Plane-wave migration in tilted coordinates

Impulse responses

Our second example is a smooth sediment velocity field embedded with a salt body with steeply dipping flanks. Figure 10 is a comparison of the impulse responses of the two-way wave equation (Figure 10a ), one-way wave-equation downward continuation (Figure 10b ) and plane-wave migration in tilted coordinates (Figure 10c). From Figures 10a and b, we observe that the one-way wave equation mimics the two-way wave equation well for energy that propagates with small angles from the vertical direction, but its accuracy drops for energy that propagates almost horizontally. Energy that overturns is lost entirely. Comparing Figure 10c with Figure 10a, we notice that there are no reflections or multiples in Figure 10c. This is not surprising, since the one-way wave-equation extrapolator is applied. But the wave front of the direct arrival matches that of the two-way wave equation very well, even at high angles and with overturned waves, despite being extrapolated with the one-way wave equation. The impulse-response comparison shows the potential to image the steeply dipping reflectors and overturned waves by plane-wave migration in tilted coordinates.

impulse
Figure 10. Impulse response comparison among (a) two-way wave equation, (b) one-way wave-equation downward continuation and (c) plane-wave migration in tilted coordinates.

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Figure 11. The velocity model of the BP velocity benchmark.

Plane-wave migration in tilted coordinates