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5 One Dimensional Problem     continued...

If the model is modified, assume that the velocity is increased by 50 percent to the right 2000 meters from the source. Then when the initial source wave impinges on the impedance a reflected wave will be generated. This inhomogeneous model is plotted in Figure 5 and the seismic waves are plotted in Figure 6. The strength of the reflected wave is determined by the reflection coefficient [19]. Given the velocities and densities the reflection coefficient R is

The subscript 0 is for the incident medium and the subscript 1 is for the transmitting medium. When the density is a constant this simplifies to

The transmitted energy is T, T = 1 - R. If the velocity function increases with depth, the reflection coefficient is positive; if it decreases, the reflection coefficient becomes negative. The sign change is physically realized as a polarity change in the reflected signal which is observed in Figure 7.

Figure 5: Inhomogeneous One Dimensional Model.

Figure 6: Reflected Waves, Velocity Increased 50 percent.

Figure 7: Reflected Waves, Velocity Decreased, 50 percent.