Analysis of 1/f noise characteristics of geo-signals

The superposition of 1/f ^γ and white noise is a useful noise-model used in many fields. The determination of the spectral exponent γ and the mixture ratios of these noises are important in many applications such as GPS (Global Positioning System) time series residual noise, soil radon gas emanation (ambient noise) data and the seismic background noise. GPS data is used to estimate the surface displacement and the strain velocity of the earth. Reliable estimations of these quantities require accurate models and proper error analysis. Radon data also provide insight on temporal variation of soil gas in porous and permeable part of the shallow crust of the earth. The anomalies (abrupt amplitude changes) in gas emanation are found to be related to the seismic activities. We analyze GPS residual noise, radon data and background noise data by a wavelet-based method which relies on a line fitting operation to the difference sequence constructed from the variance progression of the wavelet coefficients. The main goal is to estimate the noise characteristics (γ parameter and the noise amplitudes) reliably. We show that the 1/f ^γ noise part in the GPS residual signals is measured as the flicker noise (γ≈1) (induced by atmospheric effects, mismodeled satellite orbits, etc.). We also present the analysis of soil radon gas emanation data and the seismic background noise, both of which follow the 1/f noise superposed by white noise similar to GPS noise. We discuss the wavelet-based analysis method in detail and present results obtained with real data.