Abstract
Even though theoretical considerations and several observations point to the possibility that volcanic tremor may be a low-dimensional deterministic phenomenon, there has been no effort in the past to rigorously establish the presence of nonlinear dynamics. In this study we use volcanic tremor time series recorded at Sangay volcano, Ecuador, in order to find such evidence. Initially, the surrogate data test is employed and nonlinear prediction errors are used as a suitable quantity for such a test. Results indicate that tremor time series yielded slightly higher prediction errors than their corresponding surrogates, implying that they can be modeled better by a linear stochastic process at a 95% confidence level. However, the application of Casdagli’s test to the same data shows reduced prediction errors in smaller length scales that is compatible with low-dimensional chaos. The apparent conflict of the two tests can be resolved by taking a closer look at the prediction errors as a function of neighborhood size in phase space. This shows a sharp drop in the number of points available for nonlinear prediction at small length scales, probably due to the undersampling of the process that generates the tremor signal. This puts constraints on the efforts to analyze the nonlinear dynamics of volcanic tremor and calls for a reevaluation of seismic data acquisition procedures at active volcanoes.
Highlights
A central issue emerging during the analysis of time series that measure a property of a given physical system, is what kind of process is generating the observed signal
The purpose of this study is to investigate the presence of deterministic structure in volcanic tremor time series recorded at Sangay volcano, Ecuador
Surrogate data tests were designed so as to remove in theory this ambiguity, they rely on the calculation of some quantity from the data that will be compared later to the value of the same quantity calculated from the surrogates
Summary
A central issue emerging during the analysis of time series that measure a property of a given physical system, is what kind of process is generating the observed signal. Nonlinear deterministic processes offer a plausible alternative to linear models for such signals and suggest that a much richer structure may exist in the data This structure takes the form of fractal geometrical objects, often called strange attractors, that consist of trajectories moving in an m-dimensional Euclidean space (called phase or state space) and represent the evolution of the states of the system under study [2]. None of the studies mentioned above tried to establish the presence of chaos more rigorously, through a series of tests designed to detect nonlinear dynamics This is an important point, as it would determine which set of models (linear stochastic or nonlinear chaotic) are more appropriate for describing the tremor source
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