Classifications

• • 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
  • G01V1/30—Analysis
• • 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
  • G01V1/282—Application of seismic models, synthetic seismograms

Definitions

• This invention relates generally to the field of seismic prospecting. More particularly, the invention relates to a method for constructing a model seismic image of a subsurface seismic reflector.
• seismic prospecting techniques are commonly used to aid in the search for and evaluation of hydrocarbon deposits located in subterranean formations.
• seismic energy sources are used to generate a seismic signal which propagates into the earth and is at least partially reflected by subsurface seismic reflectors.
• Such seismic reflectors typically are interfaces between subterranean formations having different elastic properties.
• the reflections are caused by differences in elastic properties, specifically wave velocity and rock density, which lead to differences in impedance at the interfaces.
• the reflections are recorded by seismic detectors at or near the surface of the earth, in an overlying body of water, or at known depths in boreholes.
• the resulting seismic data may be processed to yield information relating to the geologic structure and properties of the subterranean formations and potential hydrocarbon content.
• Non-geologic amplitude effects include mechanisms that cause the measured seismic amplitudes to deviate from the amplitude caused by the reflection coefficient of the geologic target. These non-geologic amplitude effects can be related to acquisition of the data or to near surface effects. Examples of non-geologic amplitude effects that can be particularly troublesome are source and receiver variation, coherent noises, electrical noise or spikes, and overburden and transmission effects. If uncorrected, these effects can dominate the seismic image and obscure the true geologic picture.
• a seismic wave source generates a wave that reflects from or "illuminates" a portion of a reflector.
• the collection of sources that comprises an entire 3-D survey generally illuminates a large region of the reflector.
• prestack 3-D migration algorithms can produce precise images of the reflector only if illumination is relatively uniform. Lateral velocity variations within the earth and nonuniformly sampled 3-D prestack seismic data, however, generally cause reflectors to be illuminated nonuniformly. Nonuniform illumination is generally due to varying azimuths and source- receiver midpoint locations. Consequently, prestack 3-D migrated images are often contaminated with non-geologic artifacts called an "acquisition footprint". These artifacts can interfere with the ultimate interpretation of seismic images and attribute maps. Understanding and removing the effects of the acquisition footprint has thus become important for seismic acquisition design, processing, and interpretation.
• G( ⁇ ) G 0 + r G ( ⁇ - ⁇ 0 ) .
• S 0 and G 0 are coordinate vectors describing a fixed source-receiver
• the configuration matrices are determined by
• ⁇ D also called the Huygens surface
• w is a weight chosen to preserve seismic
• ⁇ D is the diffraction traveltime connecting source S, image
• imaging with migration equation (1 ) is an 0(N 5 )
• R is the reflection coefficient for the reflector
• g(t) represents the seismic
• Migration equation (1 ) becomes, upon insertion of synthetic data equation (2), , ,r . y , A g w( ⁇ J , x) R( ⁇ J ) g(t + ⁇ D ( ⁇ l , x) - ⁇ R ( ⁇ J ))
• the target-oriented imaging equation (3) can be implemented as an 0(N 4 ) process because the image location x may be restricted to only those points in image space that lie on the reflector surface.
• the migration aperture For imaging equation (3) for some image point or reflection point x on the reflector. Schleicher et al., “Minimum Apertures and Fresnel Zones in Migration and Demigration", Geophysics, 62, 183-194, (1997), showed that the optimum migration aperture contains only those traces that are reflected from the Fresnel zone area surrounding image point x . This result only applies for migrating synthetic data that are free of diffracting targets, since otherwise a large aperture is needed to adequately focus diffracted energy. The formulas derived by Schleicher et al. (1993) and (1997) apply only to an idealized situation in which offset and azimuth are strictly constant and source - receiver spacing is uniform and dense.
• the present invention is a method for constructing a model seismic image of a subsurface seismic reflector. First, a set of source and receiver pairs is located and a subsurface velocity function is determined. Specular reflection points are determined on the subsurface seismic reflector for each of the source and receiver pairs. A Fresnel zone is determined on the subsurface seismic reflector for each of the specular reflection points, using the subsurface velocity function. One or more seismic wavelets are selected. A set of image points is defined containing the subsurface seismic reflector. A
• model seismic image of the subsurface seismic reflector is constructed, using the synthetic seismic amplitudes at the image points.
• FIG. 1 is an illustration of the geometry of a dipping planar reflector
• FIG. 2 is a flow chart illustrating the processing steps for one
• FIG. 3 is a map view of the source - receiver midpoints for the
• FIG. 4 is a map view of a portion of the source and receiver locations
• FIG. 5 is a an illustration of the geometry of the dipping planar
• FIG. 6 is a plot of 3-D time migrated synthetic data for the planar reflector dipping in the inline direction of the example
• FIG. 7 is a plot of 3-D time migrated synthetic data for the planar reflector dipping 45 degrees between the inline and crossline directions of the example;
• FIG. 8 is a plot of 3-D time migrated synthetic data for the planar reflector dipping in the crossline direction of the example.
• the present invention is developed for modeling 3-D prestack migrated images of single reflectors for realistic acquisition geometries.
• the present invention combines prestack modeling and imaging into one step, allowing the creation of black box software that is very efficient and easy to use.
• the present invention as implemented in the preferred embodiment, is simple and fast, requiring minutes on a workstation. Persons skilled in the art could easily develop computer software for use in implementing the present invention based on the teachings set forth here. In the following, the general theory is described and then acquisition footprint prediction with the present invention for prestack 3-D time migration is demonstrated.
• the present invention shows how to reveal the acquisition footprint by modeling the migrated image efficiently and accurately. Note, however, that the present invention also applies to general variable velocity media and prestack 3-D depth migration. Thus, with an adequate ray tracing algorithm, wave equation modeling software could be created to efficiently model depth migrated images in real-world situations.
• the present invention develops the Fresnel zone theory for variable
• imaging equation (3) for each image point x allows imaging equation (3) to be implemented as an 0(N 3 ) process.
• This "target-oriented imaging” may be performed efficiently on a single workstation.
• a particular embodiment of the present invention as a software tool has been produced that specializes the theory to prestack 3-D time migration, for planar reflectors, where the velocity varies with depth only, that is, a v(z) medium.
• This embodiment models the subsurface illumination or acquisition footprint caused by specific acquisition geometries.
• FIG. 1 shows a dipping planar reflector ⁇ with normal vector 100 making angles ⁇ , ⁇ , and ⁇ with the x, y, and z axes, respectively.
• dashed raypath 104 illustrated with dashed raypath 104.
• ⁇ (S, Q') is the one-way seismic signal traveltime connecting points S and
• ⁇ (S, G) is the two-way reflection traveltime from points S to Q to G for
• Surface ⁇ may be a planar reflector or the tangent
• the Fresnel zone may be further described in terms of its boundary
• diffraction traveltime TD and reflection traveltime ⁇ R are defined by
• ⁇ R (S, G) ⁇ (S, G) ⁇ ⁇ (S, Q) + ⁇ (Q, G). (6)
• Equations (10) - (12) are valid
• Transformed synthetic data equation (13) and imaging equation (14) are advantageous because it is particularly easy to restrict the summation over reflection points ⁇ . to the appropriate Fresnel zone. Further, the weight
• Imaging equation (18) precisely and efficiently models the migrated image. Further, imaging equations (17) and (18) are valid for general velocity models. Calculating seismic attributes related to the wavelet in the migrated data requires considering points within an elliptic cylinder which is the extension of the Fresnel zone perpendicular to the reflector surface a distance of approximately a wavelength above and below the reflector. To achieve this with maximum computational efficiency, a first order Taylor expansion is made perpendicular to the reflector and the equation
• ⁇ is the ray incidence angle relative to the normal vector
• v is the local seismic velocity and n is the perpendicular
• FIG. 2 is a flow chart that illustrates one embodiment of the method of the present invention for constructing a model seismic image of a subsurface seismic reflector.
• a subsurface seismic reflector is selected.
• the seismic reflector is selected from among the reflectors of interest to the processing of the seismic data set of interest.
• the seismic reflector is given by specifying a subsurface position and orientation.
• source and receiver locations for a set of source and receiver pairs are determined.
• these source and receiver pairs are selected to provide common-offset gathers in the seismic data set of interest, using standard seismic processing techniques well known to those skilled in the art. These source and receiver pairs will be used in determining specular reflection points below.
• a subsurface velocity function is selected.
• this velocity function is that which is used in the seismic processing of the data set of interest. This subsurface velocity function will be used in determining Fresnel zones below.
• specular reflection points on the subsurface seismic reflector from step 200 are determined for each of the source-receiver pairs from step 202. Preferably, these specular reflection points are determined by ray tracing.
• a Fresnel zone on the subsurface seismic reflector from step 200 is determined for each of the specular reflection points from step 206, using the subsurface velocity function from step 204. Preferably, the Fresnel zone on the subsurface seismic reflector is determined by size, shape, and orientation of the Fresnel zone ellipse on the subsurface seismic reflector.
• the size, shape, and orientation of the Fresnel zone ellipse are determined from the calculated elements of a Fresnel zone matrix.
• the elements of the Fresnel zone matrix are calculated using equations (10) - (12), above.
• one or more seismic wavelets are selected.
• the seismic wavelets are selected to match the expected seismic wavelets at depth at the reflector of interest from step 200. Typically, this is determined by examination of the seismic data set of interest.
• a set of image points is defined containing the subsurface seismic reflector from step 200.
• the set of image points is defined depending upon the seismic attributes of interest. Typically, attributes such as amplitude are determined by image points on the reflector, while attributes such as pulse length are determined by including a volume of image points within approximately a spatial wavelength of the reflector.
• a synthetic seismic amplitude is determined for each of the image points from step 212 by summing Fresnel zone synthetic seismic amplitudes for all of the Fresnel zones from step 208 which contain the image point, using the seismic wavelets from step 210.
• this summing is preferably done using imaging equation (18) above.
• the summing is preferably done using imaging equations (17) or (20), with equation (20) being computationally more efficient.
• Use of equations (17), (18), or (20) makes it easy to restrict the summation to reflection points on the appropriate Fresnel zone. Since Fresnel zones vary slowly in a direction perpendicular to the reflector, for such points adjacent the reflector, the
• the model seismic image of the subsurface seismic reflector from step 200 is constructed using the synthetic seismic amplitudes from step 214 at the image points from step 212. Typically, this construction is accomplished using standard imaging techniques well known to those skilled in the art.
• Imaging equation (17), (18) and (20) have been implemented for a v(z) medium to test the image modeling technique for time migration applications, which form the majority of cases of practical exploration interest.
• Imaging equations (17), (18) and (20) can be implemented as code that runs on a single workstation. The code may be specialized for calculating acquisition
• any deviation of the output amplitudes from a value of 1.0 represents the footprint. Only source and receiver coordinates, a v(z) velocity function, and the parameters defining a reflecting plane of interest are required to be provided.
• the program outputs an amplitude horizon slice through the reflector image for plotting, as illustrated in FIGS. 6, 7, and 8, discussed below. Output data sets for seismic attribute calculations may also be generated.
• FIG. 3 shows almost 400,000 source-receiver midpoints representing a collection of 2000-meter common-offset traces from a marine seismic survey. Acquisition used a 2-source, 3-cable configuration.
• FIG. 4 shows the source- receiver positions from just 40,000 of the traces represented in FIG. 3.
• FIG. 4 illustrates that while source positions 400 are relatively uniform, cable feathering caused significant variations in receiver positions 402. However, missing source lines caused large data gaps 404.
• FIG. 4 also shows a 180- degree change 406 caused by reversal of the shooting direction.
• FIG. 5 shows the orientation of these planes to the surface X-Y coordinates 500 of FIGS. 3 and 4. All three planes 501 , 502, and 503 dip at 25 degrees, with the updip directions shown by the arrows 511 , 512, and 513, respectively, in FIG. 5.
• FIGS. 6, 7, and 8 are amplitude horizon slices through the migrated images of reflector planes 501 , 502, and 503, respectively, from FIG. 5. These plots were constructed by vertically projecting the migrated image of each reflector onto the surface of the X-Y plane. Each image was computed on a Sun Sparc 10 workstation in a few minutes. The images all show a similar acquisition footprint that appears as vertical stripes in the inline direction. Reflector plane 502 was oblique to the inline direction, which caused the skewed footprint image in FIG. 7. The amplitude variations in these images correlate well with the source-receiver midpoint variations of FIG. 3. Regions of high midpoint density caused amplitude highs, and regions of low midpoint density caused amplitude lows.
• FIGS. 6, 7, and 8 show highest definition or resolution where the dipping reflectors were shallowest, and this illustrates how Fresnel zones control imaging. These regions of shallowest reflector depth are at the bottom edge of FIG. 6, bottom-left corner of FIG. 7, and the left edge of FIG. 8, recalling the geometry of FIG. 5. Thus, the acquisition footprint is most pronounced on shallow reflectors.

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Cited By (6)

Citations (3)

• 2000
  • 2000-03-10 EP EP00917892A patent/EP1169655A1/en not_active Withdrawn
  • 2000-03-10 WO PCT/US2000/006523 patent/WO2000054074A1/en not_active Ceased
• 2001
  • 2001-09-11 NO NO20014416A patent/NO20014416L/no not_active Application Discontinuation

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