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2.5D True-amplitude diffraction-stack redatuming: numerical tests

Profile image of Jörg SchleicherJörg SchleicherProfile image of Amélia NovaisAmélia NovaisProfile image of jesse C costajesse C costa

2009, 11th International Congress of the Brazilian Geophysical Society & EXPOGEF 2009, Salvador, Bahia, Brazil, 24-28 August 2009

https://doi.org/10.1190/SBGF2009-325
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Abstract
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This research focuses on developing a true-amplitude redatuming operator using a diffraction-stack method. The operator effectively transforms seismic data acquired on a varying surface to simulate data as if recorded on a different measurement surface. The effectiveness of the approach is evaluated through numerical experiments, demonstrating accurate transformation of traveltimes, amplitudes, and wavelet shapes in simulated scenarios. Future work aims to extend this technique to curved measurement surfaces and test its robustness under varying medium inhomogeneities.

Figures (7)
where R, = \/(z—zr)2 +(x—)2 (see Figure 1). Equation Figure 1: Zero-offset redatuming in a constant-velocity medium: The output source-receiver pair at 7,z, and the desired traveltime t define the isochron z = %,(x; 7,7), this being a circle with radius R,. A reflection at a point M* recorded at E would travel along the ray with length 2+ R,. For simple situations, analytic expressions for the stacking line and weight function can be found. As the most simple case, we consider the redatuming from a planar acquisition surface at depth z= 0 to a planar datum at depth z=z, ina homogeneous medium with velocity co. In this situation, the isochron z= %,(x;n,t) of point (n,t) as defined in equation (3) becomes
where R, = \/(z—zr)2 +(x—)2 (see Figure 1). Equation Figure 1: Zero-offset redatuming in a constant-velocity medium: The output source-receiver pair at 7,z, and the desired traveltime t define the isochron z = %,(x; 7,7), this being a circle with radius R,. A reflection at a point M* recorded at E would travel along the ray with length 2+ R,. For simple situations, analytic expressions for the stacking line and weight function can be found. As the most simple case, we consider the redatuming from a planar acquisition surface at depth z= 0 to a planar datum at depth z=z, ina homogeneous medium with velocity co. In this situation, the isochron z= %,(x;n,t) of point (n,t) as defined in equation (3) becomes
Figure 2: Model for the numerical experiment: A zero- offset experiment was simulated at z = 0 above a synclinal reflector. Also shown is the datum level (dotted line) at z= 200m.
Figure 2: Model for the numerical experiment: A zero- offset experiment was simulated at z = 0 above a synclinal reflector. Also shown is the datum level (dotted line) at z= 200m.
Figure 3: Modeled seismic zero-offset section. cy and cy (see Figure 7). Analogously to the previous case, the stationary ray defining the stacking line is the one that is normal to the output isochron z = &%,(x;n,T) and thus passes through the redatumed source-receiver point at n. Therefore, it connects S to S,, where it refracts according to Snell’s law (see Figure 7). Therefore, its length is again (R, +2£). From this consideration, it is clear that it’s traveltime, which defines the redatuming stacking line, is given by
Figure 3: Modeled seismic zero-offset section. cy and cy (see Figure 7). Analogously to the previous case, the stationary ray defining the stacking line is the one that is normal to the output isochron z = &%,(x;n,T) and thus passes through the redatumed source-receiver point at n. Therefore, it connects S to S,, where it refracts according to Snell’s law (see Figure 7). Therefore, its length is again (R, +2£). From this consideration, it is clear that it’s traveltime, which defines the redatuming stacking line, is given by
Figure 4: Seismic section resulting from redatuming operation 1 to z= 200 m.
Figure 4: Seismic section resulting from redatuming operation 1 to z= 200 m.
Figure 5: Seismic section resulting from Kirchhoff modeling at z= 200 m.
Figure 5: Seismic section resulting from Kirchhoff modeling at z= 200 m.
Figure 6: Comparison of the central traces of Figures 4 and 5. Notice the almost perfect coincidence between the redatumed (dashed line) and modeled (continuous line) traces.
Figure 6: Comparison of the central traces of Figures 4 and 5. Notice the almost perfect coincidence between the redatumed (dashed line) and modeled (continuous line) traces.
Figure 7: Zero-offset redatuming to a horizontal interface separating two homogeneous media. The output source- receiver pair at n,z, and the desired traveltime t define the isochron z= %,(x;1,7), this being a circle with radius R,. A reflection at a point M* recorded at € would travel along the ray with length €+R,, which refracts at z, according to Snell’s law.
Figure 7: Zero-offset redatuming to a horizontal interface separating two homogeneous media. The output source- receiver pair at n,z, and the desired traveltime t define the isochron z= %,(x;1,7), this being a circle with radius R,. A reflection at a point M* recorded at € would travel along the ray with length €+R,, which refracts at z, according to Snell’s law.

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<title>Seismic imaging operators derived from chained stacking integrals</title>
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