US4884030A — Method and system for acquisition and separation …

Claim 1

Independent Claim 82 words

A system for acquisition and separation of components of electromagnetic fields generated by simultaneous sources of electromagnetic field in the earth comprising an array of n pick-ups about at the surface of the earth for picking up the components of the electromagnetic fields, connected to registration means, wherein the minimum number n of pick-ups in the array is equal to 2s+2, s being the number of simultaneous sources to be analyzed, and wherein each pick-up picks up the components of each source.

Claim 2

Independent Claim 82 words

A system for acquisition and separation of components of electromagnetic fields generated by simultaneous sources of electromagnetic field in the earth comprising an array of n pick-ups about at the surface of the earth for picking up the components of the electromagnetic fields, connected to registration means, wherein the minimum number n of pick-ups in the array is equal to 2s+2, s being the number of simultaneous sources to be analyzed, and wherein each pick-up picks up the components of each source.

Claim 3

Dependent Claim 21 words

A system according to claim 1, wherein said registration means store n traces coming from said pick-ups in a synchronous manner.

Claim 4

Independent Claim 82 words

A method for acquisition and separation of components of electromagnetic fields generated by simultaneous sources of electromagnetic field in the earth, comprising the step of registering n traces, coming from an array of n pick-ups about at the surface of the earth, for picking up the components of the electromagnetic fields in which n is greater than or equal to 2s+2, s being the number of simultaneous sources to be analyzed, and wherein each pick-up picks up the components from each source.

Claim 5

Independent Claim 82 words

A method for acquisition and separation of components of electromagnetic fields generated by simultaneous sources of electromagnetic field in the earth, comprising the step of registering n traces, coming from an array of n pick-ups about at the surface of the earth, for picking up the components of the electromagnetic fields in which n is greater than or equal to 2s+2, s being the number of simultaneous sources to be analyzed, and wherein each pick-up picks up the components from each source.

Claim 6

Dependent Claim 31 words

A method according to claim 3, further comprising the steps of: (i) determining the number s of active sources; and (ii) reconstituting the components of electromagnetic field generated by each source.

Claim 7

Dependent Claim 78 words

A method according to claim 4, wherein said step of determining the number of active sources comprises the step of determining the number of proper dominant values of interspectral matrices: ##EQU13## wherein g j (ω) represents the Fourier transform of a trace g(t) i=1 to n, j=1 to n, k=1 to m, where m represents the number of frequencies in each frequency interval considered, g* represents the complex conjugate of g, and f(ω k ) represents a filter.

Claim 8

Dependent Claim 22 words

A method according to claim 5, wherein appearance of a new source is detected by appearance of a new proper dominant value.

Claim 9

Dependent Claim 41 words

A method according to claim 4, wherein said step of reconstituting comprises the steps of: accumuating k observations; determining source vectors for s sources on s pick-ups; and determining source vectors for other pick-ups by the aid of a propagation operator.

Claim 10

Dependent Claim 11 words

A method according to claim 3 applied to prediction of earthquakes.

Claim 11

Dependent Claim 61 words

A method according to claim 4, wherein said step of reconstituting comprises the steps of: accumulating K successive observations g j , wherein the number K of observations is greater than the number s of sources; constituting the covariance matrix defined by ##EQU14## with i=1 to n and j=1 to n; arranging the covariance matrix Γ in the form of: ##EQU15##

Claim 12

Dependent Claim 110 words

where: Γ 0 . Γ 2 and Γ are of dimension s×s, Q + and R are of dimension s×(n-2s), and Γ 1 is of dimension (n-2s)×(n-2s); determining a propagation operator P of dimension (n-2s)×s so that P+=Γ' -1 R; determining a matrix of dimension s×s of the component S.sub.εj of the vector source of the source j, with j=1 to s on the pick-up ε, with ε=1 to s, so as to determine the source vectors S.sub.εj for s sources on s pick-ups; and determining the source vectors S s+k ,j on other pick-ups on the basis of the following equation: ##EQU16## with k=1, 2 . . . (n-2s).

Claim 13

Dependent Claim 110 words

where: Γ 0 . Γ 2 and Γ are of dimension s×s, Q + and R are of dimension s×(n-2s), and Γ 1 is of dimension (n-2s)×(n-2s); determining a propagation operator P of dimension (n-2s)×s so that P+=Γ' -1 R; determining a matrix of dimension s×s of the component S.sub.εj of the vector source of the source j, with j=1 to s on the pick-up ε, with ε=1 to s, so as to determine the source vectors S.sub.εj for s sources on s pick-ups; and determining the source vectors S s+k ,j on other pick-ups on the basis of the following equation: ##EQU16## with k=1, 2 . . . (n-2s).

Claim 14

Dependent Claim 72 words

A method according to claim 9 further comprising the steps of: determining for each observation the complex amplitude a.sub.ε (ω, k) of the source ε such that, for the observations k, the signal corresponding to the source ε at the pick-up j is g.sub.jε (ω,k)=a.sub.ε (ω,k)S.sub.jε (ω); and then determining the time trace corresponding to the component of the electromagnetic field of the source ε by inverse Fourier transform g.sub.ε (t,k)=F[g.sub.jε (ω,k)].

Claim 15

Independent Claim 197 words

A method for acquisition and separation of components of electromagnetic fields generated by simultaneous sources of electromagnetic field in the earth, comprising the steps of: registering n traces g j (t) coming from an array of n pick-ups about at the surface of the earth for picking up the components of the electromagnetic fields in which n is greater than or equal to 2s+2, s being the maximum number of simultaneous sources to be studied, and wherein each pickup picks up the components from each source; determining the number s of active sources by determining the number of proper dominant values of interspectral matrices: ##EQU17## wherein g j (ω) represents the Fourier transform of the trace g(t), i=1 to n, j=1 to n, k=1 to m, where m represents the number of frequencies in each frequency interval considered, g* represents the complex conjugate of g, f(ω k ) represents a filter; accumulating K successive observations g j , wherein the number K of observations is greater than the number s of sources; constituting the covariance matrix defined by: ##EQU18## with i=1 to n and j=1 to n; arranging the covariance matrix Γ in the form of: ##EQU19##

Claim 16

Independent Claim 197 words

A method for acquisition and separation of components of electromagnetic fields generated by simultaneous sources of electromagnetic field in the earth, comprising the steps of: registering n traces g j (t) coming from an array of n pick-ups about at the surface of the earth for picking up the components of the electromagnetic fields in which n is greater than or equal to 2s+2, s being the maximum number of simultaneous sources to be studied, and wherein each pickup picks up the components from each source; determining the number s of active sources by determining the number of proper dominant values of interspectral matrices: ##EQU17## wherein g j (ω) represents the Fourier transform of the trace g(t), i=1 to n, j=1 to n, k=1 to m, where m represents the number of frequencies in each frequency interval considered, g* represents the complex conjugate of g, f(ω k ) represents a filter; accumulating K successive observations g j , wherein the number K of observations is greater than the number s of sources; constituting the covariance matrix defined by: ##EQU18## with i=1 to n and j=1 to n; arranging the covariance matrix Γ in the form of: ##EQU19##

Claim 17

Dependent Claim 170 words

where: Γ 0 . Γ 2 and Γ are of dimension s×s, Q + and R are of dimension s×(n-2s) and Γ 1 is of dimension (n-2s)×(n-2s); determining a propagation operator P of dimension (n-2s)×s so that P + =Γ' -1 R; determining a matrix of dimension s×s of the component S.sub.εj of the vector source of the source j, with j=1 to s on the pick-up ε, with ε=1 to s, so as to determine the source vectors S.sub.εj for s sources on s pick-ups; determining the source vectors S s+k ,j on other pick-ups on the basis of the following equation: ##EQU20## with k=1,2 . . . (n-2s); determining for each observation the complex amplitude a.sub.ε(1,k) of the source ε such that, for the observation k, the signal corresponding to the source ε at the pick-up j is given by g.sub.jε (ω,k)=a.sub.ε (ω,k)S.sub.jε (ω); and determining the time trace corresponding to the component of the electromagnetic field of the source ε by inverse Fourier transform g.sub.jε (t,k)=F[g.sub.jε (ω,k)].

Claim 18

Dependent Claim 170 words

where: Γ 0 . Γ 2 and Γ are of dimension s×s, Q + and R are of dimension s×(n-2s) and Γ 1 is of dimension (n-2s)×(n-2s); determining a propagation operator P of dimension (n-2s)×s so that P + =Γ' -1 R; determining a matrix of dimension s×s of the component S.sub.εj of the vector source of the source j, with j=1 to s on the pick-up ε, with ε=1 to s, so as to determine the source vectors S.sub.εj for s sources on s pick-ups; determining the source vectors S s+k ,j on other pick-ups on the basis of the following equation: ##EQU20## with k=1,2 . . . (n-2s); determining for each observation the complex amplitude a.sub.ε(1,k) of the source ε such that, for the observation k, the signal corresponding to the source ε at the pick-up j is given by g.sub.jε (ω,k)=a.sub.ε (ω,k)S.sub.jε (ω); and determining the time trace corresponding to the component of the electromagnetic field of the source ε by inverse Fourier transform g.sub.jε (t,k)=F[g.sub.jε (ω,k)].

Claim 19

Independent Claim 226 words

A method for acquisition and separation of components of electromagnetic fields generated by simultaneous sources of electromagnetic field in the earth, comprising the steps of: registering n traces g j (t) coming from an array of n pick-ups about at the surface of the earth for picking up the components of the electromagnetic fields in which n is greater than or equal to 2s+2, s being the maximum number of simultaneous sources to be studied, and wherein each pick-up picks up the components from each source; determining the number s of active sources by determining the number of proper dominant values of interspectral matrices: ##EQU21## g j (ω) represents the Fourier transform of the trace g(t), i=1 to n, j=1 to n, k=1 to m, where m represents the number of frequencies in each frequency interval considered, g* represents the complex conjugate of g, f(ω k ) represents a filter; and if a new source is detected by appearance of a new proper dominant value, determining the components of electromagnetic field of this new source by performing the further steps of: accumulating K successive observations g j , wherein the number K of observations is greater than the number s of sources; constituting the covariance matrix defined by: ##EQU22## with i=1 to n and j=1 to n; arranging the covariance matrix in the form of: ##EQU23##

Claim 20

Independent Claim 226 words

A method for acquisition and separation of components of electromagnetic fields generated by simultaneous sources of electromagnetic field in the earth, comprising the steps of: registering n traces g j (t) coming from an array of n pick-ups about at the surface of the earth for picking up the components of the electromagnetic fields in which n is greater than or equal to 2s+2, s being the maximum number of simultaneous sources to be studied, and wherein each pick-up picks up the components from each source; determining the number s of active sources by determining the number of proper dominant values of interspectral matrices: ##EQU21## g j (ω) represents the Fourier transform of the trace g(t), i=1 to n, j=1 to n, k=1 to m, where m represents the number of frequencies in each frequency interval considered, g* represents the complex conjugate of g, f(ω k ) represents a filter; and if a new source is detected by appearance of a new proper dominant value, determining the components of electromagnetic field of this new source by performing the further steps of: accumulating K successive observations g j , wherein the number K of observations is greater than the number s of sources; constituting the covariance matrix defined by: ##EQU22## with i=1 to n and j=1 to n; arranging the covariance matrix in the form of: ##EQU23##

Claim 21

Dependent Claim 145 words

where: Γ 0 . Γ 2 and Γ are of dimension s×s, Q + and R are of dimension s×(n-2s) and Γ 1 is of dimension (2n-2s)×(n-2s); determining a propagation operator P of dimension (n-2s)×s so that P + =Γ' -1 R; determining a matrix of dimension s×s of the component S.sub.εj for s sources on s pick-ups; determining the source vectors S s+k ,j on other pick-ups on the basis of the following equation: ##EQU24## with k=1, 2 . . . (n-2s); determining for each observation the complex amplitude a.sub.ε (ω, k) of the source ε such that, for the observation k, the signal corresponding to the source ε at the pick-up j is given by g.sub.jε (ω,k)=a.sub.ε (ω,k)S.sub.jε (ω); and determining the time trace corresponding to the component of the electromagnetic field of the source ε by inverse Fourier transform g.sub.jε (ω,k)=F[g.sub.jε (ω,k)].

Claim 22

Dependent Claim 145 words

where: Γ 0 . Γ 2 and Γ are of dimension s×s, Q + and R are of dimension s×(n-2s) and Γ 1 is of dimension (2n-2s)×(n-2s); determining a propagation operator P of dimension (n-2s)×s so that P + =Γ' -1 R; determining a matrix of dimension s×s of the component S.sub.εj for s sources on s pick-ups; determining the source vectors S s+k ,j on other pick-ups on the basis of the following equation: ##EQU24## with k=1, 2 . . . (n-2s); determining for each observation the complex amplitude a.sub.ε (ω, k) of the source ε such that, for the observation k, the signal corresponding to the source ε at the pick-up j is given by g.sub.jε (ω,k)=a.sub.ε (ω,k)S.sub.jε (ω); and determining the time trace corresponding to the component of the electromagnetic field of the source ε by inverse Fourier transform g.sub.jε (ω,k)=F[g.sub.jε (ω,k)].

Claim 23

Independent Claim 199 words

A system for acquisition and separation of components of electromagnetic fields generated by simultaneous sources of electromagnetic field in the earth, comprising: an array of n pick-ups about at the surface of the earth for picking up the components of the electromagnetic fields in which n is greater than or equal to 2s+2, s being the maximum number of simultaneous sources to be studied, and wherein each pick-up picks up the components from each source; means for registering n traces coming from the n pick-ups; means for determining the number s of active sources by determining the number of proper dominant values of interspectral matrices; ##EQU25## where: g j (t) designates the traces, i=1 to n, j=1 to n, k=1 to m, where m represents the number of frequencies in each frequency interval considered, g* represents the complex conjugate of g, f(ω k ) represents a filter; means for accumulating K successive observations g j , wherein the number K of observations is greater than the number s of sources; means for constituting the covariance matrix defined by: ##EQU26## with i=1 to n and j=1 to n; means for arranging the covariance matrix Γ in the form of: ##EQU27##

Claim 24

Independent Claim 199 words

A system for acquisition and separation of components of electromagnetic fields generated by simultaneous sources of electromagnetic field in the earth, comprising: an array of n pick-ups about at the surface of the earth for picking up the components of the electromagnetic fields in which n is greater than or equal to 2s+2, s being the maximum number of simultaneous sources to be studied, and wherein each pick-up picks up the components from each source; means for registering n traces coming from the n pick-ups; means for determining the number s of active sources by determining the number of proper dominant values of interspectral matrices; ##EQU25## where: g j (t) designates the traces, i=1 to n, j=1 to n, k=1 to m, where m represents the number of frequencies in each frequency interval considered, g* represents the complex conjugate of g, f(ω k ) represents a filter; means for accumulating K successive observations g j , wherein the number K of observations is greater than the number s of sources; means for constituting the covariance matrix defined by: ##EQU26## with i=1 to n and j=1 to n; means for arranging the covariance matrix Γ in the form of: ##EQU27##

Claim 25

Dependent Claim 183 words

where: Γ 0 . Γ 2 and Γ are of dimension s×s, Q + and R are of dimension s×(n-2s) and Γ 1 is of dimension (n-2s)×(n-2s); means for determining a propagation operator P of dimension (n-2s)×s so that P + =Γ' -1 R; means for determining a matrix of dimension s×s of the component S.sub.εj of the vector source of the source j, with j=1 to s on the pick-up ε, with ε=1 to s, so as to determine the source vectors S.sub.εj for s source on s pick-ups; means for determining the source vectors S s+k ,j on other pick-ups on the basis of the following equation: ##EQU28## with k=1, 2 . . . (n-2s); means for determining for each observation the complex amplitude a 68 (ω,k) of the source ε such that, for the observation k, the signal corresponding to the source ε at the pick-up j is given by g.sub.jε (ω,k)=a.sub.ε (ω,k)S.sub.jε (ω); and means for determining the time trace corresponding to the component of the electromagnetic field of the source ε by inverse Fourier transform g.sub.jε (t,k)=F[g.sub.jε (ω,k)].

Claim 26

Dependent Claim 183 words

where: Γ 0 . Γ 2 and Γ are of dimension s×s, Q + and R are of dimension s×(n-2s) and Γ 1 is of dimension (n-2s)×(n-2s); means for determining a propagation operator P of dimension (n-2s)×s so that P + =Γ' -1 R; means for determining a matrix of dimension s×s of the component S.sub.εj of the vector source of the source j, with j=1 to s on the pick-up ε, with ε=1 to s, so as to determine the source vectors S.sub.εj for s source on s pick-ups; means for determining the source vectors S s+k ,j on other pick-ups on the basis of the following equation: ##EQU28## with k=1, 2 . . . (n-2s); means for determining for each observation the complex amplitude a 68 (ω,k) of the source ε such that, for the observation k, the signal corresponding to the source ε at the pick-up j is given by g.sub.jε (ω,k)=a.sub.ε (ω,k)S.sub.jε (ω); and means for determining the time trace corresponding to the component of the electromagnetic field of the source ε by inverse Fourier transform g.sub.jε (t,k)=F[g.sub.jε (ω,k)].

Annuity Stage	Window Opens	Payment Deadline	Surcharge Period Until	Estimated Fee	Status
3.5 Years (Year 4)	1992-11-27	1993-05-29	1993-11-28	$2000.00	Window Closed / Lapsed
7.5 Years (Year 8)	1996-11-27	1997-05-29	1997-11-28	$3760.00	Window Closed / Lapsed
11.5 Years (Year 12)	2000-11-27	2001-05-29	2001-11-28	$7700.00	Window Closed / Lapsed

Method and system for acquisition and separation of the effects of electromagnetic fields to predict earthquakes

Abstract

Inventors

Bibliographic Details

Claims Analysis

References Cited (Backward Citations)

USPTO Annuity & Maintenance Windows

Assigned Categories & Tags

Assign Category Tag