Seismic signal velocity filtering

Claim 3

A method according to claim 1, wherein the operator D z is defined by: ##EQU7## where g is some function and I is an integer.

Claim 4

The method according to claim 2, wherein I is equal to 1.

Claim 5

The method according to claim 2, wherein I is equal to 2.

Claim 6

The method according to claim 2, wherein said operator H t is defined by: H.sub.t (g(t))=FT.sup.-1 [j.sgn(ω).FT(g(t)) where: g is some function; FT represents the Fourier transform; IFT represents the inverse Fourier transform; sgn(ω) designated the sign of the variable ω, which is the dual of t; and j is the complex operator such that j 2 =-1.

Claim 7

The method according to claim 5, wherein said operator A is applied once only to the signal g(z,t).

Claim 8

The method of claim 5 further including the steps of fan filtering to reinforce waves in the signal g(z,t) having velocities lying between predetermined velocities Vc 1 and Vc 2 , said fan filtering method comprising the steps of: (A) (a) producing a first shifted two-dimensional signal by applying a time shift to the signal g i (t) for 2<i<n in order to time align the wave components of velocity Vc 1 in the signals g i (t) for 1<i<n; (b) producing a first two-dimensional signal g 1 (z,t) by time shifting the signals g i (t) for 2<i<n to cancel said time shift; (B) (a) producing a second shifted two-dimensional signal by performing a time shift on the signals g i (t) for 2<i<n in order to time align the wave components of velocity Vc 2 in the signals g i (t) for 1<i<n; (b) producing a second two-dimensional signal g 2 (z,t) by time shifting the signals g i (t) for 2<i<n to cancel the preceding time shift; and (C) taking the difference between the signals g 1 (z,t) and g 2 (z,t) to produce a signal g 12 (z,t) which is predominately constituted by waves having velocities lying between Vc 1 and Vc 2 .

Claim 9

A seismic signal velocity filter for use in a seismic exploration installation, said installation including at least one sound wave detector, means for displacing said detector along a borehole, means for recording a two-dimensional signal g(z,t) constituted by the signals g i (t) for 1<i<n produced by the detector, said signals including upgoing wave components and downgoing wave components, said signal velocity filter comprising: first memory to receive the two-dimensional signal g(z,t); first calculating means for applying a discrete differentiation operator D z with respect to the variable z in the signal contained in memory; second calculating means for applying a Hilbert operator H t with respect to the variable t to the signal of said first calculating means; third calculating means for determining the value of the coefficient B as a function of the signals in said memory and said second calculating means; multiplier to multiply the coefficients ε, B and the signal of said second calculating means; adder to add the signal of said first memory and the output signal of said multiplier; a divide-by-two circuit to receive the signal output from said adder; a multiplexer having a first input connected to the output from said divide-by-two circuit and a second input connected to the output of a counter, and having a first output connected to a second memory and a second output connected to said first calculating means; said counter to control the number of times the operator A is applied to the signal g(z,t); and recording means connected to said second memory.

Claim 10

A seismic signal velocity filter for use in a seismic exploration installation, said installation including at least one sound wave detector, means for displacing said detector along a borehole, means for recording a two-dimensional signal g(z,t) constituted by the signals g i (t) for 1<i<n produced by the detector, said signals including upgoing wave components and downgoing wave components, said signal velocity filter comprising: first memory to receive the two-dimensional signal g(z,t); first calculating means for applying a discrete differentiation operator D z with respect to the variable z in the signal contained in memory; second calculating means for applying a Hilbert operator H t with respect to the variable t to the signal of said first calculating means; third calculating means for determining the value of the coefficient B as a function of the signals in said memory and said second calculating means; multiplier to multiply the coefficients ε, B and the signal of said second calculating means; adder to add the signal of said first memory and the output signal of said multiplier; a divide-by-two circuit to receive the signal output from said adder; a multiplexer having a first input connected to the output from said divide-by-two circuit and a second input connected to the output of a counter, and having a first output connected to a second memory and a second output connected to said first calculating means; said counter to control the number of times the operator A is applied to the signal g(z,t); and recording means connected to said second memory.

Claim 11

The filter of claim 8, wherein said first calculating means implements the operator D z defined by: ##EQU8## where g is some function and I is an integer.

Claim 12

The filter of claim 9, wherein I is equal to 1.

Claim 13

The filter of claim 9, wherein I is equal to 2.

Claim 14

The filter of claim 8, wherein said second calculating means implements the operator H t defined by: H.sub.t (g(t))=FT.sup.-1 [j.sgn(ω).FT(g(t)) where: g is some function; FT represents the Fourier transform; IFT represents the inverse Fourier transform; sgn(ω) designates the sign of the variable ω which is the dual of t; and j is the complex operator such that j 2 =-1.

Claim 15

The filter of claim 8, wherein said counter controls said multiplexer so that the operator A is applied only once to the signal g(z,t).

Claim 16

The filter of claim 8 further including: means for time shifting the signals g i (t) for 2<i<n constituting the signal g(z,t) stored in said first and second memories, and means for subtracting the signals g 1 (z,t) and g 2 (z,t) from each other.