upwards and will be absorbed by the absorbing boundary condition there. Step 3: Back propagation of the forward propagated down-going wavefield D

Simultaneously with step 2 we "play the movie" from step 1 backwards from the rectangular outer injection surface 24. Again, this is done in the background model that lacks the free surface 6 and the scatterer 4 and is illustrated in Figure 4.

Step 4: Imaging condition The numerical back propagations in step 2 and step 3 are stepped backwards in time in tandem and synchronized so that we can cross-correlate the wavefield in each snapshot. The result is accumulated in an image as we step through all time steps. This forms the FWRTM image. Alternatively, instead of cross-correlation the process of deconvolution can be applied. Alternatively, imaging conditions based on inverse theory or inverse scattering theory can be applied.

Advantages

Advantages of the method described above include (but are not limited to):

a) Deghosting of multicomponent marine seismic data using Reverse Time Extrapolation (RTE) of the multicomponent recordings. The method naturally makes deghosting an intrinsic part of RTM. The deghosting is independent of the shape and properties of the sea surface 6.

b) Use of multicomponent marine seismic data for imaging of primaries 12 and multiples simultaneously.

c) Use of Finite Difference-injection of data and a background model without a free surface 6 to forward propagate the down-going wavefield D and back-propagate the up-going wavefield U separately.

d) Separating the injection surface 20 of the up- and down-going data from the (closed) back propagation surface 24 of the forward propagated downgoing wavefield D (the illuminating wavefield).

e) The method can be adapted and applied to Full Waveform inversion (FWI). f) The method can be generalized to work on data such as slanted cable or over/under geometries that enable wavefield decomposition.

g) The Finite Difference wavefield extrapolations (and injection) can be substituted by any other wavefield extrapolation operations, like Pseudo Spectral Modeling, Finite Element Modeling (FEM), Spectral Element Modeling (SEM), etc.

h) The method naturally accounts for near-field scattering terms during the separation of wavefields into up- and down-going constituents.

i) The acquisition surface geometry can vary and does not need to be flat. FWRTM requires multicomponent data recordings and is therefore ideally suited for imaging towed marine multicomponent streamer data, seabed cable or node data, or VSP (Vertical Seismic Profile) data. The method images one shot gather at a time or alternatively one receiver-gather if data are sorted into common receiver gathers (e.g., in seabed node acquisition). A gather is a collection of seismic traces which share some common geometric attribute. When the traces of the gather come from a single shot and many receivers, it is called a "common shot gather". A single receiver with many shots is called a "common receiver gather".

Example

FWRTM was tested on a simple model with a scatterer and a free surface. At the bottom of the model an artificial absorbing layer is included to absorb downgoing energy to reduce the computational efforts. This absorbing layer has the ideal property of generating no reflection at the interface between the model and the artificial absorbing layer. The absorbing layer however is not perfect, so that small amplitude reflections in practice will be generated from its top and bottom.

Figures 5 to 18 show snapshots of different simulations side by side at different times. The top snapshot in each figure shows the wavefield that at the receivers will represent the input recorded data. These are the data that will be recorded in a seismic experiment. They contain in the simple model that we use the effect of the scatterer and the effect of the free surface, and the data of the top snapshot in each figure are a superposition of both up-going and down-going parts (U and D). The main upgoing part U is the diffracted event that travels from the diffractor upwards to the receivers. The main downgoing part D is the event that passed the receivers upwards but is reflected downwards from the free surface.

The snapshots in the middle of each figure show the data from step 2 (back propagation of the up-going wavefield U through the background model without the diffractor) whereas the lower panel of each figure shows the data from step 3 (the illuminating down-going wavefield D propagated through the background model without the diffractor). Note that no explicit wavefield decomposition is done anywhere. This is simply accomplished by a combination of FD-injection, removing the free surface at the top and time reversal and switching polarity of particle velocities to obtain either forward propagation of the down-going wavefield D or back-propagation of the up- going wavefield U.

The figures are straightforward to interpret. We note that Figure 8 shows the diffracted event close after its generation. In Figure 14 we observe in U how the multiple of the scattered event is collapsed at the location of the diffractor.

Finally, Figure 19 shows the FWRTM image which has nicely imaged the scatterer as well as a faint flat image of the imperfect absorbing boundary at the bottom. Various additional remarks

Depending on the acquisition geometry it may be difficult to properly capture the direct wave. This is of major importance to be part of the down-going wavefield as it comprises the main illumination of the sub-surface. Some pre-conditioning of the data may therefore be needed to make sure that the direct source pulse is radiated downward into the model. We note that FWRTM provides a relatively straight forward means to do this as opposed to other methods where the direct wave is attempted to be modelled separately. The image in Figure 19 is clearly exceptionally good compared to many conventional RTM results. One reason may be that the forward propagated wavefield is captured on a closed boundary around the model. Most of these data will propagate straight through the model and will therefore largely be lost if we do not used a closed surface. The back-propagated down-going wavefield on the other hand will be going in the opposite direction and therefore does not suffer as much form the missing lower and side boundaries. This is of course essential since such data could never be recorded (we are limited to surface recordings in practice). When we form the image by cross- correlating the two wavefields we therefore capture most energy propagating through the model upwards and downwards respectively.

In this description we illustrated how FWRTM is applied to common shot gathers. We can also form common receiver gathers on or instance seabed nodes and attempt wavefield decomposition by means of FD-injection reciprocally (strictly not correct). FWRTM can be applied to these receiver gathers.

The rectangular injection boundary used to "play the movie" of the down-going wavefield backwards sits at the very edge of the background model. Note that "full FD- injection" is not needed to obtain this effect. The data recorded on the rectangular boundary can simply be provided as a boundary condition at the edge of the computational domain.

Finally, it is sometimes said that imaging with multiples is highly sensitive to the velocity model. In FWRTM we do not suffer from this as the error in velocity model is not accumulated. Each time the energy passes through the recording surface the "error is set to zero".

References

Amundsen, L, B. Arntsen and R. Mittet, 1993, Depth imaging of offset vertical seismic profile data. Geophysical Prospecting, 41 , 1009-1031.

Clapp, R. G., 2009, Reverse time migration with random boundaries: SEG Technical Program Expanded Abstracts 2009: 2809-2813.

Fletcher, R., and J. O. A. Robertsson, 201 1 , Time-varying boundary conditions in simulation of seismic wave propagation: Geophysics, 76, A1 -A6.

Mittet, R., 2002, Multiple suppression by prestack reverse time migration: A nail in the coffin: Expanded abstract at the 64th EAGE Annual Meeting.

Robertsson, J. O. A., and C. H. Chapman, 2000, An efficient method for calculating finite-difference seismograms after model alterations: Geophysics, 65, 907 - 918.

Symes, W. M., 2007, Reverse time migration with optimal checkpointing: Geophysics, 72, SM213-SM221 .

Claims

CLAIMS:

1. A method of imaging of marine seismic data recorded by receivers on a recording surface below an ocean surface, said seismic data being recordings, at said recording surface, of at least two data quantities of a seismic wavefield, the method comprising the steps of: injecting the recorded data quantities on a first velocity model using a forward propagator to generate a forward propagating down-going wavefield; injecting the recorded data quantities on a second velocity model using a backward propagator so that an up-going wavefield is back propagated from said recording surface, thus producing a backward propagating up-going wavefield; and comparing said backward propagating up-going wavefield with said forward propagating down-going wavefield to produce an image of at least one scatterer or reflecting boundary in the earth's interior.

2. A method as claimed in claim 1 , wherein said first velocity model does not have an ocean surface at the top so that said down-going wavefield comprises the full down- going wavefield.

3. A method as claimed in claim 1 , wherein said first velocity model has an ocean surface at the top so that said down-going wavefield comprises a direct source wavefield and its ghost reflection from said ocean surface.

4. A method as claimed in any preceding claim, wherein said second velocity model does not have an ocean surface at the top so that said up-going wavefield comprises the full up-going wavefield.

5. A method as claimed in any preceding claim, which further comprises: forward propagating the down-going wavefield from said recording surface to a recording boundary;

6. A method as claimed in any preceding claim, which further comprises: backward propagating the down-going wavefield from said recording boundary.

7. A method as claimed in any one of claims 1 to 5, which further comprises: forward propagating the down-going wavefield from said recording surface on a model with a random boundary; and backward propagating the down-going wavefield on the model with the random boundary from its final wavefield snapshots.

8. A method as claimed in any preceding claim, wherein said step of injection a wavefield is carried out by means of FD-injection from said recording surface.

9. A method as claimed in any preceding claim, wherein said step of injection a wavefield is carried out by means of the method of multiple point sources from said recording surface.

10. A method as claimed in any preceding claim, wherein said recording surface is not a closed surface.

1 1 . A method as claimed in any preceding claim, wherein said receivers are arranged along a line, and wherein said line constitutes said recording surface.

12. A method as claimed in any preceding claim, wherein a velocity model is represented without an ocean surface which is modeled by an absorbing boundary at the top.

13. A method as claimed in any preceding claim, wherein said steps of forward and backward propagating are carried out using a background model which does not have a scatterer.

14. A method as claimed in any preceding claim, which comprises, during said forward propagating of the down-going wavefield, recording said wavefield at said recording boundary.

15. A method as claimed in any preceding claim, wherein said recording boundary is a rectangular recording boundary.

16. A method as claimed in any preceding claim, which further comprises synchronising said up-going wavefield and said down-going wavefield.

17. A method as claimed in any preceding claim, wherein said data quantities comprise at least pressure and particle velocity recordings.

18. A method as claimed in any one of claims 1 to 16, wherein said data quantities comprise at least over/under streamer data recordings.

19. A method as claimed in any preceding claim, which further comprises cross- correlating said up-going wavefield and said down-going wavefield.

20. A method as claimed in any one of claims 1 to 18, which further comprises applying deconvolution to said up-going wavefield and said down-going wavefield.

21 . A method as claimed in any preceding claim, which further comprises applying imaging conditions based on inverse theory or inverse scattering theory to said up- going wavefield and said down-going wavefield.

22. A method as claimed in any preceding claim, wherein said recorded data quantities comprise at least one common shot gather.

23. A method as claimed in any one of claims 1 to 21 , wherein said recorded data quantities comprise at least one common receiver gather.

24. A method as claimed in any preceding claim, wherein the result of imaging multiple data gathers are combined to form a final image.