Abstract
Abstract 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 the solution. We test the inversion by modelling plausible NAE surfaces, calculating the radiances, adding noise and inverting for the original surface. Three or more spectral bands are required to capture the overall shape of the NAE, and recovering specific quantities is difficult. Single wavebands that yield flat kernels recover the total area emplacement curve (rate of increase of hot area – the integral of the NAE with respect to temperature) surprisingly well due to their property of conserving NAE, suggesting novel methods for calculating area emplacement rates (and effusion rates) from time series of satellite images and radiometer measurements.
Highlights
Satellite thermal images have been used to observe volcanic activity for several decades (e.g. Gawarecki et al 1965; Hanel et al 1979; Rothery et al 1988; Glaze et al 1989; Oppenheimer & Francis 1997) and have found particular use in estimating different ‘rates’ of emplacement of volcanic material on planetary surfaces, such as volumetric effusion rate, time-averaged discharge rate (TADR) and rates of areal emplacement (Harris et al 2007a)
2009), assume that the TADR is proportional to the active area of the lava flow, based on the analytical model and empirical relationships of Pieri & Baloga (1986), with a constant of proportionality that can be derived from the model or estimated empirically
We model two types of Net Area Emplacement (NAE) surfaces, which we refer to as ‘simple’ and ‘complex’
Summary
Satellite thermal images have been used to observe volcanic activity for several decades (e.g. Gawarecki et al 1965; Hanel et al 1979; Rothery et al 1988; Glaze et al 1989; Oppenheimer & Francis 1997) and have found particular use in estimating different ‘rates’ of emplacement of volcanic material on planetary surfaces, such as volumetric effusion rate, time-averaged discharge rate (TADR) and rates of areal emplacement (Harris et al 2007a). The temperature-distribution approach is based on the observation that as a lava-flow advances it exposes fresh hot material that cools in a relatively simple and predictable way This cooling trajectory combined with an area coverage rate defines a surface temperature distribution, which in turn defines an emission spectrum (Carr 1986). The emplacement history is effectively ‘written in’ to the lava surface temperature distribution, and the emission spectrum at a point in time is a function of the area emplacement rate up to that point This basic conceptual model is supported by field observations for a number of different lavaflow types. There is a relationship between the temperature of a surface, its age and, its emplacement history
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