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We can write the model residual corresponding to the model regularization
operator which differences between adjacent at a fixed (*t*,*x*).
| |
(5) |

*p* is the maximum order of multiple included in equation (2).
Here we have modified the notation a bit and written rather than
. This is because the difference (5) is blind to
the order or leg of the pegleg corresponding to ; it is simply a
straight difference across all the model panels.
By design, signal (non-crosstalk) events on the in equation
(3) are assumed physically invariant for all *i* and *k* -
everything is a ``copy of the primary''. Again, this is the crucial fact
underlying LSJIMP. Minimally, multiples provide a redundant constraint on the
amplitude of the primaries; where no data is recorded (missing traces, near
offsets), they provide additional information about the primaries. Equation
(5) is a systematic way in which to exploit the multiples'
redundancy, and to integrate any additional information that they might provide.

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Stanford Exploration Project

7/8/2003