AU710900C - Seismic reverberation and coupling error removal - Google Patents

Description

SEISMIC REVERBERATION AND COUPLING ERROR REMOVAL

BACKGROUND OF THE INVENTION This invention relates to the field of seismic data acquisition and processing In particular, this invention relates to a method for removing multiple reflections from seismic data It also relates to removal of coupling errors in dual sensor data

The problems of multiple reflections in seismic data is well known, and many attempts to remove or lessen its influence on data have been made. See, for example, U S Patent Nos 4,979,150; 5,163,028; 5,235,554; and 5,365,492 all of which are incorporated herein by reference It will be noted that the above patents are focused on the problem of free surface multiples caused by reverberations in a water column; however, the free surface multiple reflections can and do occur from reverberations between reflecting interfaces in the earth, also These four patents cite many others considered relevant for one reason or another, for example, U.S. Patent Nos. 2,757,356; 3,290,645, 3,299,397; 3,943,484; 3,979,713; 4,134,097, 4,146,871, 4,253,164, 4,296,481 , 4,348,749, 4,380,059, 4,437,175; 4,477,887; 4,486,865, 4,520,467, 4,581,724; 4,644,507; 4,644,508; 4,658,387, 4,685,090; 4,733,379; 4,736,345; 4,752,916, 4,821,241 , 4,910,716, 4,956,822, 5,251,183; and 5,257,241; all of which are incorporated herein by reference. Further, the following articles may also be considered pertinent in evaluation of the present invention Monk, D J , Wavefield Separation of Twin Streamer Data, First Break, Vol. 8, No 3, March, 1988, pgs 96-104; Brink, M , Application of Vertical Receiver Arrays in 3D Seismic Exploration, Society of Exploration Geophysicists, 1988, pgs. 460-463; Wuenschel, P.C , Removal of the Detector-Ground Coupling Effect in the Vertical Seismic Profiling Environment, Geophysics, Vol. 53, No 3, March, 1988, pgs. 359-364, Bell, D.W., et al., Two-Trace Directional Filter For Processing Offset Vertical Seismic Profiles, AAPG Bulletin, Vol 72, No 3, March 1988, pg 375, Brink, M. et al., Marine Seismic Exploration Using Vertical Receiver Arrays: Acquisition in Bad Weather, 49th Meeting of European Assn. of Exploration Geophysicists, June, 1987, Tan, T.H., Reciprocity Theorem Applied To the Geophone-Ground Coupling Problem, Geophysics, Vol 52, No. 12, Dec. 1987, pgs. 1715-1717, Krohn, C.E., Geophone Ground Coupling, Geophysics, April, 1985, pgs. 56-60; Krohn, C.E., Geophone Ground Coupling, Geophysics, Vol 49, No. 6, June 1984, pgs 722-731 , Plane-wave Decomposition of Seismograms, Geophysics, Vol. 47, No. 10, October, 1982, pgs. 1375-1401; Vol 28, No 6, December 1980, pgs. 872-901, G M Hoover, J T O'Brien, The influence of the planted geophone on seismic land data. Geophysics, Vol 45, No 8, August 1980, pgs 1239- 1253, J White, Chapter 2 - Plane Waves, Seismic Wave Radiation - Transmission and Attenuation, Seismic Waves, McGraw Hill Publish , 1965, pgs 15-41, B Widrow, J Glover, Jr , J McCool, J Kaunitz, C Williams, R Hearan, J Zeidler, E Dong, Jr , R Goodhn, Adaptive Noise Canceling: Principles and Applications, Proceedings of the IEEE, Vol 63, No 12, December 1975, pgs 1692-1716, H Washburn, H Wiley, The effect of the placement of a seismometer on its response characteristics, Presented at the Annual Meeting, Chicago, April 11 , 1940 In addition, the following U K Patents were cited in U S Patent No 4,979, 150, which may be redundant to other cited U S patents. Ruehle, U K Patent No 1316479, November 23, 1970, Broding, U K Patent No 2004648, April 4, 1979, and Hutchins, U K Patent No 2030400, April, 1980

Other references found when searching in a related area include the following U S Patent Nos., which are incorporated herein by reference 4,794,572, 4,803,666, 4,817,061 , 4,888,743, 4,903,244, 4,912,979, 4,933,913, 4,935,903, 5,027,332, 5,027,332, 5,029,146, 5,136,554, 3,350,683, 3,689,874, 4,234,938, 4,935,903, 4,937,793, 4,992,993, 5,163,028, 5,235,554, 5,365,492, and 5,396,472

Generally, these methods require calibration shooting or estimates of water bottom reflectivity CaUbration shooting is expensive and can introduce its own errors, while estimates of water bottom reflectivity are inherently inaccurate Current statistical methods are flawed by noise Further, imperfect coupling between a geophone and the earth and other response differences between co-located hydrophone and geophone pairs (a k a "dual sensors" to those of ordinary skill) exist which are different from pair to pair Application of the same correction scheme to each dual sensor pair is not an optimum solution

Accordingly, there is a need for a method for eliminating free surface multiples from seismic data where there exists a free surface reflection coefficient Further, there is a need for compensation for coupling differences between each sensor in a dual sensor pair

SUMMARY OF THE INVENTION

It is an object of the present invention to address the above needs, in one embodiment, by a method of compnsing determining an up going and down going vector wave-field from the vector wave-field, and adding the product to the up going vector wave-field It has been found that such a method avoids the problems inherent m the previous attempts to eliminate free surface multiples, which were caused by combining particle velocity and pressure data

According to another aspect of the present invention, a method is provided for eliminating the effects of receiver coupling from seismic data taken in a survey, wherein there exists a reverberation response period The method comprises describing a first cross-equalization filter as a function of the reverberation period, describing a second cross-equalization filter as a function of the seismic data; deriving an inverse coupling filter as a function of the first cross- equalization filter and the second-equalization filter; and applying the coupling filter to the seismic data

DESCRIPTION OF THE DRAWINGS

For a more complete understanding of the present invention and for further advantages thereof, reference is made to the following Detailed Description taken in conjunction with the accompanying drawings, in which

Figure I shows representation of water column reverberation

Figure 2 shows a band limited spike at 40 milliseconds

Figures 3 and 4 show the pressure and velocity response for detectors on the water bottom at 30 meters water depth

Figures 5 and 6 show the separated up going and down going vector wave-fields

Figure 7 shows the de-reverberated wave-field by adding the product of an estimated water bottom reflection coefficient and the down going vector wave-field to the up going vector wave-field It is to be noted, however, that the appended drawings illustrate only typical embodiments of this invention and are therefore not to be considered limiting of its scope, for the invention may admit to other equally effective embodiments

DETAILED DESCRIPTION Referring now to a specific example embodiment of the present invention, it will be recognized that receiver ghosts are recorded on seismic data when a receiver, located in the water column, senses reflection energy which is reverberating in the water column The present wave-fields (U(Z) and D(Z) respectively), then adding the product of the down going wave-field U(Z)

A model for the P-wave energy reverberating in the water column was outlined by Milo Backus in 1958 See, Water Reverberations - Their Nature and Elimination, Geophysics, 1958 incorporated herein by reference As shown in Fig 1, P-wave reflection energy 10 amves in the water column 12 from depth, then bounces between the water surface 14 and the water bottom 16. The relative polarity and amplitude of the P-wave 10 for any given point in time is determined by the product of the reflection coefficients for each successive bounce between the water surface and water-bottom For detectors located on the water bottom, the pressure response P(Z) and velocity response V(Z) are described by equations (1) and (2)

P(Z)=Z^ϋ-(l+r)Z^l+r(\+r)Z²-r²(\+r)Zⁱ+ - (1)

^α V(Z) = Z°+(l-r)Z'-r(l-r)Z +r2(l-r)Z³- + (2) cosθ

where

P = pressure V = particle velocity tωτ Z = β α = impedance θ = angle of incidence r = reflection coefficient of the water bottom - two - way travel time through the water column

= 2d cosθ d = vertical water depth v = water velocity

Calculating the closed form of equations (1) and (2) gives equations (3) and (4) P(Z) = l + ((l-/-)Z)/(l+rZ) (3)

= (l-Z)/(l+rZ)

3BT (Z) = ,- ^ (4)

= J±Z_

1+rZ

The up going vector wave-field, U(Z), is determined by adding equations (3) and (4) The down going vector wave-field, U(Z), is determined by subtracting (3) from (4) (See, Lowenthal and Gardner, 1985), and Lowenthal's U S Patent No 4,752,916, both of which are incorporated herein by reference) Equations (5) and (6) represent the up going and down going components on an infinite seπes of water reverberations

2 Λ+rZ 1 +rZ '

1 + rZ

1+rZ

This infinite seπes of water reverberations can be eliminated by taking the product of the down going wave-field D(Z) and adding it to the up going wave-field U(Z)

U(Z) +rD(Z) = (l/(l+rZ))+r(Z/(l+^)) (7) = (l+rZ)/(l+rZ)

= 1 where -1 ≤ r ≤ 1

This technique is demonstrated on a zero-offset model shown in Figures 2 - 7 Figure 2 shows a band limited spike at 40 milliseconds Figures 3 and 4 show the pressure and velocity response for detectors on the water bottom at 30 meters water depth Figures 5 and 6 show the separated up going and down going vector wave-fields Figure 7 shows the de-reverberated wave-field by adding the product of an estimated water bottom reflection coefficient and the down going vector wave-field to the up going vector wave-field

In summary, reverberation-free primary P-wave data is achieved in various embodiments of the invention by recording pressure and particle velocity data, separating the up going and down going vector wave-fields, and adding the product of the water bottom reflection coefficient and the down going vector wave-field to the up going vector wave-field

Many ways of deterrnining the up going and down going vector wave-fields are acceptable For example, one method includes collocating seismic data receivers at the free surface, either physically, or mathematically Also, the free surface is defined to be a reflecting interface such as, for example, an air water interface or the water bottom in the case of water column reverberations in marine seismic data. The free interface also may be defined between geologic layers to reduce reverberations that occur in the earth's structure

In another example, the determining an up going and a down going vector wave-field further comprises the step of describing the seismic data as a function of the free surface reflection coefficient and a reverberation period in an expanded form

Further, in some embodiments, the data is collected during the survey with co-located pressure and particle velocity response receivers, which are commonly known in the art. In other embodiments, the data is collected with vertically-spaced pressure receivers. Alternatively, in another example, the determining an up going and a down going vector wave-field further comprises the step of describing the seismic data as a ftinction of the free surface reflection coefficient and a reverberation period in a closed form

In one implementation of this aspect of the invention, the seismic data comprises a first set of seismic data in the closed form and a second set of seismic data in the closed form and the first set of seismic data is added to the second set of seismic data, wherein the up going vector wave¬ field is defined Alternatively, the first set of seismic data is subtracted from the second set, wherein the down going vector wave-field is defined.

As mentioned above, receiver coupling is also a factor in accuracy of seismic surveys in Dual Sensor bottom reference receiver acquisition (DSSR), where a pressure detector and a particle velocity detector are co-located on the water bottom A seismic source is fired and the returning reflection energy is recorded by the two detectors The two recorded data sets are summed and subtracted to separate the up going and down going vector wave-fields A fundamental issue with this technique is the coupling of the particle velocity detectors to the water bottom

According to one aspect of the present invention, therefore, a process is provided by which the pressure detector is used as a guide function to estimate the coupling degradation of the recorded particle velocity data. An inverse filter is derived and applied to the particle velocity data prior to vector wave-field separation.

For pressure and particle velocity detectors co-located on the water bottom, the reverberation response is given by equations (la) and (2a).

P(Z) = - 1 + rZ ^" 0*) α vm = _L±Z

^' 1 + rZ (2a) cosθ where

P = pressure

V = particle velocity

_Λι

Z = e ωτ

α = impedance θ = angle of incidence r = reflection coefficient of the water bottom τ = two-way travel time through the water column

For the purposes of this discussion, we will be looking at the zero-offset case for which cosθ = 1. We will assume a correction factor has been applied to the particle velocity data to remove α. A filter, X(ω), which will convert the pressure data into particle velocity data, can be described in the frequency domain as

P(ω)X(ω) = V(ω) (3a)

Solving for X(ω).

X(ω) = -Y . (4a)

P(ω) Substituting the frequency domain expressions of equations (la) and (2a) into equation (4a) yields equation (5a).

ι + e ιωτ

X(ω) = (5a) l - e ιωτ

Solving for the amplitude and phase components of equation (5 a) gives equation (6a).

π 2

Thus, for co-located pressure and particle velocity detectors on the water bottom, the filter X(ω) which converts pressure data into particle velocity data has an amplitude component which is solely dependent on the period of the water reverberations τ, and a constant phase component of 90 degrees Imperfect coupling of the particle velocity detector to the water bottom can be expressed as a filter, c(co), applied to the particle velocity data which distorts the amplitude and phase of the data. Thus a cross-equalization filter, X«.(ω) calculated from the recorded data will have this filter applied to the particle velocity field.

The ideal cross-equalization filter X(ω), without c(ω), can be calculated with a priori knowledge of τ using equation (6a). Dividing X(ω), by Xc(ω), results in the inverse coupling filter.

1 ^; X(ω) (8a) c(ω) Xc(ω) This filter can be applied to recorded particle velocity data in order to remove the coupling effects.

In summary, an ideal cross-equalization filter, for pressure and particle velocity detectors co- located on the water bottom, is calculated from knowledge of the period of the water reverberations This ideal cross-equalization filter is compared to the cross-equalization filter calculated from the recorded data The result of this comparison is an inverse filter which, when applied to the recorded particle velocity data, removes the effects of receiver coupling.

Other embodiments of the present invention will occur to those of skill in the art which do not depart from the spirit of the invention.

Claims (1)

1. What is claimed is

   1 A method for eliminating free surface multiples from seismic data taken in a survey wherein there exists a free surface reflection coefficient, the method comprising

   determining an up go g and a down going vector wave-field from the seismic data,

   determining a product of the free surface reflection coefficient and the down going vector wave- field, and

   adding the product to the up going vector wave-field

   2 A method as recited m claim 1 , wherein said determining an up going and a down going vector wave-field further comprises the step of collocating seismic data receivers at a free surface

   3 A method as recited in claim 2, wherein the seismic data receivers are co-located mathematically at the free surface

   4 A method as recited in claim 2, wherein the free surface comprises an interface between air and water

   A method as recited in claim 2, wherein the free surface comprises a water bottom

   6 A method as recited in claim 2, wherein the seismic data receivers comprise a pressure response receiver and a particle velocity response receiver

   7 A method as recited in claim 1 , wherein determining an up going and a down going vector wave-field further comprises the step of describing the seismic data as a function of the free surface reflection coefficient and a reverberation period in an expanded form

   8 A method as recited in claim 7, wherein the expanded form comprises a Z expansion

   9 A method as recited in claim 8, wherein the Z expansion comprises an exponential factor of a reverberation period

   10 A method as recited in claim 1, wherein determining an up going and a down going vector wave-field further comprises the step of describing the seismic data as a function of the free surface reflection coefficient and a reverberation period in an approximate closed form

   11 A method as recited in claim 10, wherein the seismic data comprises a first set of seismic data in the closed form and a second set of seismic data in the closed form 12 A method as recited in claim 11, further comprising the step of adding the first set of seismic data in the closed form to the second set of seismic data in the closed form, wherein the up going vector wave-field is defined

   13 A method as recited in claim 11 , further comprising the step of subtracting the second set of seismic data in the closed form from the first set of seismic data in the closed form, wherein the down going vector wave-field is defined

   14 A method as recited in claim 11, wherein the seismic data comprises pressure response data and particle velocity response data

   15. A method for eliminating the effects of receiver coupling from seismic data taken in a survey, wherein there exists a reverberation response period, the method comprising.

   describing a first cross-equalization filter as a function of the reverberation period,

   describing a second cross-equalization filter as a function of the seismic data,

   deriving an inverse coupling filter as a function of the first cross-equalization filter and the second equalization filter; and

   applying the coupling filter to the seismic data

   16 A method as recited in claim 15, wherein the first cross-equalization filter comprises a ratio of a first set of seismic data to a second set of seismic data

   17 A method as recited in claim 16, wherein the first and second sets of seismic data are described as a function of the reverberation response period 18 A method as recited in claim 17, wherein the first set of seismic data is particle velocity data and the second set of seismic data is pressure data

   19 A method as recited in claim 18, wherein the pressure response data and the particle velocity data is expressed as a Z expansion, wherein an expanded pressure and particle velocity data are respectively defined

   20 A method as recited in claim 19, further comprising the step of solving the expanded pressure and expanded particle velocity data respectively, in a frequency domain

   21 A method as recited in claim 20, wherein the first cross-equalization filter comprises a ratio of the expanded particle velocity data to the expanded pressure data, in the frequency domain

   22 A method as recited in claim 21, wherein the ratio of the expanded particle velocity and pressure velocity is solved for an amplitude and a phase component

   23 A method as recited in claim 15, wherein the second cross-equalization filter comprises a product of the first cross-equalization filter and a coupling filter

   24 A method as recited in claim 23, wherein the coupling filter comprises an amplitude and a phase shift of the seismic data

   25. A method as recited in claim 24, wherein the seismic data comprises particle velocity data 26. A method as recited in claim 15, wherein said deriving an inverse coupling filter further comprises the step of dividing the first cross-equalization filter by the second cross-equalization filter.

   27. A method as recited in claim 15, wherein said deriving an inverse coupling filter further comprises the step of solving the first cross-equalization filter for a known reverberation period.

   28. A method as recited in claim 15, wherein said applying the inverse coupling filter further comprises the step of applying the inverse coupling filter to the seismic data.

   29. A method as recited in claim 28, wherein the seismic data comprises particle velocity data.