# Matrix Approach of Seismic Imaging: Application to the Erebus Volcano, Antarctica

## TL;DR

This paper introduces a matrix-based seismic imaging method that effectively utilizes multiple scattered waves to image volcanic structures at depths beyond traditional limits, demonstrated on Erebus Volcano in Antarctica.

## Contribution

The novel matrix approach leverages multiple scattering and iterative time reversal to surpass conventional depth limits in seismic imaging, applicable to complex heterogeneous areas.

## Key findings

- Successfully imaged Erebus Volcano's internal structure
- Extended imaging depth beyond 10 scattering mean free paths
- Revealed detailed volcanic features such as magma reservoirs and cavities

## Abstract

Multiple scattering of seismic waves is often seen as a nightmare for conventional migration techniques that generally rely on a ballistic or a single scattering assumption. In heterogeneous areas such as volcanoes, the multiple scattering contribution limits the imaging-depth to one scattering mean free path, the mean distance between two successive scattering events for body waves. In this Letter, we propose a matrix approach of passive seismic imaging that pushes back this fundamental limit by making an efficient use of scattered body waves drowned into a noisy seismic coda. As a proof-of-concept, the case of the Erebus volcano in Antarctica is considered. The Green's functions between a set of geophones placed on top of the volcano are first retrieved by the cross-correlation of coda waves induced by multiple icequakes. This set of impulse responses forms a reflection matrix. By combining a matrix discrimination of singly-scattered waves with iterative time reversal, we are able to push back the multiple scattering limit beyond 10 scattering mean free paths. The matrix approach reveals the internal structure of the Erebus volcano: A chimney-shaped structure at shallow depths, a magma reservoir at 2500 m and several cavities at sea level and below it. The matrix approach paves the way towards a greatly improved monitoring of volcanic structures at depth. Beyond this specific case, the matrix approach of seismic imaging can generally be applied to all scales and areas where multiple scattering events undergone by body waves prevent in-depth imaging of the Earth's crust.