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Consider the Kirchhoff migration integral, 1 a O (M) = dg we;M) P(5, (;M) 412 R2 = where M = (x,y,z) E R3, = ($,$2)
Consider the Kirchhoff migration integral, 1 a O (M) = dg we;M) P(5, (;M) 412 R2 = where M = (x,y,z) E R3, = ($,$2) E R2, t > 0, W(;M) is the weight function, e(},t) is the seismic section and Tp(F;M) is the diffraction time. (a) Determine W for the case of constant migration speed, c > 0, and zero offset configuration, with S = G = ($1,$2,0). = (b) Compare the Kirchhoff migration integral obtained in (a) with the following migration integral, 1 a Y'(M) - | 4(, L(F;M)/v) L(F;M) 2 z R2 where L(B;M) = ||S M|| and v > 0 is the migration speed (constant). Consider the Kirchhoff migration integral, 1 a O (M) = dg we;M) P(5, (;M) 412 R2 = where M = (x,y,z) E R3, = ($,$2) E R2, t > 0, W(;M) is the weight function, e(},t) is the seismic section and Tp(F;M) is the diffraction time. (a) Determine W for the case of constant migration speed, c > 0, and zero offset configuration, with S = G = ($1,$2,0). = (b) Compare the Kirchhoff migration integral obtained in (a) with the following migration integral, 1 a Y'(M) - | 4(, L(F;M)/v) L(F;M) 2 z R2 where L(B;M) = ||S M|| and v > 0 is the migration speed (constant)
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