A study of time spectrum identification of induced polarization field based on Weibull distribution function

Abstract

Identification of time spectrum is one of the core issues of the time-domain induced polarization (IP) method, which can be considered as one of the bases for distinguishing various polarized rocks. Fitting the IP data based on the spectrum forward model and obtaining optimal solution of the model parameters is a key step in spectrum identification. However, the suitable forward model should consider the observation conditions, such as the charging time and the time window. The time spectrum identification may be difficult to implement stably due to the lack of objective reference for the optimal solution. Therefore, our purpose is to improve the forward model and implement the spectrum identification for IP data. First, using the Weibull (WB) distribution function as the basis, a time spectrum forward model considering the charging time and observation time window is provided according to the typical measurement mode. Then, based on the WB spectrum model and Barzilai-Borwein gradient optimization, a method for solution of apparent spectral model parameters for spectrum identification is developed. Finally, this method is used to process the IP data from a mine in which the anomalies related to ore-bearing beds are identified based on the processing results. Results obtained demonstrate that the spectrum forward model based on the WB function is feasible in describing the IP data. The limited charging time and a wide observed time window should be considered to realize accurate simulations and description of the time-domain IP data. The essence of the time spectrum identification is to comprehensively reflect the time-varying state of the whole time channel through the spectral model parameters, whereas the decay field ratio of the adjacent time channel can be used as an objective reference. The parameters of the spectrum model characterizing the time-varying state are independent of polarization and resistivity and thus can be directly used for identification of IP anomalies.