A Method for Calculating Attenuation in Creeping Materials

The phase lag between an applied forcing and a response to that forcing is a fundamental parameter in geophysical signal processing. For solid deforming materials, the phase lag between an oscillatory applied stress and the resulting strain response encapsulates information about the dynamical behavior of materials. The phase lag is not directly measured and must be extracted through multiple steps by carefully comparing two time-series signals. The extracted value of the phase lag is highly sensitive to the nature of the signals and the analysis method. Here, we propose a method for extracting the phase lag between two signals when either one or both include an underlying nonlinear trend, which is very common when measuring attenuation in creeping materials. We demonstrate the robustness of the method by analyzing artificial signals and quantifying their absolute and relative errors. We apply the method to two experimental datasets and compare our results with previous studies.