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Introduction

Light propagation is similar in both nature and theory to seismic wave propagation in the subsurface. It is not surprising to see a large number of common problems between the fields of seismology and optics. Claerbout (2007) poses a question about the relationship between light patterns under water and seismology. One prominent problem in reflection seismology is estimating seismic velocities in the heterogeneous subsurface. Velocity is a measure that depends on travel time; i.e. it is determined by the moveout of seismic events. It is always costly to estimate subsurface velocities, whether using conventional velocity analysis or inversion methodologies. Unfortunately, imaging algorithms rely on the accuracy of velocity models. Therefore, a curious scientist might ask: Can we use amplitudes alone for imaging?

For the sake of simplicity, let us consider a simple imaging problem involving a single wavefield caustic: a single reflector including a syncline. Using the exploding reflector concept, we can simulate a zero-offset section (Claerbout, 1985). What we will observe in the section is a bowtie that is caused by the syncline. The syncline causes many ray paths between the exploding reflector to the receiver to converge at some point before reaching the surface, forming a caustic. Given the correct velocity model, migration algorithms like Kirchhoff migration will resolve the bowtie into a syncline (Yilmaz, 2001).

Now, let us consider a swimming-pool experiment where the goal is to infer the water surface from the light patterns on the floor of the pool like the ones shown in Figure 1. We might encounter similar difficulties as in seismic imaging. It is hard to estimate the exact speed of light in the pool. In this case the question is as follows: Can we use the light intensity field at the bottom of the pool to infer the surface of water?

The two questions are closely related, and the pool experiment is easier to comprehend intuitively. In this paper, I implement the forward simulation using ray theory to build a light intensity field at the pool floor that can be used for inferring the surface. I will not follow the exact physics as it is done in optical simulations: I assume infinite frequencies for ray theory and representing light with a finite number of rays. The forward simulation is done using ray tracing and beam tracing. I finally discuss a Monte Carlo ray tracing inversion that is based on ray counting.

fig-jonpool
Figure 1.
Light patterns at the bottom of a pool (Claerbout, 2007). [NR]
fig-jonpool
[pdf] [png]


next up previous [pdf]

Next: Forward Simulation Up: Ray tracing modeling and Previous: Ray tracing modeling and

2009-04-13