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At its core, when searching for the best fit model to predict seismic measurements, XWITM swaps a conventional point-to-point misfit measure to one based on an adaptive cost function (Warner and Guasch, 2016). This gives a superior quality gradient or update direction in terms of pointing towards the global minimum misfit minimiser. Further it gives longer length scales deeper down, in particular length scales which setting derivative constraints can latch onto for flooding large scale structures like salt. The results below show the combination of an adaptive cost function (AWITM) with spatial derivative constraints (CWI).

 

Starting Model

Starting Model

Target Model

Target Model

XWI without CWI model

XWI without CWI model

XWI with CWI model

XWI with CWI model

XWITM with directional derivative constraints

Automated salt flooding leading to global minimum convergence

 

Horizontal slice through starting model

Horizontal slice through starting model

Vertical slice through starting model

Vertical slice through starting model

Horizontal slice through intermediate model with CWI

Horizontal slice through intermediate model with CWI

Vertical slice through intermediate model with CWI

Vertical slice through intermediate model with CWI

Horizontal slice through final model with CWI

Horizontal slice through final model with CWI

Vertical slice through final model with CWI

Vertical slice through final model with CWI

Horizontal slice through true model

Horizontal slice through true model

Vertical slice through true model

Vertical slice through true model

XWITM without directional derivative constraints

Unable to recover salt body leading to local minimum convergence

Horizontal slice through  starting model

Horizontal slice through starting model

Vertical slices through  starting model

Vertical slices through starting model

Horizontal slice through  final model  without CWI

Horizontal slice through final model without CWI

Vertical slice through  final model  without CWI

Vertical slice through final model without CWI

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