Method of generating seismic wavelets using seismic range equation
First Claim
1. A method of modeling an amplitude spectrum of a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprisingdetermining values for the factors corresponding to the source, the medium, the target, and the receiving system, said factors including radiated energy density, directivity, capture area, target reflection coefficient, divergence, and loss factor, andcombining said values for said factors simultaneously in one concise analytical formulation to produce a model amplitude spectrum of the seismic wavelet.
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Abstract
A method of deterministically computer generating a model of a response voltage waveform of a seismic receiver employed in a seismic, particularly marine, data gathering system, the model incorporating factors that have been identified as significant contributions to amplitude, such as directivity, divergence, attenuation, interbed multiples, and transmissivity. The model is generated from the mathematical manipulation of well log data and data gathering system characteristics into a seismic range equation, namely: ##EQU1## where Er (f)=received energy density
E(f)=radiated energy density
D(θs, φs, f)=source directivity along θs, φs direction at the source
Ac (θH, φH, f)=Capture area along θH, φH direction at the hydrophone array
RT =target reflection coefficient
Dv =divergence ##EQU2## One preferred use of the resulting modeled waveform is in a pre-process comparison with actual seismic data for validating and interpreting such actual data. Another use is in the deconvolution of seismic data for improved resolution.
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Citations
69 Claims
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1. A method of modeling an amplitude spectrum of a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining values for the factors corresponding to the source, the medium, the target, and the receiving system, said factors including radiated energy density, directivity, capture area, target reflection coefficient, divergence, and loss factor, and combining said values for said factors simultaneously in one concise analytical formulation to produce a model amplitude spectrum of the seismic wavelet.
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17. A method of modeling a phase spectrum of a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining phase components of an electromotive force (φ - .sub.ε
(f)) generated by the seismic wavelet,deriving the value of any phase components of load and receiving array impedances, and combining said phase components of said electromotive force and said load and receiving array impedances to produce a metal phase spectrum of the seismic wavelet. - View Dependent Claims (18, 19, 20, 21)
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22. A method of modeling a frequency spectrum of a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining values for factors corresponding to the source, the medium, the target, and the receiving system, said factors including radiated energy density, directivity, capture area, target reflection coefficient, divergence, and loss factor, combining said values for said factors to produce a model amplitude spectrum of the seismic wavelet, determining phase components of an electromotive force (φ - .sub.ε
(f)) generated by the seismic wavelet,deriving the value of any phase components of load and receiving array impedances, combining said components of said electromotive force and said load and receiving array impedances to produce a model phase spectrum of the seismic wavelet, and combining said model amplitude spectrum with said model phase spectrum to produce a model frequency spectrum of the seismic wavelet.
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23. A method of determining the effect of an offset variation in an analog receiving and recording system that would affect a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining a capture area along the acoustic axis for a source-to-receiver offset, determining additional capture areas along the acoustic axis for other source-to-receiver offsets, and finding the ratio of said capture area to said additional capture areas and said capture area to determine an offset variation in the analog receiving and recording system.
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24. A method of determining a transmitting pattern of a receiving array to show the effect of the receiving array and an image array (or ghost reflection) that affects an amplitude spectrum of a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining the directivity of the receiving array along an incident direction, determining the directivity of the receiving array along an acoustic axis, and taking the ratio of said directivity of the receiving array along the incident direction to said directivity of the receiving array along the acoustic axis to determine a transmitting pattern of the receiving array.
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25. A method of determining a phase component of an array image that affects a phase spectrum of a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining an incident angle of the seismic wavelet, determining a cable depth in water, combining said incident angle and said cable depth in water to provide a time delay associated with the array image, and determining the phase component associated with the array image from said time delay.
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26. A method of modeling an amplitude spectrum of a downgoing interbed multiple that would affect a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining a ray path of the downgoing interbed multiple that would be received by a seismic data gathering system, determining value for factors corresponding to the source, the medium that would be transversed by the downgoing interbed multiple, the target, and the receiving system, said factors including radiated energy density, directivity, capture area, reflection coefficients, divergence, and loss factor, and combining said values for said factors to produce a model amplitude spectrum of the downgoing interbed multiple.
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27. A method of modeling an amplitude spectrum of an downgoing interbed multiple that would affect a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining a ray path of the upgoing interbed multiple that would be received by a seismic data gathering system, determining value for factors corresponding to the source, the medium that would be transversed by the upgoing interbed multiple, the target, and the receiving system, said factors including radiated energy density, directivity, capture area, reflection coefficients, divergence, and loss factor, and combining said values for said factors to produce a model amplitude spectrum of the downgoing interbed multiple.
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28. A method of modeling a phase spectrum of a downgoing interbed multiple that would affect a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining a ray path of the downgoing interbed multiple that would be received by a seismic data gathering system, determining phase components of an electromotive force (φ -
68 (f)) generated by the downgoing interbed multiple,
deriving the value of any phase components of load and receiving array impedances, and combining said phase components of said electromotive force and said load and receiving array impedances to produce a model phase spectrum of the downgoing interbed multiple.
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68 (f)) generated by the downgoing interbed multiple,
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29. A method of modeling a phase spectrum of an upgoing interbed multiple that would affect a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining a ray path of the upgoing interbed multiple that would be received by a seismic data gathering system, determining phase components of an electromotive force (φ -
68 (f)) generated by the upgoing interbed multiple,
deriving the value of any phase components of load and receiving array impedances, and combining said phase components of said electromotive force and said load and receiving array impedances to produce a model phase spectrum of the upgoing interbed multiple.
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68 (f)) generated by the upgoing interbed multiple,
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30. A method for modeling an interbed multiple loss factor that would affect a primary seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
selecting a number Jmax representing a number of subsurface layers an interbed multiple will cross after being reflected once, but before being reflected again, determining a frequency spectrum for the primary seismic wavelet, determining a frequency spectrum for each downgoing interbed multiple associated with each subsurface layer down to a target layer, assuming Jmax +1 interbed multiples will be generated per said subsurface layer, determining a frequency spectrum for each upgoing interbed multiple associated with each subsurface layer down to a target layer, assuming Jmax +1 interbed multiples will be generated per said subsurface, determining downgoing ratios by dividing said frequency spectrum for each downgoing interbed multiple by said frequency spectrum for the primary seismic wavelet, determining upgoing ratios by dividing said frequency spectrum for each upgoing interbed multiple by said frequency spectrum of said primary seismic wavelet, taking the reciprocal of the squared magnitude of the sum of 1, the sum of said downgoing ratios, and the sum of said upgoing ratios (eliminating redundancy) to determine the interbed multiple loss factor.
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32. A method for modeling an unprocessed seismic trace, said method comprising
determining values for factors corresponding to the source, the medium that would be transversed by a seismic wavelet, the target, and the receiving system that would affect said seismic wavelet, said factors including, source-to-receiver offset, radiated energy density, directivity, capture area, target reflection coefficient, divergence, and loss factor, combining said values for said factors to produce a model amplitude spectrum of said seismic wavelet, determining phase components of an electromotive force (φ - .sub.ε
(f)) generated by said seismic wavelet,deriving the value of any phase component of load and receiver array impedances, combining said components of said electromotive force and said load and receiver array impedances to produce a model phase spectrum of said seismic wavelet, combining said model amplitude spectrum with said model phase spectrum to produce a model frequency spectrum for a model seismic wavelet for said source-to-receiver offset, determining a time-reflection sequence from a parallel layered subsurface, and convolving said model seismic wavelet with said time reflection sequence to develop a model of the unprocessed seismic trace for said source-to-receiver offset.
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33. A method of affecting an enhanced amplitude-versus-offset analysis by comparing unprocessed seismic data and modeled data, said method comprising
generating a model of an unprocessed seismic trace at a source-to-receiver offset, generating several models of unprocessed seismic traces for other source-to-receiver offsets corresponding to those recorded for the seismic data, combining said models for said source-to-receiver offsets to develop an unprocessed model gather, and comparing variations in the amplitude versus offset of unprocessed seismic data to variations in amplitude versus offset of said unprocessed model gather for corresponding source-to-receiver offsets.
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34. A method of affecting an enhanced amplitude-versus-offset analysis on recorded seismic data wherein the seismic data and modeled data are processed and compared at any step therein, said method comprising
generating a model of an unprocessed seismic trace for a source-to-receiver offset, generating a plurality of additional models of unprocessed seismic traces for other source-to-receiver offsets corresponding to those recorded for the recorded seismic data, combining said models for source-to-receiver offsets to develop an unprocessed model gather, processing said unprocessed model gather to produce a processed model gather, processing the recorded seismic data to produce processed seismic data, and comparing variations in the amplitude versus offset of said processed seismic data to variations in amplitude versus offset of said processed model gather.
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38. A prestack deconvolution method of processing seismic data, said method comprising
determining values for factors corresponding to the source, the medium that would be transversed by a seismic wavelet, the target, and the receiving system, said factors including, source-to-receiver offset, radiated energy density, directivity, capture area, target reflection coefficient, divergence, and loss factor, combining said values for said factors to produce a model amplitude spectrum of said seismic wavelet, determining phase components of an electromotive force (φ - .sub.ε
(f)) generated by said seismic wavelet,deriving the value of any phase contributions of load and receiver array impedances, combining said components of said electromotive force and said load and receiver array impedances to produce a model phase spectrum of a seismic wavelet, combining said model amplitude spectrum with said model phase spectrum to produce a model frequency spectrum for a model seismic wavelet for said source-to-receiver offset, and deconvolving a seismic trace for said source-to-receiver offset by said model seismic wavelet.
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39. An average-amplitude correction factor method of processing seismic data, which comprises
determining values for factors for a source-to-receiver offset in a frequency band, corresponding to the source, the medium that would be transversed by a seismic wavelet, and the receiving system, said factors including directivity, capture area, divergence, and loss factor, combining said values for said factors to produce a first average amplitude for said source-to-receiver offset for said frequency band, generating average amplitudes for each source-to-receiver offset in said frequency band, calculating average amplitude correction factors as the ratios of said average amplitudes to said first average amplitude, and multiplying seismic traces at said source-to-receiver offsets by said average amplitude correction factors at the respective offsets.
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40. A zero phase filtering method of processing recorded seismic data, which comprises
determining an amplitude spectrum for a model seismic wavelet for a source-to-receiver offset corresponding to one in the recorded seismic data and frequency band, generating an amplitude spectrum for each model seismic wavelet at each source-to-receiver offset corresponding to those in the recorded seismic data for said frequency band to determine amplitude spectra, calculating the zero phase filters from the ratios of said amplitude spectra to said amplitude spectrum, and multiplying the zero phase filters by seismic traces in said frequency band at respective source-to-receiver offsets.
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41. A prestack deconvolution method of processing a model seismic trace, which comprises
determining values for factors corresponding to the source, the medium that would be transversed by a seismic wavelet, the target, and the receiving system, said factors including, source-to-receiver offset, radiated energy density, directivity, capture area, target reflection coefficient, divergence and loss factor, combining said values for factors to produce a model amplitude spectrum of said seismic wavelet, determining phase components of an electromotive force (φ - .sub.ε
(f)) generated by said seismic waveletderiving the value of any phase contributions of load and receiver array impedances, combining said components of said electromotive force and said load and receiver array impedances to produce a model phase spectrum of a seismic wavelet, combining said model amplitude spectrum with said model phase spectrum to produce a model frequency spectrum for a model seismic wavelet, determining a time-reflection sequence developed from a parallel layered subsurface, convolving said model seismic wavelet with said time reflection sequence to develop a model seismic trace for said source-to-receiver offset, and deconvolving said model trace by said model seismic wavelet.
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42. An average-amplitude correction factor method of processing a model seismic gather, which comprises
determining values for factors for a source-to-receiver offset in a frequency band, corresponding to the source, the medium that would be transversed by a seismic wavelet, and the receiving system, said factors including directivity, capture area, divergence, and loss factor, combining said values for said factors to produce a first average amplitude for said source-to-receiver offset for said frequency band, generating an average amplitude for each source-to-receiver offset in said frequency band, calculating average amplitude correction factors as the ratios of said average amplitudes to said first average amplitude, and multiplying the average amplitude correction factors by seismic traces at respective source-to-receiver offsets.
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43. A zero phase filtering method of processing a model seismic gather, which comprises
determining an amplitude spectrum for a model seismic wavelet for a source-to-receiver offset and frequency band, generating an amplitude spectrum for each model seismic wavelet at each source-to-receiver offset for said frequency band to determine amplitude spectra, calculating zero phase filters from the ratios of said amplitude spectra to said amplitude spectrum, and multiplying the zero phase filters by model traces in the frequency domain at respective source-to-receiver offsets.
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44. A method creating a stacked modeled seismic wavelet that simultaneously incorporates therein a multiplicative effect of source-to-receiver factors which would affect a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
generating models of unprocessed seismic wavelets for source-to-receiver offsets, and processing said models of unprocessed seismic wavelets at different source-to-receiver offsets into a model stacked wavelet.
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45. A post stack deconvolution method of processing stacked seismic data, which comprises
generating models of unprocessed seismic wavelets for source-to-receiver offsets, processing said models of unprocessed seismic wavelets at different source-to-receiver offsets into a model stacked wavelet, and deconvolving stacked seismic data by said model stacked wavelet.
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46. A method of deriving a seismic data gathering system frequency response required to produce requisite received electrical energy density of a seismic wavelet issued from a source, transverses a medium, is reflected from a target, and is received by a receiving system by utilizing the following seismic range equation:
- ##EQU27## having seven elements
1) E(f) is the radiated energy density from a source at frequency, f;2) D(θ
s,φ
s,f) is source directivity along the θ
s, φ
s direction;3) Ac (θ
H,φ
H,f) is the capture area of a receiving system for incident angle θ
H,φ
H ;4) RT is the P-wave reflection coefficient of a target interface; 5) Dv is the divergence; 6) L(f) is representative of the losses associated with seismic data gathering; and 7) Er (f) is the received energy density at a receiver array, said method comprising selecting a system requisite received electrical energy density of the seismic wavelet returned from subsurface, determining physical subsurface characteristics, for subsurface layers (i) transversed by the seismic wavelet, including P-wave velocity (α
i), S-wave velocity (β
i), density (ρ
i), and thickness (hi), assuming the seismic wavelet path begins at the source of a seismic data gathering system, at frequency (f), through the medium at ray angle (θ
s) with respect to the normal to the surface and at corresponding ray angles (θ
i) through subsurface layers, to the predetermined target bed at depth (d) through said subsurface layers to a receiving system of the seismic data gathering system,determining the target'"'"'s power reflection coefficient (RT2), calculating divergence (Dv) for a given offset, calculating the loss factor (L(f)) associated with the subsurface layers, and determining a system frequency response as a function of radiated energy density from the source, source directivity, and capture area from the product of received electrical energy density (Er (f)), the divergence (Dv), and the loss factor divided by the square of the target'"'"'s power reflection coefficient. - View Dependent Claims (47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63)
- ##EQU27## having seven elements
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64. A method of modeling an amplitude spectrum of a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining values for the factors corresponding to the source, the medium, the target, and the receiving system that would affect the seismic wavelet, and combining said values for said factors multiplicatively to produce a model amplitude spectrum of the seismic wavelet.
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65. A method of modeling a frequency spectrum of a seismic wavelet that issues from a seismic source, traverses a medium, is reflected from a target, and is received by a receiving system, said method comprising
determining values for factors corresponding to the source, the medium, the target, and the receiving system that would affect a seismic wavelet, combining said values for said factors multiplicatively to produce a model amplitude spectrum of the seismic wavelet, determining phase components of an electromotive force (φ - .sub.ε
(f)) generated by the seismic wavelet,deriving the value of any phase components of load and receiving array impedances, combining said components of said electromotive force and said load and receiving array impedances to produce a model phase spectrum of the seismic wavelet, and combining said model amplitude spectrum with said model phase spectrum to produce a model frequency spectrum of the seismic wavelet.
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66. A method of interpreting stacked seismic traces derived from recorded seismic data, said method comprising
generating a model of an unprocessed seismic trace at a source-to-receiver offset corresponding to one in the recorded seismic data, generating several models of unprocessed seismic traces for different source-to-receiver offsets corresponding to those in the recorded seismic data, combining said models for said source-to-receiver offsets to develop an unprocessed model gather, processing said unprocessed model gather into a stacked model trace, and comparing variations in stacked seismic trace to variations in said stacked model trace.
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67. A method of interpreting stacked seismic data derived from recorded seismic data wherein seismic data and modeled data are processed, stacked, and compared, said method comprising
generating a model of an unprocessed seismic trace for a source-to-receiver offset corresponding to one in the recorded seismic data, generating a plurality of additional models of unprocessed seismic traces for different source-to-receiver offsets corresponding to those in the recorded seismic data, combining said models to develop an unprocessed model gather, processing said unprocessed model gather to produce a processed model gather, processing the recorded seismic data to produce processed seismic data, processing said processed model gather into a stacked model trace, processing said processed seismic data into a stacked seismic trace, and comparing said stacked seismic trace to said stacked model trace.
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68. A method of interpreting stacked seismic data derived from recorded seismic data wherein seismic data and modeled data are stacked, processed, and compared at any step therein, said method comprising
generating a model of an unprocessed seismic trace for a source-to-receiver offset corresponding to one in the recorded seismic data, generating a plurality of additional models of unprocessed seismic traces for different source-to-receiver offsets corresponding to those in the recorded seismic data, combining said models to develop an unprocessed model gather, processing said unprocessed model gather into an unprocessed stacked model trace, processing the unprocessed recorded seismic data into an unprocessed stacked seismic trace, processing said unprocessed model stacked trace to produce a processed model stacked trace, processing said unprocessed stacked seismic data to produce model stacked data, and comparing variations of said processed stacked seismic data to variations in said processed model stacked trace.
Specification