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Appendix A: Pseudocode for a Picking Algorithm Utilizing Continuation

Algorithm 1 contains pseudocode which could be used to create a variational picking algorithm. Algorithm 2 shows how a variational picking algorithm may be used in a continuation framework. Here, $ \rho_o$ and $ \rho_f$ are strictly positive numbers denoting the minimum and maximum possible step sizes at each iteration, $ \gamma$ and $ \xi$ are positive early termination parameters, $ N$ is the maximum number of iterations at each continuation level, $ v(\mathbf{x})$ is a velocity model, $ v_0(\mathbf{x})$ is a starting velocity model, $ g(\mathbf{x})$ is the functional gradient, and $ h(\mathbf{x})$ is the search direction. $ M$ is the number of continuation levels, $ \mathbf{r}_j$ is a vector holding the triangle smoothing radius for each spatial dimension at continuation level $ j$ , and $ \sigma_j$ is the semblance scaling factor at continuation level $ j$ . We assume that scaling and smoothing increase with increasing $ j$ . $ \alpha_0 \left[v,\mathbf{x}\right]$ is the least-smoothed semblance-like volume, and $ \alpha \left[v,\mathbf{x}\right]$ denotes a semblance-like volume. These algorithms assume one has the following methods defined:


\begin{algorithm}
% latex2html id marker 519
[H]
\caption{Variational Picking}
\...
...x})$ \Comment{return final model}
\EndFunction
\end{algorithmic}\end{algorithm}


\begin{algorithm}
% latex2html id marker 582
[H]
\caption{Continuation Picking}
...
...)$ \Comment{return final model}
\EndFunction
\end{algorithmic}\end{algorithm}


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Next: Appendix B: A Primitive, Up: Decker & Fomel: Variational Previous: Acknowledgements

2022-05-24