SimPEG.regularization.PGIsmallness.compute_quasi_geology_model

PGIsmallness.compute_quasi_geology_model()

Compute and return quasi geology model.

For each active cell in the mesh, this method returns the mean values in the Gaussian mixture model for the most representative rock unit, given the current model. See the Notes section for a comprehensive description.

Returns:

(n_param, ) numpy.ndarray

The quasi geology physical property model.

Notes

Consider a Gaussian mixture model (GMM) for \(K\) physical property types and \(N\) rock units. The mean model parameter values for rock unit \(n \in \{ 1, \ldots , N \}\) in the GMM is represented by a vector \(\boldsymbol{\mu}_n\) of length \(K\). For each active cell in the mesh, the compute_quasi_geology_model method computes:

\[g_i^ = \min_{\boldsymbol{\mu}_n} \big \| \mathbf{m}_i - \boldsymbol{\mu}_n \big \|^2\]

where \(\mathbf{m}_i\) are the model parameter values for cell \(i\) for the current model. The ordering of the output vector \(\mathbf{g}\) is the same as the model \(\mathbf{m}\).