Dynamic equivalence

Comparing Expression 8 with Expression 13, it is evident that they are identical in form. That is, any heterogeneous sequence of layers has the same wave behavior - to second order in $i\omega$ - as a particular homogeneous material of the same total thickness

provided that lines of best fit to the elastic parameters have zero slope with respect to the direction of layering.

The startling thing for me is that the second-order term says nothing about the second-order structure of the layers, and so contains no information about the loss of energy from the main pulse to the coda. If we wish to see how energy is lost to the coda we must examine higher-order terms in the Taylor series expansion.