APPLICATION OF THE EMPIRICAL MODE DECOMPOSITION TO FIELD TILTMETER DATA FOR HYDRAULIC FRACTURE MAPPING

Abstract

Empirical Mode Decomposition (EMD) is a fully data-driven, adaptive technique for analyzing time series from nonlinear and nonstationary processes. The starting point of EMD is to treat the signal as a superposition of different intrinsic modes of oscillations (fast oscillations superimposed on slow oscillations). The essence of this method is to empirically identify the intrinsic oscillatory modes by their characteristic time scale imbedded in a signal, and then decompose the signal into a collection of a finite and often small number of intrinsic mode functions (IMF) through a so-called sifting process. Each IMF component then represents only one mode of both amplitude and frequency modulated oscillation of the signal at a certain time scale or frequency band, and the sum of all the IMF components as well as a residual produces a perfect reconstruction of the original signal. Partial reconstruction can be achieved by selectively removing fast or slowly varying IMFs, which provides a method to remove unwanted (noise) parts of the signal. In this paper, the EMD is applied to quantitative analysis of field tiltmeter data collected to monitor and map hydraulic fractures. The fracture-related tilt components are extracted by identifying the relevant IMFs that contribute to them, which allows removing the noise and background trend components from the raw data. The extracted tilt data are then inverted to obtain the volume and orientation of the hydraulic fractures. Physically reasonable prediction of the hydraulic fracture volume is used to demonstrate that the application of EMD to field tiltmeter data analyzing can be successfully carried out.