Post-Stack Kirchhoff Depth De-Migration Method for Tilted Transverse Isotropic (TTI) and Heterogeneous Media Based on Ray Tracing on Migrated Data

Abstract

The present invention is related to a specific de-migration method based on ray tracing algorithms characterized in that the interpolation procedure involved in the computation of the travel time required by the de-migration is being modified. The interpolation according to the invention obtains an accurate travel time for those rays departing from sources being interpolated.

Claims

1. A post-stack Kirchhoff depth de-migration method for tilted transverse isotropic (TTI) and heterogeneous media based on ray tracing on migrated data comprising: providing a seismic image (I(x,z)) of subsurface points in a depth domain () generated by migration wherein said depth domain () comprises subsurface points and surface points (); providing a wave propagating velocity model on the depth domain (); determining anisotropy parameters, dip angle and azimuthal angle of a tilted transverse isotropic media in the depth domain (); generating a fine grid of surface sources (S.sub.1, S.sub.2, S.sub.3, S.sub.4, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d, S.sub.i); generating a coarse grid of surface sources (S.sub.1, S.sub.3, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d) by coarsening the fine grid of the surface sources (S.sub.1, S.sub.2, S.sub.3, S.sub.4, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d, S.sub.i); generating a travel time table storing at least the travel time between a surface source (S.sub.1, S.sub.3, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d) of the coarse grid and the subsurface points of the seismic image (I(x,z); carrying out de-migration by solving the Kirchhoff equation wherein the travel time between a surface source (S.sub.1, S.sub.2, S.sub.3, S.sub.4, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d, S.sub.i) and a subsurface point (P) of the seismic image (I(x,z)) in the depth domain () required when solving the Kirchhoff equation is taken from the travel time table if the surface source (S.sub.1, S.sub.3, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d) is in the coarse grid; or calculated by interpolation if the surface source (S.sub.1, S.sub.2, S.sub.3, S.sub.4, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d, S.sub.i) is in the fine grid but not in the coarse grid, wherein the interpolation of the travel time between a surface source (S.sub.1, S.sub.2, S.sub.3, S.sub.4, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d, S.sub.i) in the fine grid and a subsurface point (P) is as follows: determining a first pattern (PT1) comprising an arrangement of points defined by the locations of: a set of surface sources (S.sub.3, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d) of the coarse grid surrounding the surface source (S.sub.4, S.sub.i) of the fine grid and, the surface source of the fine grid (S.sub.4, S.sub.i) where the travel time is being calculated; determining the subsurface points (R.sub.3, R.sub.5, R.sub.a, R.sub.b, R.sub.c, R.sub.d, P) of the image (I(x,z)) in the depth domain () according to a second pattern (PT2), being said second pattern (PT2) an arrangement of subsurface points having the same number of nodes, the same shape and same dimensions than the first pattern (PT1), the second pattern (PT2) being parallel to the surface () and, located such that the location of the subsurface point (P) of the second pattern (PT2) corresponding to the surface source (S.sub.4, S.sub.i) of the first pattern (PT1) at the fine grid is located at the subsurface point (P) of the image (I(x,z)) where the travel time is being calculated; determining the interpolated travel time as a weighted average of all the travel time values calculated between a surface source (S.sub.3, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d) of the first pattern (PT1) and the corresponding subsurface point (R.sub.3, R.sub.5, R.sub.a, R.sub.b, R.sub.c, R.sub.d) of the image (I(x,z)) of the second pattern (PT2); making available the de-migrated data.

2. A method according to claim 1, wherein a kernel of the integral expression of the Kirchhoff equation further comprises an amplitude weighting function w.sub.dip for enhancing dipping events being expressed as: $w_{\mathrm{dip}}=\sqrt{1+{\left(\frac{\mathrm{dz}}{\mathrm{dx}}\right)}^2+{\left(\frac{\mathrm{dz}}{\mathrm{dy}}\right)}^2}$ wherein dz/dx and dz/dx are the slope along an inline direction, that is, the shooting line, and a crossline direction, that is, the direction that is perpendicular to the inline direction, of the depth domain respectively.

3. A method according to claim 1, wherein a kernel of the integral expression of the Kirchhoff equation further comprises an anti-alias filter F.

4. A method according to claim 3, wherein the image of the migrated depth domain is mapped into the time domain and the anti-alias filter is a triangle filter for anti-alias the image in the time domain.

5. A method according to claim 1, wherein the fine grid and the coarse grid are structured grids.

6. A method according to claim 5, wherein the domain () is a 3D domain and, the fine grid and the coarse grid are rectangular.

7. A method according to claim 1, wherein the weights weighting the travel times determined between the sources (S.sub.3, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d) of the first pattern (PT1) and the corresponding subsurface point (R.sub.3, R.sub.5, R.sub.a, R.sub.b, R.sub.c, R.sub.d) of the image (I(x,z)) of the second pattern (PT2) are inversely proportional to the distance between the interpolated source (S.sub.3, S.sub.i) and the surface source (S.sub.3, S.sub.5, S.sub.a, S.sub.b, S.sub.c, S.sub.d) corresponding to the travel time being weighted.

8. A method according to claim 1, wherein the post-stack Kirchhoff depth de-migration method is applied for a plurality of source grids and the resulting de-migrated data are being stacked.

9. A post-stack Kirchhoff depth migration method comprising: a) carrying out a prestack depth Kirchhoff migration on a plurality of shot data; b) stacking the plurality of migrated data; c) carrying out a post-stack Kirchhoff depth de-migration method according to claim 1; d) carrying out a post-stack Kirchhoff depth migration on the de-migrated data providing seismic data; e) making available the obtained depth migration of seismic data.

10. A non-transitory computer program product stored on a computer-readable medium and comprising computer-implementable instructions, which, when executed by a computer, cause the computer to carry out the method according to claim 1.

11. A data processing system having a processor and a non-transitory computer-readable medium storing computer-executable instructions which, when executed by the processor, cause the processor to carry out a method according to claim 1.

Description

DESCRIPTION OF THE DRAWINGS

[0081] These and other features and advantages of the invention will be seen more clearly from the following detailed description of a preferred embodiment provided only by way of illustrative and non-limiting example in reference to the attached drawings.

[0082] FIG. 1 This figure shows a data processing system for carrying out a method according to the invention.

[0083] FIG. 2A This figure shows an 2D example of de-migration data by using an interpolation method according to the prior art.

[0084] FIG. 2B This figure shows the same 2D example of de-migration data as the previous figure wherein the interpolation method is carried out according an embodiment of the invention.

[0085] FIG. 3 This figure shows an embodiment of the invention wherein the domain is a 3D domain and the interpolation is carried out by using rectangular structured fine and coarse grids.

[0086] FIG. 4 This figure shows the inline image from a 2.5D example of model at the left side and, the corresponding slopes derived from said image at the right side.

[0087] FIG. 5 This figure shows the re-migrations of the de-migrations of the example shown in the previous figure without slope weighting (right side) and with slope weighting (left side) respectively.

DETAILED DESCRIPTION OF THE INVENTION

[0088] As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a circuit, module or system. Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon.

[0089] Any combination of one or more computer readable medium(s) may be utilized. The computer readable medium may be a computer readable signal medium or a computer readable storage medium. A computer readable storage medium may be, for example, but not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. More specific examples (a non-exhaustive list) of the computer readable storage medium would include the following: an electrical connection having one or more wires, a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing. In the context of this document, a computer readable storage medium may be any tangible medium that can contain, or store a program for use by or in connection with an instruction execution system, apparatus, or device.

[0090] A computer readable signal medium may include a propagated data signal with computer readable program code embodied therein, for example, in baseband or as part of a carrier wave. Such a propagated signal may take any of a variety of forms, including, but not limited to, electro-magnetic, optical, or any suitable combination thereof. A computer readable signal medium may be any computer readable medium that is not a computer readable storage medium and that can communicate, propagate, or transport a program for use by or in connection with an instruction execution system, apparatus, or device.

[0091] Program code embodied on a computer readable medium may be transmitted using any appropriate medium, including but not limited to wireless, wireline, optical fiber cable, RF, etc., or any suitable combination of the foregoing.

[0092] Computer program code for carrying out operations for aspects of the present invention may be written in any combination of one or more programming languages, including an object oriented programming language such as Java, Smalltalk, C++ or the like and conventional procedural programming languages, such as the C programming language or similar programming languages. The program code may execute entirely on the user's computer, partly on the user's computer, as a stand-alone software package, partly on the user's computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user's computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider).

[0093] Aspects of the present invention are described below with reference to illustrations and/or diagrams of methods, apparatus (systems) and computer program products according to embodiments of the invention. It will be understood that each illustration can be implemented by computer program instructions. These computer program instructions may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

[0094] These computer program instructions may also be stored in a computer readable medium that can direct a computer, other programmable data processing apparatus, or other devices to function in a particular manner, such that the instructions stored in the computer readable medium produce an article of manufacture including instructions which implement the function/act specified in the flowchart and/or block diagram block or blocks.

[0095] The computer program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other devices to cause a series of operational steps to be performed on the computer, other programmable apparatus or other devices to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide processes for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks.

[0096] Turning now to the drawings and more particularly, FIG. 1 shows an example of a system 100 for determining zero offset seism data in the time domain equivalent to the acquired field seismic data with a source and a sensor in the same surface location by a post-stack Kirchhoff depth de-migration method carried out for anisotropic tilted isotropic (TTI) media based on ray tracing on migrated data, according to a preferred embodiment of the present invention.

[0097] The preferred system 100 determines a de-migrated data in an efficient manner as an interpolation method is used for the look-up time table's generation as those are limited to a sub-set of sources. The interpolation method according to the invention reduces the distortion of the seismograms from de-migration.

[0098] A preferred computing system 100 includes one or more computers 102, 104, 106 (3 in this example), coupled together, e.g., wired or wirelessly over a network 108. The network 108 may be, for example, a local area network (LAN), the Internet, an intranet or a combination thereof. Typically, the computers 102, 104, 106 include one or more processors, e.g., central processing unit (CPU) 110, memory 112, local storage 114 and some form of input/output device 116 providing a user interface. The local storage 114 may generate and/or include the time table or time tables stored as look-up tables being accessible by the plurality of computers 102, 104, 106, processing in parallel a plurality of migrated data in order carry out in a later stage a post-stack process over the de-migrated data provided by each computer 102, 104, 106.

[0099] FIG. 2B shows an example of one aspect of the invention using a preferred computing system (e.g., 100 of FIG. 1) wherein an anisotropic ray tracing algorithm is used to compute the travel time required by de-migration. Therefore, the proposed de-migration method is suitable for complicated structures.

[0100] Theoretically, de-migration requires travel time tables for every image traces. The source (S.sub.1, S.sub.2, S.sub.3 S.sub.4, S.sub.5) corresponding to a table is located at a surface () location of the domain () and rays from the source (S.sub.1, S.sub.2, S.sub.3 S.sub.4, S.sub.5) traveling into all subsurface points (P) within a given aperture ().

[0101] Therefore, travel time computation requires massive computation power. For anisotropic media, it even needs further more computational cost than isotropic media. To reduce computational cost, travel time tables are computed and stored only for given sparse surface source (S.sub.1, S.sub.3, S.sub.5) locations. In an embodiment of the invention said travel time tables are stored into a disk file on the local storage 114 (FIG. 1).

[0102] Those sources (S.sub.1, S.sub.3, S.sub.5) where the time table has been determined are represented in FIGS. 2A and 2B by a pointer departing from the source (S.sub.1, S.sub.3, S.sub.5) and pointing to a graphical representation table. Travel time determined between a source (S.sub.2, S.sub.4) not having a time table available and a subsurface point (P) is determined by interpolating data that involves the reading of time tables of surrounding sources (S.sub.1, S.sub.3, S.sub.5) having time tables.

[0103] During process of de-migration, travel time between a certain source (S.sub.4) and a subsurface point (P) with a value defined by the migrated image I(x,z) is computed by interpolating the values stored (114) in the time tables. As it is shown in FIGS. 2A and 2B, sources (S.sub.3, S.sub.5) are surface sources having a time table that are surrounding the surface source (S.sub.4) which has not a time table available.

[0104] FIG. 2A shows a conventional interpolation algorithm according to the prior art. According to said conventional interpolation algorithm and being a 2D domain, two surface sources (S.sub.3, S.sub.5) adjacent to the location of the interpolated source (S.sub.4) are first selected.

[0105] FIG. 2A shows this algorithm for a two dimensional case. The horizontal axis is the surface x coordinate and vertical axis is the depth z coordinate.

[0106] The travel time tables for the surface sources (S.sub.1, S.sub.3, S.sub.5) have been computed by a pre-processing step while the travel table for surface source (S.sub.4) is required to get using interpolation.

[0107] Taking subsurface point (P) as an example for interpolation, the travel times from S.sub.3 to P and from S.sub.5 to P are used to interpolate travel time from S.sub.4 to P. This algorithm is identified as conventional algorithm. This conventional algorithm is very efficient while it results in errors in travel time, especially for shallow part even by using a velocity model where the velocity is constant. The travel time error results in distorted seismogram from de-migration.

[0108] FIG. 2B shows and embodiment of the invention applied over a two dimensional domain improving the accuracy of interpolation.

[0109] For any subsurface point P, two adjacent points corresponding to two surface sources (S.sub.3, S.sub.5) are selected. The two selected surface sources (S.sub.3, S.sub.5) having a time table plus the intermediate interpolating source (S.sub.4) defines a first pattern. This first pattern is shown in FIG. 3B using thicker connecting lines between sources S.sub.3, S.sub.4, and S.sub.5.

[0110] A second pattern is defined as the first pattern. In this embodiment the second pattern has also three points with the same separating distances determining two subsurface points (R.sub.3, R.sub.5) separated from the subsurface point P as defined by said second pattern.

[0111] Travel times involving these two adjacent points (R.sub.3, R.sub.5) are used to interpolate the travel time from the interpolated source S.sub.4 to the subsurface point P. Under the constant velocity assumption, the proposed algorithm generates accurate travel time as the computed one.

[0112] FIG. 2B shows this equal offset interpolation for the two dimensional case wherein the subsurface point R.sub.3 corresponds to source S.sub.3; subsurface point R.sub.5 corresponds to source S.sub.5 and P corresponds to the interpolated source S.sub.4. Travel times from S.sub.3 to R.sub.3, and from S.sub.5 to R.sub.5 are used to interpolate travel time from S.sub.4 to R.sub.4 by a weighted averaged computation.

[0113] An example of weights for said weighted averaged computation makes use of weights inversely proportional to the distance between the surrounding source having a time table and the interpolated source. According to an example, a trilinear interpolation based on the distance is used.

[0114] FIG. 3 shows a schematic graphical representation of a 3D domain with the upper surface comprising a plurality of sources located at the nodes of a fine rectangular and structured grid. A coarse grid is being represented over-imposed on the fine grid by using thicker lines.

[0115] The travel time tables for those surface sources located at the nodes of the coarse grid have been calculated by a pre-processing step.

[0116] FIG. 3 shows a surface source S.sub.i of the fine grid which is not in the coarse grid that is surrounded by four surface sources (S.sub.a, S.sub.b, S.sub.c S.sub.d) located on the coarse grid. Those five sources (S.sub.i, S.sub.a, S.sub.b, S.sub.c S.sub.d) define a first pattern (PT1).

[0117] A second pattern (PT2) having the same shape and dimensions than the first pattern (PT1) is defined and located within the domain under the surface 652. Said second pattern (PT2) is oriented parallel to the first pattern (PT1) and moved to a position such that the point corresponding to the interpolated source (S.sub.i) is now located at the point P under the surface where the travel time is being interpolated. The wording moved to must be construed as that the second pattern (PT2) is being located at a different location than the first pattern (PT1) as it has been disclosed.

[0118] This FIG. 3 also shows the connecting lines between each point of the first pattern (PT1) and the corresponding point of the second pattern (PT2) by using thin lines. All those connecting lines are parallel.

[0119] For validating the present invention, the proposed de-migration method has been used into both synthetic and field data examples. The examples shows the improvements from the implementation. To validate the proposed de-migration method, we re-migrate the de-migration result using the same models. In ideal situation, the image input for de-migration and the image from re-migration should be the same.

[0120] FIGS. 4 and 5 show the application to the 2.5D synthetic examples. The 2.5 velocity model for the examples is the modification from Hess VTI datasets wherein the 2.5D velocity model is a 3D model wherein 2D data is repeated along the third dimension; therefore, the 3D interpolation method according to an embodiment of the invention can be directly applied for the 2.5D data. The Hess model is available at http://software.seg.org/datasets/2D/Hess_VTI/.

[0121] FIG. 4 shows the inline image from a 2.5D model at the left side and, the corresponding slopes derived from said image at the right side.

[0122] FIG. 5 are the re-migrations of the de-migrations without slope weighting (right side) and with slope weighting (left side) respectively. Comparing two re-migrations, the slope weighting enhances the wavefield from the steep structures, especially in areas marked by the two ovals drawn over the picture.