### Multiple Scattering and Coda Localization at Merapi Volcano

AB: Due to their eruptive history the cones of strato volcanoes consist of different materials such as hardened lava, tephra, and volcanic ash. Additionally, due to their rough topography, e.g. caused by erosion, deposition is irregular and the volcanic structure cannot be described by a simple 1D layered model. The 3D small scale heterogeneities with large impedance contrast cause multiple scattering of seismic waves and are important features for the modelling of seismic wave propagation in strato volcanoes. Active seismic experiments at Merapi and Vesuvius volcanoes have shown that the transport mean free path of strato volcanoes is as small as some hundreds of meters and, therefore, is about three orders of magnitude smaller than the transport mean free path of usual Earth's crust. Moreover, the transport mean free path is at least one order of magnitude smaller than the characteristic scale length of intrinsic attenuation. Finally, the transport mean free path is in the same order as the inverse of the wave number. This indicates, that in strato volcanoes heterogeneity is so strong that we approach the regime of strong scattering where the classical theories such as radiative transfer and diffusion become invalid. All this makes strato volcanoes a natural laboratory for the application of multiple scattering theories. One important recent observation at Merapi volcano is an abnormal spatial concentration of coda energy in the summit region. This observed coda localization can be interpreted as an indication of Anderson localization, which is a theoretically predicted effect of strong scattering beyond the validity of diffusion theory. We show that the Anderson localization model better fits the data observed at Merapi than a standard half space diffusion model. However, we also show that, alternatively, the observation can also be explained within the classical diffusion approach by assuming leakage of energy from the strongly scattering volcanic edifice into the much more homogeneous underlying earth crust. Similar to Anderson localization the leakage results in an inhomogeneous distribution of energy in space, where the energy is low near the volcano-crust boundary and large inside the strongly scattering volcano far from that boundary. Additionally to the Anderson localization model, we use two classical models to explain coda localization: The first one is based on an analytical solution of the diffusion equation for a scattering cylinder (representing the volcano) embedded in a homogeneous half-space (representing the surrounding crust). The second model is based on a Monte-Carlo simulation of the acoustic equation of radiative transfer. In this simulation we take into account multiple scattering inside the volcanic edifice as well as leakage at the bottom of the volcano into the less heterogeneous crust. Additionally, in this model we also consider the true topography of the volcano by simulating reflections at the free surface, where we use a digital elevation model of the volcano and the Kirchhoff tangent plane method.

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