UHlted States Patent [19]
`Norton et al.
`
`US005353223A
`[11] Patent Number:
`[45] Date of Patent:
`
`5 353 223
`9
`9
`Oct. 4, 1994
`
`[54] MARINE NAVIGATION METHOD FOR
`GEOPHYSICAL EXPLORATION
`[75] Inventors: John P. Norton; Noel D. Zinn; Phillip
`J. V. Rapatz, all of Houston, Tex.
`[73] Assignee: Western Atlas International, Inc.,
`Houston’ Tex-
`[21] APPL NO’; 967,673
`_
`oet' 26’ 1992
`[22] Flled‘
`[51] Int. Cl.5 ....................... .. G01V 1/28; G04B 17/00
`[52] US. (:1. .................................... .. 364/421; 367/40;
`367/41; 367/19; 367/125; 367/130; 364/443
`[58] Field of Search ............. .. 364/421, 433, 443, 460,
`364/554, 573; 367/19, 125, 130, 40’ 41
`_
`References C‘ted
`U.S. PATENT DOCUMENTS
`367/13
`4,777,628 10/1988 Rietsch
`.. 364/421
`4,852,004 7/1989 Manin
`367/75
`4,858,202 8/1989 Fitch et a1. .......... ..
`367/19
`4,912,682 3/1990 Norton, Jr. et a1. ..
`4,970,696 11/1990 Crews et a1. ........................ .. 367/15
`
`[56]
`
`5,166,905 11/ 1992 Currie ................................. .. 367/19
`Primary Examiner—Thomas G. Black
`ASSl'SldnI EXaminer—SuSan Wieland
`Attorney, Agent, or Firm—Pau1 S. Madan
`[57]
`ABSTRACT
`The present invention provides a method for on-line
`real-time processing of processing navigational data for
`determining the location of sensor and receiver points in
`a navigational network having a number of different
`types of devices- Observations from these devices are
`Obtained using a Coordinate System that follows appro
`priate nominal sailing lines. Outlying observations are
`discarded using w-statistics for the Observations‘ Any
`correlated observations such as compass azimuths are
`uncorrelated. The uncorrelated observations are then
`sequentially processed in an extended sequential Kal
`man ?lter, which provides the best estimate of the sta
`tion coordinates. These estimated coordinates are then
`used to determine the location of the source and re
`ceiver points.
`
`8 Claims, 3 Drawing Sheets
`
`I
`
`INITIALIZATION
`
`l
`
`NEW EVENT
`
`TRANSITION TO EVENT TIME
`
`NEW DATA OR SHOTPOINT?
`
`SHOTPOINT
`
`IF x2 TEST FAILS, THEN
`UPDATE STATION COVARIANCE
`MATRIX
`
`I
`
`INTERPOLATE SEISMIC
`SPREAD ELEMENT POSITIONS
`
`DUPLICATE LAST ENTRY IN
`COORDINATE HISTORY
`
`FORM OBSERVATION EQUATION
`VECTOR 8 INNOVATION
`I
`COMPUTE SNOOPING
`STATISTIC
`
`PASS SNOOPING TEST? I
`
`YES
`
`COMPUTE GAIN FACTOR
`
`UPDATE STATE VECTOR
`
`UPDATE VARIANCE
`COVARIANCE MATRIX
`
`"'0 ALL OBSERVATIONS PROCESSE
`THIS DATA EVENT?
`YES
`
`COMPUTE OBSERVATION VARIANCES
`AND THE UNIT VARIANCE
`_____'|
`
`PGS v. WESTERNGECO (IPR2014-00689)
`WESTERNGECO Exhibit 2056, pg. 1
`
`

`

`US. Patent
`
`Oct. 4, 1994
`
`Sheet 1 0f 3
`
`5,353,223
`
`OF
`
`Iv
`
`omm DON
`
`2.5% 0%
`
`
`
`0mm 3.
`
`PGS v. WESTERNGECO (IPR2014-00689)
`WESTERNGECO Exhibit 2056, pg. 2
`
`

`

`US. Patent
`
`0a. 4, 1994
`
`Sheet 2 of 3
`
`5,353,223
`
`a“
`VESSEL' s
`HEADING \'\ U
`
`AZIMUTH OF
`/ AZIMUTH FIXED
`;
`SYSTEM = 7/v
`E
`é / U
`5
`-\ '
`
`\
`\\\“‘
`
`NRP
`
`‘ACROSS TRACK
`DISTANCE
`
`NOMINAL SAILING
`LINE
`
`omem
`
`v
`
`FIG. 2
`
`PGS v. WESTERNGECO (IPR2014-00689)
`WESTERNGECO Exhibit 2056, pg. 3
`
`

`

`US. Patent
`
`0a. 4, 1994
`
`Sheet 3 0f 3
`
`5,353,223
`
`INITIALIZATION
`
`No NEw EVENT?
`YES
`
`TRANSITION TO EVENT TIME
`
`I
`SHOTPOINT
`NEW DATA
`\NEW DATA OR SHOTPOINT>——
`
`I
`FORM OBSERVATION EQUATION
`VECTOR a INNOVATION
`‘
`
`COMPUTE SNOOPING
`STAT'ST'C
`
`I
`No
`< PASS SNOOPING TEST? '
`
`YES
`
`I
`COMPUTE GAIN FACTOR
`
`I
`
`UPDATE STATE VECTOR
`
`I
`UPDATE VARIANCE
`COVARIANCE MATRIX
`
`lF x2 TEST FAILS, THEN
`UPDATE STATION COVARIANCE
`MATRIX
`
`INTERPOLATE SEISMIC
`SPREAD ELEMENT POSITIONS
`
`DUPLICATE LAsT ENTRY IN
`COORDINATE HISTORY
`
`NO ALL OBSERVATIONS PROCESSE
`_< THIS DATA EVENT? -
`I >
`YES
`
`FIG. 3
`
`COMPUT'E OBSERVATION VARIANCES
`AND THE UNIT VARIANCE
`______'I
`
`PGS v. WESTERNGECO (IPR2014-00689)
`WESTERNGECO Exhibit 2056, pg. 4
`
`

`

`1
`
`MARINE NAVIGATION METHOD FOR
`GEOPHYSICAL EXPLORATION
`
`5,353,223
`2
`art techniques do not provide the desired accuracy,
`partially due to their inability to correct the errant mea~
`surements.
`The present invention provides an on-line, real-time
`method for processing navigational observations for
`computing more accurate locations of the source and
`receiver points.
`
`5
`
`10
`
`SUMMARY OF THE INVENTION
`The present invention provides a method for deter
`mining the location of sensor and receiver points in a
`navigational network having a number of different
`types of devices. Observations from these devices are
`obtained using a coordinate system that follows appro
`priate nominal sailing lines. The w-statistics for the
`observations are computed to discard observations
`which fall outside the norm for those observations. Any
`correlated observations are uncorrelated. The uncorre
`lated observations are then sequentially processed in an
`extended sequential Kalman ?lter, which provides the
`corrected or estimated values of the observations.
`These estimated values are then used to determine the
`location of the source and receiver points.
`Examples of the more important features of the
`method of the invention have been summarized rather
`broadly in order that the detailed description thereof
`that follows may be better understood, and in order that
`the contribution to the art may be better appreciated.
`There are, of course, additional features of the invention
`that will be described hereinafter and which will form
`the subject matter of the claims appended hereto.
`
`BRIEF DESCRIPTION OF THE DRAWINGS
`For detailed understanding of the present invention,
`references should be made to the following embodi
`ment, taken in conjunction with the accompanying
`drawings, in which like elements have been given like
`numerals and wherein:
`FIG. 1 shows a network of stations, sources and re
`ceivers;
`FIG. 2 shows a graphical representation of a coordi
`nate system for use in the method of the invention;
`FIG. 3 shows a ?ow diagram of containing certain
`steps used in the method of the present invention.
`
`DESCRIPTION OF THE PREFERRED
`EMBODIMENT
`The present invention provides a method for comput
`ing in real time the positions of source and receiver
`points in a navigational network using diversi?ed navi
`gational devices. The method utilizes sequential pro
`cessing of connected uncorrelated observations (inno
`vations) in the order they are received to determine the
`location of source and receiver points.
`FIG. 1 shows a typical network of stations, source
`points, receiver points and certain ranges between cer
`tain of the stations. This ?gure shows a placement of
`three streamer cables 10, 12 and 14 and two air gun
`sub-arrays 70 and 72 behind a vessel 100. Each air gun
`subarray contains several individual air guns typically
`forming a single source point. Each streamer cable
`contains a number of receivers (hydrophones) placed
`along the length of the cable. These hydrophones or
`groups of hydrophones form receiver points. Cable
`compasses are placed along the streamer cables to pro
`vide tangential azimuths at these locations. FIG. 1
`shows cable compasses 22a . . . 22m1 for cable 10, 26a .
`
`BACKGROUND OF THE INVENTION
`1. Field of the Invention
`This invention relates generally to marine seismic
`surveying and more particularly to a method of deter
`mining the position of sources and receivers used in the
`seismic spread in marine geophysical surveying.
`2. Background of the Invention
`In marine seismic exploration, one or more streamer
`cables, each typically between 2000 and 5000 meters
`long and one or more acoustic pulse sources, usually air
`gun subarrays containing several individual air guns are
`towed behind a vessel in a body of water. Each streamer
`cable contains several sensors, typically hydrophones,
`spaced along the length of the streamer cable. During
`operation, the air guns are activated every few seconds
`20
`to produce a shock wave or an acoustic pulse. The
`acoustic pulse is transmitted to the earth’s substrata
`lying underneath the air gun. The acoustic pulse is re
`?ected and refracted by the substrata layers back to the
`earth’s surface and then to the sensors located in the
`streamer cables. These sensors detect the returning
`acoustic pulses and produce signals (dam) representa
`tive of such returning acoustic pulses. The dam is then
`processed to determine the structure of the earth below
`the surveyed area.
`During the survey, the vessel is constantly moving
`along a predetermined course at a predetermined speed.
`Thus, the air guns and the sensors contained in the
`streamer cables are constantly moving while the survey
`is being performed. In order to accurately process the
`signals from the hydrophones (the dam), the location of
`the hydrophones and the location of the air gun subar
`rays must be determined at the time the air guns are
`activated.
`'
`To determine the positions of the sources and the
`receivers, it is typical to use a network containing a
`large number of different types of navigational devices.
`These navigational devices are placed at known loca
`tions along the streamer cable, on the air gun subarrays,
`on the vessel and at various other locations on various
`other equipment used for performing geophysical sur
`veying. The placement of the navigational devices form
`a complex network which provides many hundreds of
`observations.
`In recent years, more and more surveys are being
`done to obtain three-dimensional (3-D) mapping of the
`earth’s substrata. Additionally, larger vessels using sev
`eral streamer cables and air gun subarrays and multiple
`vessels are now routinely used for performing geophysi
`cal surveys. Use of such surveying methods requires
`more accurately determining the positions of the
`sources and receivers than has been done in the past.
`To obtain more accurate positions of the sources and
`receivers, the trend in the industry has been to use an
`increasingly complex network of stations consequently
`increasing the number of observations by several folds.
`Experience has shown that errant measurements (ob
`servations) are quite common and that if not corrected,
`can reduce the quality of the results obtained by pro—
`cessing such data. Various methods have been em
`ployed in the prior art to process the observations in
`real time on-board the seismic vessel. However, due to
`the increased complexity of the networks used, the
`diversity and sheer number of observations, these prior
`
`25
`
`35
`
`45
`
`50
`
`55
`
`60
`
`65
`
`PGS v. WESTERNGECO (IPR2014-00689)
`WESTERNGECO Exhibit 2056, pg. 5
`
`

`

`3
`. 29m3 for
`.
`. 26mg for cable 12 and compasses 29a .
`.
`cable 14. In streamer cable 10, the receiver points are
`shown by 20a, 20b, .
`.
`. 20n1. Similarly, streamer cable
`12 has receiver points 24a, 24b . .
`. 24n2 and streamer
`cable 14 has receiver points 28a, 28b .
`.
`. 28n3. These
`streamer cables may or may not have the same number
`of receiver points.
`Still referring to FIG. 1, elements 40, 42 and 43 repre
`sent stations along the streamer cable 10, each station
`having a desired transducer for receiving and/or trans
`mitting desired signals. Cables 12 and 14 have similar
`transducer stations represented by elements 48-51 for
`streamer cable 12 and 54-57 for cable 14. The number of
`such stations is a matter of design choice. The network
`of FIG. 1 also contains a forward buoy 84, which con
`tains transducers for receiving and transmitting signals.
`Also, each streamer cable has a tail buoy shown by
`elements 60, 62 and 64 at or near the end of each such
`streamer cable for receiving and transmitting signals.
`Navigation positioning satellites and/or on-shore trans
`mitters (not shown) are commonly used to transmit
`signals to certain receivers in the network, such as those
`on the buoys and other transducers placed on the vessel.
`Elements 74 and 76 are additional sensors placed in the
`water at known locations while elements 75 and 77 are
`transducers on the vessel 100. The line 81 between sta
`tions 41 and 49 represents the range (distance) between
`those stations. Other lines such as 82, the unnumbered
`lines and the ones with arrows represent ranges be
`tween their respective stations.
`It should be noted that FIG. 1 is presented to merely
`show a rudimentary network containing some of the
`important elements used in a typical navigational net
`work for determining the location of the source and
`receiver points. Still from FIG. 1, it should be obvious
`that navigational networks contain source points, re
`ceiver points, several tens of stations, and as many as
`several hundred observations. The network, like that
`shown in FIG. 1, provides information that is used in
`the method of the present invention to accurately deter
`mine the location of the source and receiver points.
`The stations as described above in reference to FIG.
`1 form the basic elements of the navigation network.
`They typically pertain to the coordinates of a device,
`such as an acoustic node or a cable compass or a surface
`reference like a tail buoy. The stations are used as points
`or nodes for determining the locations of the source and
`receiver points. The coordinates of these points are
`adjusted to provide the best ?t to the measurements. In
`many cases, the stations themselves do not directly
`provide the measurements but are linked to other sta
`tions. Acoustic range measurements are an example of
`such a condition.
`Thus far a typical stationary network of stations has
`been described. However, in operation the stations are
`in constant motion. With an appropriate choice of a
`coordinate frame absolute motion of the stations can be
`frozen. FIG. 2 shows a coordinate system having an
`origin at the perpendicular projection of the vessel’s
`navigation reference point onto the survey line (nomi
`nal track). The axes of this coordinate system are repre
`sented by u and v. The orientation of the coordinate
`frame of FIG. 2 is the instantaneous azimuth of the
`survey line at the origin point. Here, the coordinate
`Frame freezes the absolute motion of the described
`network. Only relative motion remains.
`The result of using the many different types of de
`vices in the network is a set of observations. An obser
`
`4
`vation may be an acoustic range between two stations,
`21 cable compass azimuth, the coordinates of a station or
`any other useful measurement obtained from the net
`work. Observations are expressed in their appropriate
`units of measurement. The method of the invention
`utilizes the observations obtained from the network to
`determine the positions of the sources and the receivers.
`Kalman ?ltering, a well known technique, is fre
`quently used in processing observations to obtain a best
`estimate of sensor and receiver positions in a naviga
`tional system. Uncorrelated observations can be sequen
`tially processed in an appropriately modi?ed Kalman
`?lter. However, correlated observations, especially
`chord azimuths derived from magnetic compass azi
`muths cannot be sequentially processed in a Kalman
`?lter.
`The present invention provides a method for sequen
`tially processing all observations obtained from the
`network in a Kalman ?lter in the order they are re
`ceived to determine the positions of the source and the
`receiver points. The sequential processing of all obser
`vations provides computational ef?ciency and numeri
`cal stability over non-sequential methods. This method
`allows mixing of different observations during process
`ing, which means that magnetic compasses and other
`sensors may be placed anywhere in the network. This
`allows greater design ?exibility respecting the use and
`placement of various sensors in the network. The
`method of the invention will now be described while
`referring to FIG. 3, which is a simpli?ed ?ow diagram
`containing the method steps.
`The model used in the method of this invention uti
`lizes a transition (or system) equation and an observa
`tion equation. The transition equation used is a linear
`equation and is given by:
`
`where x is a state column vector of dimensions 2 n by 1
`consisting of n station coordinates. F(8) is the state
`vector transition matrix for interval 6 and T(8) is the
`state noise transition matrix for interval 8. The k/k—1
`subscript indicates that the state vector x has been tran
`sitioned forward in time by F(8) and T(8). When mea
`surements are processed in time k, and when x is a func
`tion of those measurements, then k/k-—l subscript be
`comes k. As the time moves on to the next event, the k
`subscript becomes k— l.
`The observation (or measurement) equation used is a
`nonlinear equation and is given by:
`
`where z is the numeric value of an observation, such as
`a range, an azimuth, a direct position measurement, etc.,
`h is a nonlinear function of some elements of the state
`vector that predicts z, and q is the state noise. r repre
`sents the vector of the zero-mean, white noise vector of
`the observations and, in the case of the sequential pro
`cessing of the present method, r is a scalar that pertains
`to a particular observation.
`An initial step in the method of the invention is to
`estimate the variance of each observation, which may
`be done by using well known linear regression tech
`niques using several prior measurements of that obser
`vation. Utilizing the variance of the observations, the
`
`5,353,223
`
`3O
`
`45
`
`55
`
`60
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`
`PGS v. WESTERNGECO (IPR2014-00689)
`WESTERNGECO Exhibit 2056, pg. 6
`
`

`

`5,353,223
`5
`variance of the innovation is determined. This yields a
`diagonal variance-covariance matrix, represented
`herein by R. An innovation is the difference between
`the actual (or measured) value of an observation and the
`predicted value of that observation. The innovation
`variance 6-2,)", is obtained by utilizing the following:
`
`0
`
`aM=T
`
`where H is the Jacobian matrix that linearizes h(x), P is
`the variance-covariance matrix of the state vector x and
`R is the variance- covariance matrix of the observa
`tions. The row vector H is computed by:
`
`The chord azimuths are given by:
`
`alN=a 2hb+€ al-l'zah a2
`
`10
`
`15
`
`The matrix P is theoretically de?ned by:
`
`The chord azimuth variances are given by:
`
`0 (11+ 2a+22hbic a2
`
`35
`
`25
`where E is the statistical expectation operator and T
`represents the transpose function.
`Typically, in the prior art, a diagonal variance
`covariance matrix is used to initialize the state variance
`covariance matrix P. Such a diagonal variance-covari
`ance matrix has been found to be inadequate for initial
`izing the sequential Kalman ?lter. It is necessary to
`determine a fully populated P matrix to initialize the
`sequential Kalman ?lter. In the present invention, this is
`done by sequentially processing a full set of possible
`observations within the network while updating the
`variance-covariance matrix P and by not updating the
`state vector x. After startup, the P matrix and the state
`vector x are updated as usual within the Kalman ?lter.
`Since the network contains several different observa
`tion types, such as acoustic ranges, chord azimuths from
`cable compasses, true azimuths, direct and relative lon
`gitude and latitude positions, different equations are
`used for different observation types to determine the
`Jacobian matrix H. The prior art provides techniques
`4-5
`(equations) for various types of observations which
`allows for sequential processing of such observations.
`However, prior art methods have not provided means
`by which chord azimuths derived from compass obser
`vations could be processed sequentially, which has re
`quired nonsequential processing of such observations.
`The present invention provides a decorrelation tech
`nique which allows sequential processing of chord azi
`muth observations, like all the other observation types,
`while maintaining correct error propagation character
`istics.
`The chord azimuths are obtained from magnetic com
`passes, typically installed on the streamer cables. As is
`well known in the art, the chord azimuths are corre
`lated and thus must be uncorrelated before they can be
`sequentially processed in a Kalman ?lter.
`The decorrelation equations used for chord azimuths
`are as follows:
`Assume that there are compasses 1 and 2, and that the
`acoustic nodes are N and M. The distance between 1
`and N is a, between N and M is b, and between M and
`2 is 0, so that a+b+c=h. The cable tangent azimuths
`are given by:
`
`2
`(‘Tel + 0.2412)
`h
`2
`o-alN = _a_ 2—
`
`h
`02
`‘WM: 7
`
`2
`2
`(0-0.1 + 0-112)
`2
`
`(“in + 0'30)
`h
`2
`OI‘IMZ : T T
`
`The chord distances are given by:
`
`The chord distance variances are given by:
`
`o‘2cm! = ‘f- ("72
`
`UZCNM = % (‘02
`
`vzcm = 2- (<02
`
`where d is an empirically obtained constant.
`As can be seen, the above derivations will provide
`uncorrelated chord distances and azimuth observations,
`which may be sequentially processed in the Kalman
`?lter. It is important to note that the equations given
`above provide for realistic and appropriate error propa
`gation.
`The data snooping statistic (also called w-statistic) is
`then computed for each observation to discard the out
`lying observations, i.e., observations which are found to
`be outside a predetermined norm. The method of the
`invention utilizes the w-statistic described by W.
`Baarda, in a paper entitled “A Testing for Use in Geo
`detic Networks,” Netherlands Geodetic Commission,
`
`50
`
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`
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`
`PGS v. WESTERNGECO (IPR2014-00689)
`WESTERNGECO Exhibit 2056, pg. 7
`
`

`

`7
`1968, as modi?ed by Teunissen et al., in a paper entitled
`“Performance Analysis of Kalman Filters,” Delft Uni
`versity of Technology, 1988. The elements required to
`compute the w-statistic for an observation are the inno
`vation of that observation and the estimated variance of
`that innovation. The w-statistic is the ratio of the inno
`vation to the square root of its estimated variance, i.e.,
`the normalized innovation. The mathematical relations
`used to compute the w-statistic are given below:
`
`inn
`
`_ inn
`(Til-m
`
`where inn is the innovation and aim, is the standard
`deviation of that innovation. The remaining elements
`have the same meaning as described earlier.
`After each observation has passed the w-statistic test,
`each observation is then processed in an extended se
`quential ?lter (Kalman ?lter). The result of this process
`ing is the best estimate of the coordinates of all the
`stations within the network which may now be used to
`determine the location of the source and receiver points
`in the network by any number of well known methods,
`such as interpolation.
`The sequential processing contains three steps. First,
`a gain factor or a gain matrix is determined for the
`Kalman ?lter, which is given by:
`'
`
`inn
`
`where P is the covariance matrix of the state vector and
`H is the Jacobian matrix of the observation equations.
`
`25
`
`35
`
`Each innovation is then distributed over the pre
`dicted state which is represented by the transformation
`
`45
`
`The third step involves updating the covariance ma
`trix. The updating of the covariance matrix represents
`the improvement in positional accuracy afforded by the
`processing of an observation and the update of the state
`vector. Also, updating the covariance matrix after each
`observation is processed, and the consequent preserva
`tion of station correlations provides meaningful station
`accuracy reports. The covariance matrix P is updated as
`follows:
`
`55
`
`where I is the identity matrix.
`As noted earlier, the receiver points are typically
`placed along the cables between known stations. The
`source points may be between the stations or may them
`65
`selves represent stations. Thus, the positions of the
`source and the receiver points can be determined by
`interpolation techniques.
`
`5,353,223
`8
`The variance-covariance scaling factor (CSF) is de
`?ned by the w-statistic over a period covered by a pre
`determined number of shot points and is given by:
`
`5
`
`15
`
`A
`
`1
`"12
`
`where In is the number of observations in a predeter
`mined number of shot points.
`The CSF obtained at a shot point is then used to scale
`the variance-covariance matrix P for subsequent use.
`This has the effect of accommodating relative motion in
`the network.
`The foregoing description is directed to a particular
`embodiment of the invention for the purpose of illustra
`tion and explanation. It will be apparent, however, to
`one skilled in the art that many modi?cations and
`changes to the embodiment set forth above axe possible
`without departing from the scope and the spirit of the
`invention. It is intended that the following claims be
`interpreted to embrace all such modi?cations and
`changes.
`What is claimed is:
`1. A method of determining the location of source
`and receiver points in a navigation network utilizing a
`set of observations obtained from the navigation net
`work, the method comprising the steps of:
`(a) determining the variance of each observation;
`(b) uncorrelating any correlated observation;
`(0) computing a statistic or each uncorrelated obser
`vation and discarding the observations which fall
`outside a predetermined norm;
`(d) sequentially processing the each uncorrelated
`observation to obtain estimated coordinates for
`each station in the network; and
`(e) determining the location of the source and re
`ceiver points from the estimated station coordi
`nates.
`2. A method of processing data from a moving navi
`gational network having a source point, a plurality of
`receiver points and a plurality of stations, the method
`comprising the steps:
`(a) obtaining a set of observations from the network
`stations, each observation being obtained by using
`a coordinate system whose origin lies along a nomi
`nal sailing line;
`(b) determining the variance of each observation;
`(0) decorrelating any correlated observation;
`(d) computing a statistic for each decorrelated obser
`vation and discarding observations which fall out
`side a predetermined norm;
`(e) sequentially processing each of the decorrelated
`observation to obtain estimated coordinates for
`each station int he network; and
`(f) interpolating the estimated station coordinates to
`determine the location of the source and receiver
`points.
`3. A method of determining the location of seismic
`sources and seismic receivers contained in a marine
`seismic survey system utilizing a navigation network
`having a plurality of stations, said navigation network
`providing a plurality of navigational observations, cer
`tain number of such observations being correlated, the
`method comprising the steps of:
`(a) estimating the variance of each observation;
`(b) uncorrelating each of the correlated observations;
`
`PGS v. WESTERNGECO (IPR2014-00689)
`WESTERNGECO Exhibit 2056, pg. 8
`
`

`

`5,353,223
`10
`(a) estimating the variance of each of the observa
`(c) computing innovation for each of the observa~
`tions;
`tions, an innovation being de?ned as the difference
`(b) uncorrelating any correlated observations in said
`between the actual value of the observation and a
`plurality of observations;
`predicted value for such observation;
`(0) computing innovation for each of the observa
`(d) computing the variance of the innovations;
`tions, an innovation being de?ned as the difference
`(t) computing a statistic for each observation and
`between the actual value of the observation and its
`discarding those observations which fall outside a
`predicted value;
`predetermined norm;
`(d) computing the variance of the innovation;
`(g) sequentially processing the undiscarded observa
`(t) computing a snooping or w-statistic for each said
`tions to estimate the coordinates of the stations int
`observation and discarding those observations
`he network; and
`which fall outside a predetermined norm;
`(h) determining the location of the source and re
`(g) sequentially processing the undiscarded observa
`ceiver points from the estimated coordinates of the
`tions to obtain the coordinates of the stations in the
`stations.
`network; and
`4. A method of determining the location of seismic
`(h) determining the locations of the at lest one source
`sources and seismic receivers contained in a marine
`and the receivers in said plurality of receivers using
`seismic survey system utilizing a navigation network
`from the location of the stations;
`having a plurality of stations and which provides a
`(i) determining scaling factor at the at least one
`plurality of navigational observations, certain number
`source point over a period of covered by a prede
`termined elapsed time; and
`of such observations being correlated, the method com
`(j) updating the Kalman ?lter by using the scaling
`prising the step of:
`factor for processing subsequent observations.
`(a) estimating the variance of each observation;
`(b) uncorrelating each of the correlated observations;
`7. In a marine seismic survey system having a source
`point, a plurality of receivers and a navigation network,
`(0) computing an innovation for each of the observa
`said navigation network containing a plurality of sta
`tions, an innovation being de?ned as the difference
`tions and providing a plurality of observations, a
`between the actual value of the observation and a
`method for on-line determining the location of the at
`predicted value;
`least one source and the receivers in said plurality of
`(d) computing the variance of the innovations;
`receivers when the seismic survey system is being
`(t) computing a statistic for each observation and
`towed behind a vessel, said method comprising the steps
`discarding the observations which fall outside a
`Of:
`’
`predetermined norm;
`(g) sequentially processing the undiscarded observa
`tions using a Kalman ?lter to estimate the coordi
`nates of the stations in the network;
`(h) computing a scaling factor utilizing the statics of
`the observations; and
`(i) updating the Kalman ?lter by utilizing the scaling
`factor and using the updated Kalman ?lter for
`further processing observations.
`5. A method of determining the location of seismic
`sources and seismic receivers contained in a marine
`seismic survey system utilizing a navigation network
`having a plurality of stations and which provide a plu
`45
`rality of navigational observations, certain number of
`such observations being correlated, the method com
`prising the step of:
`(a) estimating the variance of each observation;
`(b) uncorrelating each of the correlated observations;
`(0) computing a w-statistic for each uncorrelated
`observation and discarding observations which fall
`outside a predetermined norm;
`(d) sequentially processing each undiscarded uncor
`55
`related observation to obtain the coordinates of
`each station in the network; and
`(e) interpolating the station coordinates to determine
`the location of the source and receiver points.
`6. In a marine s'eismic survey system having a source
`point, a plurality of receivers and a navigation network,
`said navigation network containing a plurality of sta
`tions and providing a plurality of observations, a
`method for on-line determining the location of the at
`lest one source and the receivers in said plurality of
`65
`receivers when the seismic survey system is being
`towed behind a vessel, said method comprising the steps
`Of:
`
`(a) estimating the variance of the observations in said
`plurality of observations;
`(b) uncorrelating any correlated observations in said
`plurality of observations;
`(c) computing innovation for each of the observations
`in said plurality of observations, an innovation for
`each of the observations in said plurality of obser
`vations, an innovation being de?ned as the differ
`ence between the actual value of the observation
`and a predicted value for such observation;
`(d) computing the variance of the innovations;
`(f) computing a snooping or w-statistic for each said
`observation and discarding those observations
`which fall outside a predetermined norm;
`(g) sequentially processing the undiscarded observa
`tions using a Kalman ?lter to estimate the coordi
`nates of the stations in the network; and
`(h) determining the locations of the source and the
`receivers in said plurality of receivers using the
`location of the stations;
`(i) determining a scaling factor using the w-statistics;
`and
`(j) updating the Kalman ?lter by using the scaling
`factor for processing subsequent observations.
`8. The method of claim 7 wherein the sequentially
`processing of the observations is done by using the
`equation
`
`where H is a Jacobian matrix, P is the variance-covari
`ance matrix of the state vector of the coordinates of the
`stations, and R is the variance-covariance matrix of the
`observations.
`
`* * * *
`
`=1‘
`
`15
`
`35
`
`50
`
`