# Missing trace interpolation of 3D seismic data using the Hierarchical Tucker tensor format

This applications is available only in the software release for members of SINBAD consortium.

This software provides an algorithm for missing trace/receiver interpolation of 3D seismic data using the latent Hierarchical Tucker tensor format. The algorithm operates on a single frequency slice, although an extension to an arbitrary number of frequency slices is straightforward.

Author: Curt Da Silva (curtd@math.ubc.ca)

Date: March, 2014

## Contents

## Downloading & Dependencies

The synthetic examples code can be found in the SLIM software release under `applications/Processing/HierarchicalTuckerOptimization`.

The code has been tested with *Matlab R2013a* and supports, but does not require, the Parallel Computing Toolbox.

This code uses the following packages, also found in the `tools` part of the SLIM software release.

- utilities/SPOT-SLIM - object oriented framework for matrix-free linear algebra.
- tools/solvers/HTOpt - Hierarchical Tucker tensor algorithms

## Running & Parallelism

All of the examples and results are produced by the scripts found in this software release under `applications/Processing/HierarchicalTuckerOptimization/examples`. Start matlab from `applications/Processing/HierarchicalTuckerOptimization` to add the appropriate paths.

To run the scripts, follow the instructions in the README.md file enclosed with the code

## Functions

The missing-trace tensor interpolation using Hierarchical Tucker tensors can be found in `tools/algorithms/HTOpt`, with accompanying documentation in the README.md file.

## Examples and results

Several examples (serial and parallel versions) of missing trace interpolation using these methods can be found in `applications/Processing/HierarchicalTuckerOptimization/examples`

Results are of missing-receiver interpolation is shown in interp4Dview.m

## References

[1] C. Da Silva and F. J. Herrmann, 2014. Optimization on the Hierarchical Tucker manifold - applications to tensor completion

[2] C. Da Silva and F. J. Herrmann, 2013. Hierarchical Tucker Tensor Optimization - Applications to Tensor Completion

## Acknowledgements

Thanks to our sponsors and NSERC for their financial support.