METHOD AND SYSTEM OF PROCESSING SEISMIC DATA BY PROVIDING SURFACE APERTURE COMMON IMAGE GATHERS

Abstract

The method processes, for each of a plurality of shots at respective source locations, seismic traces recorded at a plurality of receiver locations. Common-mid-point-modulated data are also computed by multiplying the seismic data in each seismic trace by a horizontal mid-point. A depth migration process is applied to the seismic data to obtain a first set of migrated data, and to the mid-point-modulated data to obtain a second set of migrated data. For each shot, aperture values are estimated and associated with respective subsurface positions. A migrated value for a depth and an aperture in a surface aperture common image gather at a horizontal position is a migrated value of the first set of migrated data for a shot such that the estimated aperture value associated with that subsurface position is the aperture.

Claims

1. A method of processing seismic data, comprising: inputting as seismic data including, for each of a plurality of shots at respective source locations, a plurality of seismic traces recorded at a plurality of receiver locations; applying a depth migration process to the seismic data to obtain a first set of migrated data including, for each shot, a first migrated value respectively associated with a plurality of subsurface positions; computing a mid-paint-modulated data by multiplying the seismic data in each seismic trace by a function of a center of the source and receiver locations for said seismic trace; applying the depth migration process to the mid-point-modulated data to obtain a second set of migrated data including, for each shot, a second migrated values respectively associated with the plurality of subsurface positions; applying a subtraction process comprising a projection of a lateral distance between the an image position and a common mid-point location; for each shot, estimating an aperture value respectively associated with at least some of, the subsurface positions, by a division process performed in a Radon domain applied to the first and second sets of migrated data; and estimating an aperture indexed common image gather at a horizontal position, comprising respective migrated values for a parameter pair, each including a depth parameter and an aperture parameter, wherein the migrated value for the parameter pair in the common image gather at said horizontal position is a first migrated value of the first set of migrated data associated with a subsurface position determined by said horizontal position and the depth parameter of said parameter pair for a shot such that the estimated aperture value associated with said subsurface position is the aperture parameter of said parameter pair.

2. The method as claimed in claim 1, wherein the division process used for estimating the aperture values associated with a subsurface position comprises minimizing a cost function defined by an aperture variable and local values of the first and second migrated values in a neighborhood of said subsurface position.

3. The method as claimed in claim 1, wherein the depth migration process is a reverse-time migration process.

4. The method as claimed in claim 1, wherein the depth migration process is a wave equation pre-stack depth migration process.

5. A system for processing seismic data, comprising computer resource configured to carry out a method as claimed in claim 1.

6. A computer program product for a system for processing seismic data, comprising instructions to carry out a method as claimed in claim 1 when said program product is run in a computer processing unit of the system for processing seismic data.

Description

BRIEF DESCRIPTION THE DRAWINGS

[0031] FIG. 1 is a schematic diagram illustrating the acquisition of seismic data.

[0032] FIG. 2 is a flowchart of a method of processing seismic data in accordance with an embodiment of the invention.

[0033] FIG. 3 is a diagram illustrating the derivation of aperture indexed CIGs in accordance with the method.

DETAILED DESCRIPTION OF THE DRAWINGS

[0034] One way to obtain aperture indexed CIGs for PSDM (e.g. RTM migration methods) would be to compute one migration per shot and per trace, requiring a number of migrations equal to the total number of shots times the average number of receivers per shot. This is clearly impractical for the time being, especially for 3D cases. Instead, it is proposed to use a more feasible solution, namely attribute migration, also called double migration.

[0035] In the double migration method as introduced by N. Bleistein (On the imaging of reflectors in the earth, Geophysics, Vol. 52, No. 7, July 1987, pp. 931-942), two migrations are computed with the same data, the second one involving a migration operator multiplied by the specular reflection angle. The division of the two migrated images then gives the specular angle along the reflectors.

[0036] A similar method can be used with the common mid-point (as defined above) instead of the specular reflection angle as the migrated attribute. The migration can be performed using various PSDM methods including standard shot-record RTM.

[0037] The methodology then comprises (e.g. for 2D case, 3D we have three images where two images are encoded with CMPx and CMPy respectively): [0038] performing a first standard RTM migration (step 20 in FIG. 3); [0039] performing a second mid-point attribute RTM migration, where the data are multiplied by the common mid-point values (m) prior to migration (steps 30 and 40 in FIG. 3); [0040] perform a division of the two migrated data obtained, in a least square sense, to obtain the common mid-point (step 50 in FIG. 3); [0041] for each point of the image subtract the lateral coordinate of the corresponding location to obtain the aperture migrated attribute; [0042] add the reflectivity obtained from the first migrated data to the corresponding subsurface and aperture indexed gather location given by the obtained attribute map to reconstruct the attribute migrated aperture CIGs (step 60 in FIG. 3).

[0043] In this way we are able to obtain classical aperture indexed CIGs using a PDSM migration method such as RTM which is the best wavefield extrapolation method available nowadays for seismic migration.

[0044] In FIG. 2, the seismic traces input in step 10 from the field measurements are noted D.sub.S,G[t], where S denotes a source location, G denotes a receiver location and t is for time. Each trace is modulated in step 30 by multiplying it by the corresponding mid-point value, namely the horizontal midpoint distance between the center of the segment defined by the source location S and the receiver location G and the receiver location G or the source location S. The mid-point-modulated traces are D.sub.S,G[t]=m.D.sub.S,G[t].

[0045] The seismic data D.sub.S,G[t] and mid-point-modulated data D.sub.S,G[t] are respectively migrated in steps 20 and 40 to provide PSDM data/image M.sub.S[x,y,z] and M.sub.S[x,y,z]. The first set of migrated data produced in step 20 includes, for each shot at a source location S, a cube of migrated values M.sub.S[x,y,z] associated with subsurface positions x, y, z. Likewise, the second set of migrated data obtained in step 40 using the same depth migration process includes another cube of migrated values M.sub.S[x,y,z] for each shot.

[0046] Before accessing to the aperture value, it is mandatory to apply a subtraction process comprising the projection of said lateral distance between the said image position and the common mid-point location.

[0047] In order to estimate an aperture value .sub.S[x, y, z] for a migrated value M.sub.S[x,y,z], i.e. a value for a shot S and a subsurface position x, y, z, a division process is performed in step 50 to evaluate M.sub.S[x,y,z]/M.sub.S[x,y,z].

[0048] A raw division of the two numbers may give rise to stability issues but is possible. Instead, it may be better to cast the division as a set of local least square problems. The aperture value .sub.S[x, y, z] is then found by minimizing a cost function J.sub.S,x,y,z(a) defined in a neighborhood (x,y,z) centered on the location x, y, z. A possible expression of the cost function J.sub.S,x,y,z(a) is:

[00001]$\begin{array}{cc}{J}_{S,x,y,z}\left(a\right)=\frac{1}{2}.Math.{}_{\left(u,v,w\right)\left(x,y,z\right)}^{}.Math.{.Math.M_S^a\left[u,v,w\right].Math.a-M_S^{.Math..Math.a}\left[u,v,w\right].Math.}^2.Math.\mathrm{du}.Math.\mathrm{dv}.Math.\mathrm{dw}& \left(1\right)\end{array}$

where M.sub.S.sup.a[x, y, z]=M.sub.S[x,y,z]+i.H(M.sub.S[x,y,z]) is the analytic signal of the reflectivity, H denoting the Hilbert transform, and M.sub.S.sup.a[x, y, z]=M.sub.S[x,y,z]+i.H(M.sub.S[x,y,z]). The size of the neighborhood (x,y,z) is variable and can depend on the application. It is selected such that the value of the migrated attribute a can reasonably be assumed to be constant over (x,y,z) for a given shot.

[0049] The aperture values .sub.S[x, y, z] may then be contained as:

[00002]$\begin{array}{cc}{\hat{a}}_S\left[x,y,z\right]=\underset{a}{\mathrm{Arg}.Math..Math.\min }.Math.\left(J_{S,x,y,z}\left(h\right)\right)=\frac{{}_{\left(x,y,z\right)}^{}.Math.M_S^{.Math..Math.a}\left[u,v,w\right].Math.{\left(M_S^a\left[u,v,w\right]\right)}^{*}.Math.\mathrm{du}.Math.\mathrm{dv}.Math.\mathrm{dw}}{{}_{\left(x,y,z\right)}^{}.Math.M_S^a\left[u,v,w\right].Math.{\left(M_S^a\left[u,v,w\right]\right)}^{*}.Math.\mathrm{du}.Math.\mathrm{dv}.Math.\mathrm{dw}}& \left(2\right)\end{array}$

where the superscript (.)* denotes the Hermitian. Note that the upper part of the right-hand side of equation (2) is the cross-correlation of the two images, the standard migrated image and the attribute-migrated image. The lower part is the auto-correlation of the standard migrated image, or the envelope. In this way, the stability of the division is increased.

[0050] The aperture values .sub.S[x, y, z] thus obtained are used to map the reflectivity values M.sub.S[x,y,z] to corresponding apertures a, which reflectivity values can then arranged as surface aperture indexed CIGs at the horizontal positions x, y:

[00003]$\begin{array}{cc}{R}_{x,y}\left[z,a\right]={}_S.Math.M_S\left[x,y,z\right].Math.\left(a-{\hat{a}}_S\left[x,y,z\right]\right)& \left(3\right)\end{array}$

[0051] This process of computing the surface aperture indexed CIGs is illustrated in the diagram of FIG. 3. The aperture attribute is obtained by the double migrated map division. The two upper panels of the diagram depict two common shot migrated images showing a horizontal reflector. The first image is obtained by means of Reverse Time migration of plain seismic data, while the second is the output of migration where the data have been multiplied by the common mid-point distance m. In this panel, amplitudes vary laterally along the reflector and are proportional to the receiver position and, therefore, to the aperture. In particular, starting from the left side, the amplitude is negative, it reaches zero exactly below the point C as defined in FIG. 1 and becomes positive afterwards.

[0052] For a specific position (x.sub.0, z.sub.0) in the shot migrated image (here, the horizontal position x.sub.0 may be 2D, with x and y components), we have a particular value of reflectivity R. At the same position in the attribute-migrated image, the value of the reflectivity is R multiplied by the common mid-point m. The aperture is function of the division of the two quantities. With these four values (x.sub.0, z.sub.0, a, R), we can now build the migrated aperture cube. The lower panel the diagram of FIG. 3 represents a common-midpoint section at the location x.sub.0. The contribution of the reflectivity R is added to the position whose coordinates are given by the couple depth/aperture (z.sub.0,a).

[0053] The proposed method to obtain classical surface gathers for various PSDM techniques including Reverse Time migration showed to be successfully applicable in the context of band-limited propagation. The proposed methods do not depend on a particular implementation of wave-field extrapolation method, since it can be performed after shot-record migration in Fourier domain, time domain, etc.

[0054] An advantage of this method is that it allows the use of better propagators than rays to propagate the wave-field, making it possible to adopt the full arsenal of standard tools for post-processing developed for asymptotic migration schemes. Compared to Subsurface-Offset and Scattering Angle Subsurface-Offset, Aperture CIGs for RTM are way less expensive to compute, and they preserve the kinematic move-out.

[0055] The embodiments of the method described herein may be implemented on any form of computer or computers and the components may be implemented as dedicated applications or in client-server architectures, including a web-based architecture, and can include functional programs, codes, and code segments. Any of the computers may comprise a processor, a memory for storing program data and executing it, a permanent storage such as a disk drive, a communications port for handling communications with external devices, and user interface devices, including a display, keyboard, mouse, etc.

[0056] Typically, the method is carried out using software modules which may be stored as program instructions or computer readable codes executable on the processor on a computer-readable media such as read-only memory (ROM), random-access memory (RAM), CD-ROMs, magnetic tapes, floppy disks, and optical data storage devices. The computer readable recording medium can also be distributed over network coupled computer systems so that the computer readable code is stored and executed in a distributed fashion. This media is readable by the computer, stored in the memory, and executed by the processor.

[0057] It will be appreciated that the embodiments described above are illustrative of the invention disclosed herein and that various modifications can be made without departing from the scope as defined in the appended claims.