WO2000042448A1 - Method of attenuating noise in three dimensional seismic data using a projection filter - Google Patents
Method of attenuating noise in three dimensional seismic data using a projection filter Download PDFInfo
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- WO2000042448A1 WO2000042448A1 PCT/GB2000/000058 GB0000058W WO0042448A1 WO 2000042448 A1 WO2000042448 A1 WO 2000042448A1 GB 0000058 W GB0000058 W GB 0000058W WO 0042448 A1 WO0042448 A1 WO 0042448A1
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- seismic data
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- 238000000034 method Methods 0.000 title claims abstract description 38
- 230000003595 spectral effect Effects 0.000 claims abstract description 33
- 230000001427 coherent effect Effects 0.000 claims abstract description 8
- 238000012545 processing Methods 0.000 claims description 10
- 230000002238 attenuated effect Effects 0.000 claims description 5
- 230000003247 decreasing effect Effects 0.000 claims description 3
- 238000013507 mapping Methods 0.000 claims 2
- 238000004422 calculation algorithm Methods 0.000 abstract description 63
- 230000009466 transformation Effects 0.000 abstract description 7
- 238000001914 filtration Methods 0.000 description 10
- 239000000654 additive Substances 0.000 description 9
- 230000000996 additive effect Effects 0.000 description 9
- 230000001364 causal effect Effects 0.000 description 8
- 238000001228 spectrum Methods 0.000 description 4
- 229910052704 radon Inorganic materials 0.000 description 3
- 230000009467 reduction Effects 0.000 description 3
- 238000012552 review Methods 0.000 description 3
- 238000013459 approach Methods 0.000 description 2
- 238000005311 autocorrelation function Methods 0.000 description 2
- 238000013499 data model Methods 0.000 description 2
- 230000008569 process Effects 0.000 description 2
- SYUHGPGVQRZVTB-UHFFFAOYSA-N radon atom Chemical compound [Rn] SYUHGPGVQRZVTB-UHFFFAOYSA-N 0.000 description 2
- 238000000926 separation method Methods 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- 230000002411 adverse Effects 0.000 description 1
- 230000008901 benefit Effects 0.000 description 1
- 238000005094 computer simulation Methods 0.000 description 1
- 239000012141 concentrate Substances 0.000 description 1
- 238000007796 conventional method Methods 0.000 description 1
- 230000001934 delay Effects 0.000 description 1
- 230000003111 delayed effect Effects 0.000 description 1
- 238000009795 derivation Methods 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000007598 dipping method Methods 0.000 description 1
- 238000012886 linear function Methods 0.000 description 1
- 238000004321 preservation Methods 0.000 description 1
- 230000004044 response Effects 0.000 description 1
- 238000005070 sampling Methods 0.000 description 1
- 238000012546 transfer Methods 0.000 description 1
- 230000007704 transition Effects 0.000 description 1
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
- G01V1/36—Effecting static or dynamic corrections on records, e.g. correcting spread; Correlating seismic signals; Eliminating effects of unwanted energy
- G01V1/364—Seismic filtering
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V2210/00—Details of seismic processing or analysis
- G01V2210/30—Noise handling
- G01V2210/32—Noise reduction
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
- G01V2210/00—Details of seismic processing or analysis
- G01V2210/30—Noise handling
- G01V2210/32—Noise reduction
- G01V2210/324—Filtering
- G01V2210/3246—Coherent noise, e.g. spatially coherent or predictable
Definitions
- the present invention relates to the field of seismic data processing.
- the present invention relates to methods of attenuating noise in three- dimensional seismic data.
- a seismic signal which consists of only linear events has an f-x domain representation which is predictable in x for each frequency/
- a generalization of this results is easy to show: the/- y domain representation of a 3-D (time-space-space) seismic signal, which consists of only planar events, is perfectly predictable in the xy- plane for each frequency/
- the significance of this result is that, some problems such as reducing noise in a 3-D volume can be reduced to a set of 2-D problems in the xy- plane, which are easier to solve.
- the noise is attenuated regardless of the data at other frequencies.
- what is needed is an algorithm which separates 2-D predictable data from additive noise.
- F-xy prediction (i.e./- y deco ⁇ ) is conventionally used for this purpose.
- FXY prediction filtering EAGE Conf. Exp. Abs., Paris, pp. 164-165, 1992
- M. Chase "Random noise reduction by 3-D spatial prediction filtering” SEG Ann. Mtg. Exp. Abs., New
- the/- y prediction methods suffer from model inconsistency problems.
- the model inconsistency in the/- y prediction method adversely affects signal preservation and noise attenuation when applied to seismic data.
- This disadvantage is similar to the model inconsistency problem in the 1-D counterpart to the/-xy prediction method, namely the/-* prediction algorithm.
- /-jc prediction see: Canales, "Random noise reduction,” 54 th SEG Ann. Mtg. Exp. Abs., Atlanta, pp. 525-527, 1984; and N. Gulunay, "FXDECON and complex wiener prediction filter," SEG Ann, Mtg. Exp. Abs., Houston, pp. 279-281, 1986.
- the f-x projection algorithm is described in for example, the following references: R. Soubaras, "Signal-preserving random noise attenuation by the f-x projection," SEG Ann Mtg. Exp. Abs., Los Angeles, pp. 1576-1579, 1994; R Soubaras, "Deterministic and statistical projection filtering for signal-preserving noise attenuation,” EAGE Conf. Exp. Abs., Glasgow, A051, 1995; R. Soubaras, "Prestack random and impulsive noise attenuation by f-x projection filtering," SEG Ann. Mtg. Exp. Abs., Houston, pp. 711-714, 1995; R.
- a method of attenuating noise in three dimensional seismic data includes receiving seismic data representing data gathered in at least two spatial dimensions and a time dimension.
- the seismic data includes both a noise component and a seismic signal component. The latter of which represents signals originating from at least one seismic disturbance.
- Values are computed for use in a projection filter, which is used to estimate the noise component of the seismic data.
- Spectral factorization is then performed in at least two dimensions to obtain additional two-dimensional values for use in the projection filter.
- the noise component in said received seismic data is estimated by using the projection filter which includes at least some of the additional two-dimensional values.
- the estimated noise component is then subtracted from the received data to obtain attenuated seismic data having a decreased noise component.
- the method also includes causing at least one seismic disturbance, recording raw data from a plurality of sensors distributed in at least two spatial dimensions; and then processing the recorded raw data to form said seismic data.
- the method also includes performing a Fourier Transform with respect to time of the seismic data to obtain frequency domain seismic data, selecting a single frequency from said frequency domain seismic data; and repeating for each desired frequency said steps of computing values, performing spectral factorization, estimating the noise component, and subtracting the estimated noise.
- the method also includes creating an initial estimate for an initial spectral factor sequence of values to be used in the projection filter, applying an all-pole filter based on the inverse of the square of the initial spectral factor sequence of values to obtain an intermediate sequence of values; computing an autocorrelation of the intermediate sequence of values; and finding coefficients for use in the projection filter by solving normal equations using the autocorrelation of the intermediate sequence of values.
- the spectral factorization is performed using a helical coordinate transform on the autocorrelation of the intermediate sequence of values to obtain a one-dimensional sequence, and the factorization is performed on the one-dimensional sequence to obtain a one- dimensional factor, which is mapped into two-dimensions using an inverse of the helical coordinate transform to obtain a two-dimensional factor which represents some of said additional two-dimensional values.
- the noise component of the seismic data is primarily random noise
- the projection filter estimates primarily random noise
- the noise component of the seismic data is primarily coherent noise
- the projection filter estimates primarily coherent noise
- Figure 1 illustrates the allowable support for a 2-D causal sequence
- Figures 2a and 2b illustrate the support of the linear predictor and prediction error filter, respectively, with parameters X and Y;
- Figure 3 illustrates an example of a 2-D autocorrelation sequence on the left and its helical coordinate transform on the right;
- Figure 4 illustrates an example of a 1-D sequence on the left and its inverse helical coordinate transform on the right;
- Figure 5 illustrates an example of a helical coordinate transform or the ⁇ -
- Figure 6 shows the space domain implementation of the f-xy projection filtering, according to a preferred embodiment of the invention.
- Figure 7 shows the computation of the projection filter output, according to a preferred embodiment of the invention.
- Figure 8 illustrates an example of one in-line of the noise-free seismic data cube on the left and the noisy seismic data cube on the right;
- Figure 10 illustrates the outputs of the/- y prediction algorithm on the left and the/- y projection algorithm on the right;
- Figure 11 illustrates the estimation errors of the/- y prediction algorithm on the left and the/- y projection algorithm on the right;
- Figure 12 illustrates one in-line of a real data cube
- Figure 13 illustrates the output of the/-xy prediction algorithm when applied to the real data set
- Figure 14 illustrates the output of the f-xy projection algorithm when applied to the real data set, according to a preferred embodiment of the invention
- Figure 15 illustrates the noise estimate of the/- y prediction algorithm, magnified by 2X;
- Figure 16 illustrate the noise estimate of the/- y projection algorithm, magnified by 2X, according to a preferred embodiment of the invention
- Figure 17 is a flow chart illustrating a method of attenuating noise in three dimensional seismic data using a projection filter, according to a preferred embodiment of the invention.
- Figure 18 is a flow chart illustrating a method of computing values for a noise estimation filter, according to a preferred embodiment of the invention.
- Figure 19 is a flow chart illustrating a method of recording raw data from seismic disturbances, according to a preferred embodiment of the invention. Detailed Description of the Invention
- a 2-D filter is stable in the bounded-input, bounded-output sense if its impulse response is absolutely summable.
- Minimum— phase We define a 2-D minimum-phase (min- ⁇ > ) filter to be a 2-D, causal, stable filter which has a causal, stable inverse.
- a ⁇ (z x , Z y ) l + a XY[ X , > (2) with the support shown in Fig. 2 is causal according to our definition of causality.
- This linear PEF is also called the forward linear prediction error filter to emphasize the fact that only the past samples (recall our causality definition) of the predicted sample are used in the prediction.
- the resulting method for computation of the PEF coefficients is called the co- variance method or the autocorrelation method, depending the range of summation in (4).
- the range of summation is chosen such that only the known (available) data sample are used in the computation.
- this range is extended by assuming that unknown (unavailable) data samples are zero. That is, the known segment of the input sequence h[x, y] is extrapolated with zeros.
- r h [k, l] - ⁇ (h[x + k, y + l]h * [x, y ⁇ + h[x, y]h * [x - k, y - l ⁇ ) (5) ⁇ ,y
- the range of summation is chosen such that only the known values of the data are used in the summation.
- the 2-D spectral factorization problem can be phrased as follows: Given an autocorrelation sequence r c [k, I] with a real and nonnegative Fourier transform R c (k x , k y ) > 0, find a causal and min- ⁇ sequence c[x, y) such that:
- R c (k x , k y ) ⁇ C(k x , k y ) ⁇ 2 , (8)
- R c (z x , z y ) C(z x , z y )C * (l/z x * , l/z;) . (9)
- the 2-D spectral factorization problem differs significantly from its 1-D counterpart.
- the fundamental theorem of algebra states that a polynomial of order N can be always factored as the product of N first order polynomials over the field of complex numbers.
- the 1-D spectral factorization problem is easy to solve: First find all the zeros (roots) of the autocorrelation function, then synthesize a sequence with the subset of these zeros which are smaller than 1 in magnitude (i.e., inside the unit circle).
- An implication of this spectral factorization algorithm is that, a finite extent autocorrelation sequence has a finite extent spectral factor.
- the 2-D spectral factorization problem is complicated by the lack of a theorem similar to the "fundamental theorem of algebra" which applies to only 1-D polynomials. Another complication arises because a "finite” extent sequence may have an "infinite” extent spectral factor. To solve this difficult problem, some researchers have proposed to convert this 2-D problem into a 1-D problem, solve this 1-D simplified problem, then map the obtained solution back to 2-D.
- the zero-padded autocorrelation sequence r c [k, I] is mapped to a 1-D sequence using the helical coordinate transformation as shown in Fig. 3 .
- this transformation involves concatenating the rows of the zero-padded autocorrelation sequence to obtain a 1-D sequence.
- its 1-D spectral factor is computed (Fig. 4) using one of the 1-D spectral factorization algorithms, such as the Wilson's method - see, e.g., G.
- the delay functions, d 3 (x, y) determine the shape of the seismic events in a 3-D volume. If we take the Fourier transform of u 0 (t, x, y) along the time dimension, we find the f-xy domain representation of the clean seismic signal as:
- V 3 (f) denotes the Fourier transform of the wavelet v 3 (t). If we assume that events are locally planar, then the delay functions can be represented as linear functions of the space variables x and y:
- Attenuation of the background noise can be achieved either in the f-xy domain, or in the t-xy domain.
- the f-xy domain algorithms have the advantage of separating a three dimensional problem into independent two dimensional problems. According to a preferrd embodiment, we shall be dealing with f-xy domain random noise attenuation. After describing the general framework in the next section, we shall present the f-xy projection algorithm for noise attenuation.
- U 0 (f, x, y) T[U(f, x, y)) , V/, (18)
- T is an unspecified 2-D (i.e., space x space domain) noise attenuation algorithm
- U 0 (f, x, y) is the f-xy domain representation of the seismic signal estimate.
- u[x, y] U(f, x, y) : Available data at frequency / (20)
- u 0 [x, y] U 0 (f, x, y) : Noise-free seismic component at frequency / (21)
- e[x, y] — E(f, x, y) Random noise component at frequency / .
- u[x, y] consists of a quasi-predictable (rather then perfectly predictable) seismic component u 0 [x, y] in additive noise e[x, y].
- the noise can in general be random or coherent.
- V ⁇ G x ⁇ k x , k y ) ⁇ 2 + ⁇ G 2 ⁇ k x , k y ) ⁇ 2 , (27)
- V k y )E(k x , k y ) ⁇ 2 .
- N(k x , k y ) is the noise estimation filter and e is e ⁇ /e 2 . Note that, only the relative value of ⁇ and e 2 is important, because only their ratio appears in (31). N(k x , k y ) is a projection filter because its spectrum mainly consists of l's and O's apart from the transition zones:
- E,z z ) A 'W* Q (* ⁇ > Utz z ) (39) h ⁇ z " z ' ] C-(l/z i t l/z;) C(z impart z v ) U (z " z >> • (39 >
- the min- ⁇ property of C(z x , z y ) ensures that first filter is stable when filtering is performed "forwards" in space and the second filter is stable when the filtering is performed “backwards” in space.
- the noisy input record is obtained by adding white noise to a clean, synthetic data record.
- the signal to noise ratio is -1.2 dB (peak-to-peak) and -12.9 dB (RMS).
- the 3-D data cube used in this simulation consists of 60 x 60 traces and 251 time samples.
- Fig. 8 shows one in-line of the data cube.
- the zero-dipping events have non-zero dip in the cross-line direction.
- the spectrum of the noise estimation filter is close to 0 at the wavenumbers where the signal component is present.
- the output signals and estimation errors of the two algorithms given in Fig. 10 and Fig. 11 justify the conclusion that the f-xy projection algorithm has a superior performance than f-xy prediction.
- Fig. 12 shows one in-line of the real data cube.
- the 3-D data set consists of 200 x 21 traces and Algorithm 1 Computation of the PEF.
- the initial estimate for c[x, y] may be chosen as the converged c[x] filter of the previous frequency.
- an f-xy projection algorithm has been provided.
- the algorithm exploits the predictability of the seismic signals in the f-xy domain. With computer simulations conducted on the synthetic data, it has been shown that the algorithm can be used at very low SNRs and it outperforms the f-xy prediction algorithm. While the preferred embodiments of the invention have been described, the examples and the particular algorithm described are merely illustrative and are not intended to limit the present invention.
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Priority Applications (6)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
EP00900259A EP1145046B8 (en) | 1999-01-14 | 2000-01-12 | Method of attenuating noise in three dimensional seismic data using a projection filter |
US09/889,239 US6668228B1 (en) | 1999-01-14 | 2000-01-12 | Method of attenuating noise in three dimensional seismic data using a projection filter |
CA002358512A CA2358512C (en) | 1999-01-14 | 2000-01-12 | Method of attenuating noise in three dimensional seismic data using a projection filter |
AU19923/00A AU773131B2 (en) | 1999-01-14 | 2000-01-12 | Method of attenuating noise in three dimensional seismic data using a projection filter |
DE60023109T DE60023109D1 (en) | 1999-01-14 | 2000-01-12 | METHOD FOR REDUCING NOISE IN THREE-DIMENSIONAL SEISMIC DATA WITH A PROJECTION FILTER |
NO20013501A NO332712B1 (en) | 1999-01-14 | 2001-07-13 | Method of attenuating noise in three-dimensional seismic data using a projection filter |
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GB9900723.9 | 1999-01-14 | ||
GB9900723 | 1999-01-14 |
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PCT/GB2000/000058 WO2000042448A1 (en) | 1999-01-14 | 2000-01-12 | Method of attenuating noise in three dimensional seismic data using a projection filter |
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US (1) | US6668228B1 (en) |
EP (1) | EP1145046B8 (en) |
AU (1) | AU773131B2 (en) |
CA (1) | CA2358512C (en) |
DE (1) | DE60023109D1 (en) |
NO (1) | NO332712B1 (en) |
WO (1) | WO2000042448A1 (en) |
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WO2004020972A2 (en) * | 2002-08-30 | 2004-03-11 | Robinson, John, M. | Removal of noise from seismic data using improved radon transformations |
GB2411473A (en) * | 2004-02-27 | 2005-08-31 | Westerngeco Ltd | Method and apparatus for filtering irregularly sampled data |
US6987706B2 (en) | 2002-08-30 | 2006-01-17 | John M. Robinson | Removal of noise from seismic data using high resolution radon transformations |
US7239578B2 (en) | 2005-03-03 | 2007-07-03 | John M. Robinson | Removal of noise from seismic data using radon transformations |
US7366054B1 (en) | 2002-08-30 | 2008-04-29 | John M. Robinson | Tau-P filters for removal of noise from seismic data |
WO2008005798A3 (en) * | 2006-07-07 | 2009-02-12 | Geco Technology Bv | Seismic data processing |
US7561491B2 (en) | 2005-03-04 | 2009-07-14 | Robinson John M | Radon transformations for removal of noise from seismic data |
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- 2000-01-12 DE DE60023109T patent/DE60023109D1/en not_active Expired - Lifetime
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US7561491B2 (en) | 2005-03-04 | 2009-07-14 | Robinson John M | Radon transformations for removal of noise from seismic data |
WO2008005798A3 (en) * | 2006-07-07 | 2009-02-12 | Geco Technology Bv | Seismic data processing |
US10353098B2 (en) | 2009-11-03 | 2019-07-16 | Westerngeco L.L.C. | Removing noise from a seismic measurement |
CN104422956A (en) * | 2013-08-22 | 2015-03-18 | 中国石油化工股份有限公司 | Sparse pulse inversion-based high-accuracy seismic spectral decomposition method |
CN112014884A (en) * | 2019-05-30 | 2020-12-01 | 中国石油天然气集团有限公司 | Method and device for suppressing near-shot strong energy noise |
CN112014884B (en) * | 2019-05-30 | 2023-11-28 | 中国石油天然气集团有限公司 | Method and device for suppressing near shot point strong energy noise |
Also Published As
Publication number | Publication date |
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EP1145046B8 (en) | 2005-12-28 |
NO20013501L (en) | 2001-09-13 |
EP1145046A1 (en) | 2001-10-17 |
US6668228B1 (en) | 2003-12-23 |
NO20013501D0 (en) | 2001-07-13 |
DE60023109D1 (en) | 2005-11-17 |
AU773131B2 (en) | 2004-05-20 |
EP1145046B1 (en) | 2005-10-12 |
NO332712B1 (en) | 2012-12-17 |
CA2358512C (en) | 2007-06-12 |
AU1992300A (en) | 2000-08-01 |
CA2358512A1 (en) | 2000-07-20 |
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