Energy partitioning (Attenuation)

[stubbe11]

Homework Statement

A seismic wave travel from surface, is reflected at the fifth of a series of horizontal interfaces. Each has a reflection coefficient "R" of 0.15. What is the total attenuation in amplitude caused by energy partitioning at all encountered interfaces, when the wave returns to the surface?

Homework Equations

total loss = (1-R)(1+R) = (1-R^2) [for one layer]

The Attempt at a Solution

We have a discussion here, where some argue that the equation should be used 4 times, hence the answer is 9% of the amplitude has been attenuated. And some who argue that it should be used 5 times (11.25%). Any inputs as what could be the correct one?

 

[haruspex]

the equation should be used 4 times, hence the answer is 9% of the amplitude has been attenuated. And some who argue that it should be used 5 times

Up to what point in the whole process? It has to be transmitted through 4, reflected at 1, then transmitted back through the first 4, no? Or have I misunderstood the question?

 

[stubbe11]

Up to what point in the whole process? It has to be transmitted through 4, reflected at 1, then transmitted back through the first 4, no? Or have I misunderstood the question?

Thanks for your interest and time.

Well, it seems like you understood it like I did. Transmitted through 4 interfaces and reflected on the 5th, then transmitted back up to the surface through the same 4 interfaces. So would you agree on 4 times then?

 

[haruspex]

Thanks for your interest and time.

Well, it seems like you understood it like I did. Transmitted through 4 interfaces and reflected on the 5th, then transmitted back up to the surface through the same 4 interfaces. So would you agree on 4 times then?

Yes.

 

[stubbe11]

Yes.

Big thanks!