Looking closer at equations (48) and (49), we can observe that for each condition at the -th interface, there are generally three terms:
(52)
where
for a medium with layers. The source at is fixed and therefore,
. Moreover, the receiver is located at
, which leads to
. Therefore, we can derive the following set of equations in the general case of multi-layer media:
(53)
which leads to the recursive formula
(54)
where due to
. This newly developed equation is an exact extension of the two-layer case result (equation (42)) to the multi-layer case and is similar to equation (12) in the main text.
Effects of lateral heterogeneity on time-domain processing parameters