Patent Document ID: 20130083973
Application ID: 13604964
Patent Flag: 0

Claim One:
1. A method for searching for a seismic horizon in a seismic image of the subsoil, the method comprising: designating two points of respective coordinates x 1 , y 1 and x N , y N in the seismic image as being two points belonging to the horizon sought, an integer number N of discrete abscissae x 1 , x 2 ,. .. , x N being defined between the abscissae x 1 , x N of the two designated points; considering a fault position at a discrete abscissa x n α where n α is an integer between 1 and N−1 and a fault amplitude C d in a discrete domain; by taking two functions f and g 0 which can be derived over the interval [x 1 , x N ], initializing a fault amplitude in a continuous domain with the value C 0 =C d −[f(x n α +1 )−f(x n α )], a pseudo-continuous component {tilde over (τ)} 0 (x n ) and a jump component {circumflex over (τ)} 0 (x n ) defined over the N discrete abscissae according to {tilde over (τ)} 0 (x n )=f(x n ) and {circumflex over (τ)} 0 (x n )=g 0 (x n )+C 0 ·H(n−n α ), where H(·) designates the Heaviside function; performing a number of iterations of a sequence of computation steps for an iteration index k initialized at k=0 then incremented by units, the sequence comprising, for an index k: computing a residue r k (x n )=∇{tilde over (τ)} k (x n )+∇g k (x n )−p(x n , {tilde over (τ)}(x n )+{circumflex over (τ)} k (x n )), where ∇ designates the gradient operator and p(x n , y) designates the tangent of an inclination estimated for a position of discrete abscissa x n and of ordinate y in the seismic image; solving a Poisson equation Δ(δ{tilde over (τ)} k )=−div(r k ) to determine an update term δ{tilde over (τ)} k (x n ), with conditions at the Dirichlet limits: { δ τ ~ 0 ( x 1 ) = y 1 - f ( x 1 ) - g 0 ( x 1 ) δ τ ~ 0 ( x N ) = y N - f ( x N ) - g 0 ( x N ) - C 0 on the first iteration and { δ τ ~ k ( x 1 ) = g k - 1 ( x 1 ) - g k ( x 1 ) δ τ ~ k ( x N ) = g k - 1 ( x N ) - g k ( x N ) + C k - 1 - C k on each iteration of index k≧1, where g k is a function that can be derived over the interval [x 1 , x N ]; updating the pseudo-continuous component according to 
 {tilde over (τ)} k+1 ( x n )={tilde over (τ)} k ( x n )+δ{tilde over (τ)} k ( x n ); updating the fault amplitude in the continuous domain according to 
 C k+1 =C d −└{tilde over (τ)} k+1 ( x n α +1 )−{tilde over (τ)} k+1 ( x n α )┘; updating the jump component according to 
 {tilde over (τ)} k+1 ( x n )= g k+1 ( x n )+ C k+1 ·H ( n−n α ); if a final value of the iteration index k is reached, computing a function τ n α ,C d (x n ) representing the ordinate in the seismic image of a horizon estimated as a function of the discrete abscissa x n , from a sum of the pseudo-continuous component and of the jump component; and if the final value of the iteration index k is not reached, executing the next iteration of the sequence.