Abstract:
A system and method perform structure-preserving smoothing (SPS) using a data adaptive method for smoothing 3D post-stacked seismic attributes which reduces random noise while preserving the structure without prior computation of its orientation. The data is smoothed within a neighborhood sub-window along a set of predefined orientations, and the best smoothing result is then selected for output. The orientation corresponding to the best result often approximates the true structure orientation embedded in the data, so that the embedded structure is thus preserved. The SPS method can also be combined with median, alpha-trim, symmetric near neighbor, or edge-preserving filters. The SPS method is an effective way to reduce random noise and eliminate noise footprints, and to enhance coherence and curvature attributes.

Description:
FIELD OF THE INVENTION 
       [0001]    This invention relates to the processing of seismic data, and in particular to a system and method for smoothing seismic data while preserving structural information. 
       BACKGROUND OF THE INVENTION 
       [0002]    As referred to herein, the term “structure” includes a planar feature in three-dimensional (3D) datasets as well as a linear feature in two-dimensional (2D) datasets. Examples of structures are horizons in post-stacked amplitude seismic data and faults, or unconformities in coherence or curvature volumes. 
         [0003]    Seismic data often contain both useful structural information and useless random noise. It is desirable to enhance the structures and reduce the random noise. It is commonly known that smoothing is an effective way of reducing random noise. An article by Hall, M., “Smooth Operator: Smoothing Seismic Interpretations and Attributes”, The Leading Edge, pp. 16-20, 2007, summarizes eight smoothing methods and discusses their effects. Gaussian and mean filters are structure in-distinguishable and smear the edges and texture boundaries. After these filters are applied, the resolution of horizons, faults, and unconformities are reduced or even lost. Edge-preserving smoothing, such as the known Kuwahara filter, is able to keep edges in 2D, but its 3D counterpart, as described in AlBinHassan, N. M., Luo, Y., and Al-Faraj, M. N., “3D Edge-Preserving Smoothing and Applications”, Geophysics, Vol. 71, pp. 5-11, 2006, is designed to preserve body segmentation and cannot keep planar structures, such as faults. 
         [0004]    Structure-oriented filtering, as described in Fehmers, G. C. and Hocker, C. F. W., “Fast Structural Interpretation with Structure-Oriented Filtering”, Geophysics, Vol. 68, pp. 1286-1293, 2003, solves this problem by computing the structural orientation first, and applies a diffusion scheme along the known orientation. The prior computation of structural orientation and the diffusion algorithm are computational costly, inaccurate for noisy regions, and impossible for non-structured areas which are commonly found in coherence or curvature data. 
         [0005]    Another method of filtering known to the prior art is edge-preserving smoothing (EPS), also known as the Kuwahara filter, is described in Luo, Y., Marhoon, M., Al-Dossary, S., and Al-Faraj, M. N., “Edge-Preserving Smoothing and Applications”, The Leading Edge, pp. 136-158, 2002; and also in Hall, M., “Smooth Operator: Smoothing Seismic Interpretations and Attributes”, The Leading Edge, pp. 16-20, 2007. In the application of EPS, a set of predefined neighborhood sub-windows are used and the best result, which is usually the one with minimum deviation, is selected for smoothed output. 
       SUMMARY OF THE INVENTION 
       [0006]    A data adaptive smoothing method, referred to herein as a structure-preserving smoothing (SPS) method, is provided that does not require prior computation of structural orientation and serves to preserve the structures, if they exist. Compared to structure-oriented filtering, as described in Fehmers, G. C. and Hocker, C. F. W., “Fast Structural Interpretation with Structure-Oriented Filtering”, Geophysics, Vol. 68, pp. 1286-1293, and in U.S. Pat. Nos. 6,473,697 and 6,725,174, the method of the invention is faster and more robust because it works for both structured and non-structured areas. 
         [0007]    The concept of SPS constitutes an improvement over EPS alone. SPS and EPS work in parallel ways. In EPS, a set of predefined neighborhood sub-windows are used and the best result, which is usually the one with minimum deviation, is selected as smoothed output. In SPS, a set of predefined orientations are used for smoothing, and the best result is selected. If structures exist, such as planar or linear features, the selected result is likely to be the best in alignment with the true structure. 
         [0008]    The selection rule of SPS can be a minimum deviation rule, such as is commonly used in EPS. For polar data containing both positive and negative numbers, such as seismic amplitude, the selection rule can also be absolute maximum. For mono-polar data, having only positive numbers, such as coherence or curvatures, the selection rule can be maximum or minimum summation, depending on which end the structure resides. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0009]    Preferred embodiments of the invention are described below and with reference to the drawings, in which: 
           [0010]      FIG. 1  is a schematic block diagram of the system of the present invention; 
           [0011]      FIG. 2  is a flowchart of operation of the method of the present invention; 
           [0012]      FIGS. 3A-3B  illustrate the geometry of a cube and orientation slices thereof; 
           [0013]      FIG. 4  illustrates a hexagonal slice of a 5×5×5 sub-window of a cube; 
           [0014]      FIGS. 5A-5B  illustrate reduction of random noise in a seismic section; 
           [0015]      FIGS. 6A-6B  illustrate elimination of a patterned noise footprint in a seismic data image; 
           [0016]      FIGS. 7A-7C  illustrate reduction of coherence noise; 
           [0017]      FIGS. 8A-8D  illustrate filtering of a seismic section with faults showing a cleaner curvature attribute; and 
           [0018]      FIGS. 9A-9D  illustrate filtering of a seismic section with faults using a time slice and showing a cleaner curvature attribute. 
       
    
    
     DETAILED DESCRIPTION 
       [0019]    As illustrated in  FIGS. 1-9D , a system and method perform structure-preserving smoothing (SPS) on seismic data to generate a smoothed image which retains structures in reservoirs for visual inspection and analysis by a user. The system  10  in  FIG. 1  includes a computer  14  accessed by the user  12 , a computer-based system  16 , and a seismic data source  18  which provides seismic data obtained from a reservoir study to the computer-based system  16 . The computer-based system  16  processes the seismic data from the seismic data source  18  to generate an SPS smoothed image  20  which is displayed to the user  12  on a display monitor  22  of the computer  14 . The user  12  can control the system  10  and the display of the SPS smoothed image  20  using an input device  24 . 
         [0020]    The computer-based system  16  includes a processor  26  and a memory  28 , where the memory  28  is capable of storing the seismic data from the seismic data source  18 . The processor  26  executes predetermined software  30  to implement the SPS method of the invention as described herein to process the seismic data and to generate the SPS smoothed image  20 . 
         [0021]    As shown in  FIG. 2 , the disclosed SPS method  32 , implemented by the predetermined software  30 , includes the steps of receiving the seismic data in step  34 , testing the smoothing in a set of different orientations in step  36 , filtering through a data volume in step  38 , selecting the best smoothing result using a minimum deviation in step  40 ; and displaying to the user  12  on display device  22  in step  42  a structure-preserving smoothed image of the best smoothing result, which includes the preserved structures in the seismic data. 
         [0022]    An optional further step can include using a supplemental filtering method to generate a supplemental smoothed image in step  44 . The supplement filtering step can employ the EPS method, a median filter method, symmetric-near-neighbor method, or any 2D smoothing algorithm in order to produce various filtering effects. 
         [0023]    In an alternative embodiment, step  40  of selecting the best smoothing result can include using a maximum summation method for coherence data in which interesting structures reside near the high end. Alternatively, step  40  can use an absolute-maximum summation method for seismic amplitudes where positive and negative values are layered over each other. 
         [0024]    Referring to  FIGS. 3-9B , the operation of the system  10  and method  32  are illustrated in greater detail to show that the essence of the disclosed SPS method of the present invention is to test smoothing in a set of different orientations, and to select the best smoothing result. First, a description is provided as to how the set of orientations are defined. 
         [0025]    As disclosed herein, the notation by Bakker, P., “Image Structure Analysis for Seismic Interpretation”, PhD Thesis, Universiteit Delft, 2002, for defining orientations and directions is used to distinguish “orientation” from “direction”. A direction is 360 degrees rotationally symmetric. If the coordinate system rotates 360 degrees about an axis perpendicular to a specific direction, the direction is unchanged. In contrast to this, an orientation is 180 degrees rotationally symmetric. For example, a flat sheet of paper has two surfaces and two normal directions, but only one orientation. 
         [0026]    For simplicity and computational efficiency, a neighborhood sub-window is assumed to be a centered cube with dimensions 3×3×3 or 5×5×5 etc. All data points must be on a regular grid and interpolation should be avoided. 
         [0027]    As shown in  FIGS. 3A-3B , the geometry of a cube is defined by six sides, with a set of orientation slices defined for the cube. Using an orientation slice between each pair of opposite sides, as shown in  FIG. 3A , then there are three slices. Similarly, using orientations midway between opposite edges, as shown in  FIG. 3B , there are six slices between twelve edges. Similarly, using orientations midway between the corners, as shown in  FIG. 3C , there are four slices between eight corners. For a particular application, a selection of predefined orientation slices is defined, and so one may use three orientations between six sides, or nine orientations plus those slices between edges, or all thirteen orientations as in the examples described below: As will be understood by one of ordinary skill in the art, the choice of pre-defined sets is a compromise between accuracy and computational cost. 
         [0028]    It is also to be understood that the number of data points on each orientation slice could be different. For instance in a 3×3×3 cube, a slice between edges contains nine points, while a slice between corners has only seven points. 
         [0029]    As shown in  FIG. 4 , a hexagonal slice of a 5×5×5 sub-window of a cube, similar to the slice shown in  FIG. 3C , has the normal direction that is diagonal in an axis frame, and all data points are on a regular grid for any size of the sub-window, so that corner-facing slices are in a hexagon shape and are not parallel to any axis. Some geometric properties of a hexagon slice are listed in Table 1 for ease of implementation. 
         [0000]    
       
         
               
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                   
                   
                 NUMBER OF 
                 TOTAL NUMBER 
               
               
                   
                   
                 POINTS IN THE 
                 OF POINTS IN A 
               
               
                 SUB-WINDOW 
                 RADIUS 
                 OUTER RING 
                 SLICE 
               
               
                   
               
             
             
               
                 3 × 3 × 3 
                 1 
                  6 
                  7 
               
               
                 5 × 5 × 5 
                 2 
                 12 
                 19 
               
               
                 . . . 
                 . . . 
                 . . . 
                 . . . 
               
               
                 (2R + 1) 3   
                 R 
                 6R 
                 1 + 3R(R + 1) 
               
               
                   
               
             
          
         
       
     
         [0030]    Selection of predefined orientation slices can be adjusted according to applications. For example, coherence and curvature attributes are intended to view dykes and faults. The interesting features are in near-vertical planes; therefore, the horizontal slice should be excluded. To smooth seismic events for easier auto-tracking of horizons, the four vertical slices are not required. 
         [0031]    After testing and selecting the set of orientation slices in step  36 , filtering through a data volume is performed by the system  10  and method of the present invention in step  38  using known filtering methods. The best smoothing result in step  40  can be selected using the minimum standard deviation. For example, the average value and standard deviation is computed for each of the 13 predetermined directions. The direction with the minimum standard deviation is selected as the best direction to smooth. The minimum standard deviation is determined from the input data, which could be seismic amplitude or any other attribute such as coherence or curvature, which has shown to be a reasonable choice for almost any data type. 
         [0032]    In addition, for coherence data in which interesting structures reside near the high end, maximum summation is also appropriate. For seismic amplitude where positive and negative values are layered over each other, absolute-maximum summation can be used. The selection rule can vary depending on particular applications. 
         [0033]    After identifying the best orientation within a specified sub-window in step  40 , the smoothed image  20  is generated using a known smoothing method applied to the best orientation, with the smoothed image  20  sent to the display  22  for display in step  42 . Examples of the smoothed images shown in  FIGS. 5B ,  6 B,  7 C,  8 C- 8 D, and  9 C- 9 D are described in more detail below. 
         [0034]    In alterative embodiments, further filtering can be performed on the smoothed images  20 , by which the SPS method  32  of the present invention can be combined with an EPS method, a median filter method, a symmetric-near-neighbor method, or any 2D smoothing algorithm used in order to produce various filtering effects, as in step  44  in  FIG. 2 . 
       APPLICATION EXAMPLES 
       [0035]    Preliminary results of using SPS filtering in order to reduce random noise in seismic sections, eliminate noise footprints, and enhance coherence image are described below. 
         [0036]    In a first example, a seismic section is displayed in  FIG. 5A . After SPS filtering with a 5×5×5 sub-window and minimum deviation rule, as shown in  FIG. 5B , the random noise is obviously reduced and horizon continuity is improved. These improvements would aid in interpretation by the user 12 of features and structures, for example, in a reservoir, as well as auto-tracking horizons. 
         [0037]    In another example, a footprint may be visible in seismic data images, where the footprint is a patterned noise resulting from acquisition or processing bias. It usually appears in a time slice in seismic amplitude data.  FIG. 6A  is a seismic time slice in which horizontal stripes are visible. The horizontal direction is sub-line and the vertical direction is cross-line, and the line spacings are 50 m and 25 m respectively. Because the line spacings are unequal, the observed horizontal stripes are likely to be processing artifacts. The SPS method is applied using a 5×5×5 sub-window and a minimum deviation rule. The resultant image, as shown in  FIG. 6B , is much cleaner and the footprint is completely removed. 
         [0038]    In a further example using 3D data volumes, coherence measures the similarity between neighboring vertical traces, as described in Bahorich, M. S. and Farmer, S. L., “ 3 -D Seismic Discontinuity for Faults and Stratigraphic Features: The Coherence Cube”, The Leading Edge, pp. 1053-1058, 1995. This attribute often highlights plane-like features such as dykes, faults, unconformities and fractures. An initial seismic time slice is illustrated in  FIG. 7A . After polarization and skeletonization, these features are illustrated in  FIG. 7B  as lineaments which can be overlaid on seismic data to aid the user in the interpretation of the seismic data. Applying the SPS method to coherence data with application of the maximum summation rule, the resultant skeleton is cleaner, as shown in  FIG. 7C , with a reduction of coherence noise. 
         [0039]    In another example, the most-negative/positive seismic curvature measures the rate of angular changes of seismic events along a horizontal direction, as described in Al-Dossary, S. and Marfut, K. J., “3D Volumetric Multispectral Estimates of Reflector Curvature and Rotation”, Geophysics, Vol. 71, pp. 41-51, 2006. As with coherence data, the curvature attribute also extracts faults and fractures for seismic interpretation.  FIGS. 8A-9D  show examples of using the SPS system and method of the present invention to clean the curvature attribute and achieve more readily interpretable images. 
         [0040]      FIG. 8A  illustrates a seismic section with faults, and  FIG. 8B  illustrates the seismic section of  FIG. 8A  filtered to show the most-positive curvatures.  FIG. 8C  illustrates the data of  FIG. 8B  with an SPS filtering using a 3×3×3 sub-window, while  FIG. 8D  illustrates the data of  FIG. 8B  with an SPS filtering using a 5×5×5 sub-window;  FIGS. 8C-8D  show resulting images which are better correlated with faults and that exhibit a cleaner curvature attribute. 
         [0041]      FIGS. 9A-9B  illustrate the same seismic section with faults as in  FIG. 8A , but viewed in time slice.  FIG. 9A  illustrates seismic amplitudes and  FIG. 9B  illustrates the seismic section of  FIG. 9A  filtered to show the most-positive curvatures.  FIG. 9C  illustrates the data of  FIG. 9B  with an SPS filtering using a 3×3×3 sub-window, while  FIG. 9D  illustrates the data of  FIG. 9B  with an SPS filtering using a 5×5×5 sub-window;  FIGS. 9C-9D  show resulting images which are better correlated with faults and exhibit a cleaner curvature attribute. 
         [0042]    As demonstrated by the examples of processed seismic image data, the system  10  and method  32  of the present invention for implementing SPS provide a new smoothing apparatus and method for filtering out the random noise in post-stacked seismic attributes. Preliminary tests show that SPS can clear up seismic sections, eliminate footprints, and enhance the coherence image. SPS is simple and robust, and works for both structured and non-structured data. The SPS system  10  and method  32  of the present invention can also be used in broader applications for seismic interpretation, and more generally, in the image processing field. 
         [0043]    While the preferred embodiment of the present invention has been shown and described herein, it will be obvious that such embodiment is provided by way of example only. Numerous variations, changes and substitutions will occur to those skilled in the art without departing from the invention herein. Accordingly, it is intended that the invention be limited and defined by the claims that follow.