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Now that we have derived appropriate imaging and amplitude correction operators,
we are ready to translate the general LSJIMP modeling equation
() to my particular implementation. The primary image,
, is mapped into data space primary events by NMO, .
Similarly, a given pegleg image, , is mapped into data space by
sequentially applying the differential geometric spreading correction
(), Snell resampling (), HEMNO (),
and finally, a reflection coefficient (). Let us rewrite
equation () accordingly:
| |
(28) |

We see that in equation (), the analog to
in equation () is
.
The data residual weight in equation (), , can often
strongly influence the success of the inversion. Technically, carries
a heavy burden: it must decorrelate and balance the residual. However, I have
found that a simpler form for nontheless pays dividends. I set
, which has the same dimension as a CMP gather, to zero where the data,
, has an empty trace, and also above the onset of the seabed reflection.

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Stanford Exploration Project

5/30/2004