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We present a novel method for interpreting time series of multispectral observations of volcanic eruptions. We show how existing models relating to radiance and area emplacement can be generalized into an integration-convolution of a Net Area Emplacement (NAE) function and a cooling function, assuming all surfaces follow the same cooling curve. The NAE describes the variation in the rate of emplacement of hot material with time and temperature, while the cooling function describes the cooling of a hot surface with time. Discretizing the integration-convolution equation yields an underdetermined matrix equation that we solve using second-order Tikhonov regularization to stabilize...

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