For the first time, we obtained high-resolution images of Earth's interior of the La Palma volcanic eruption that occurred in 2021 derived during the eruptive process. We present evidence of a rapid magmatic rise from the base of the oceanic crust under the island to produce an eruption that was active for 85 days. This eruption is interpreted as a very accelerated and energetic process. We used data from 11,349 earthquakes to perform travel-time seismic tomography. We present high-precision earthquake relocations and 3D distributions of P and S-wave velocities highlighting the geometry of magma sources. We identified three distinct structures: (1) a shallow localised region (< 3 km) of hydrothermal alteration; (2) spatially extensive, consolidated, oceanic crust extending to 10 km depth and; (3) a large sub-crustal magma-filled rock volume intrusion extending from 7 to 25 km depth. Our results suggest that this large magma reservoir feeds the La Palma eruption continuously. Prior to eruption onset, magma ascended from 10 km depth to the surface in less than 7 days. In the upper 3 km, melt migration is along the western contact between consolidated oceanic crust and altered hydrothermal material.

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Short period small magnitude seismograms mainly comprise scattered waves in the form of coda waves (the tail part of the seismogram, starting after S-waves and ending when the noise prevails), spanning more than 70% of the whole seismogram duration. Corresponding coda envelopes provide important information about the earth inhomogeneity, which can be stochastically modeled in terms of distribution of scatterers in a random medium. In suitable experimental conditions (i.e. high earth heterogeneity) either the two parameters describing heterogeneity (scattering coefficient), intrinsic energy dissipation (coefficient of intrinsic attenuation) or a combination of them (extinction length and seismic albedo) can be used to image Earth structures. Once a set of such parameter couples has been measured in 1 a given area and for a number of sources and receivers, imaging their space distribution with standard methods is straightforward. However, as for finite-frequency and full-waveform tomography, the essential problem for a correct imaging is the determination of the weighting function describing the spatial sensitivity of observable data to scattering and absorption anomalies. Due to the nature of coda waves, the measured parameter-couple can be seen as a weighted space average of the real parameters characterizing the rock volumes illuminated by the scattered waves. This paper uses the Monte Carlo numerical solution of the Energy Transport Equation to find approximate but realistic 2D space-weighting functions for coda waves. Separate images for scattering and absorption based on these sensitivity functions are then compared with those obtained with commonly-used sensitivity functions in an application to data from an active seismic experiment carried out at Deception Island (Antarctica). Results show the that these novel functions are based on a reliable and physically grounded method to image magnitude and shape of scattering and absorption anomalies. Their extension to 3D holds promise to improve our ability to model volcanic structures using coda waves.