Fractal dimension analysis of the magnetic time series associated with the volcanic activity of Popocatépetl

Abstract

Abstract. Fractal analysis of the total magnetic field (TMF) time series from 1997 to 2003 at Popocatépetl Volcano is performed and compared with the TMF-series of the Teoloyucan Magnetic Observatory, 100 km away. Using Higuchi's fractal dimension method (D). The D changes over time for both series were computed. It was observed, when the time windows used to compute D increase in length, both series show nearly the same behavior. Some criteria of comparison were employed to discriminate the local effects inherent to volcano-magnetism. The simultaneous maximum in D (1.8) of the TMF series at Popocatépetl Volcano and the recovered volcanic activity indicates a scaling relation of the TMF at Popocatépetl Volcano and demonstrates a link between the magnetic field and volcanic activity.

Comparison of box counting and correlation dimension methods in well logging data analysis associate with the texture of volcanic rocks

“…In practice, the box-counting algorithm estimates fractal dimension by counting the number of boxes required to cover S for several box sizes, and fitting a straight line 5 to the log-log plot of N δ (S) vs. δ. The slope of the least square best fit straight line is taken as the box-counting dimension D B .…”

“…The method of phase space reconstruction expand the data series that observed at different times within a certain time to a vector space, that is, phase space. Well logging data is associated with the formation of physical properties, which is measured with the same depth sampling 5 interval. So we first expand the well logging data to phase space, then calculate its correlation dimension.…”

“…The geological processes that the earth experienced is considered as a non-linear process, which led to strong heterogeneity in rock lithology, permeability and porosity distribution (Vadapalli et al, 2014). The heterogeneity provides premise and feasibility 20 that the study of fractal theory is applied to geophysics (Flores-Marquez et al, 2012). To solve the problems in geology, many scholars investigate the fractal characteristics of well logging data, and make a great progress (Li, 2003).…”

“…Furthermore, fractal dimension has a wide application in the prediction of fracture, reservoir heterogeneity, sedimentary facies analysis and rock pore structure description. Fractal characteristics of well logging curves reflect the volcanic rock lithology, 5 physical property, cracks and fluid nature comprehensively. The value of well logging parameters often reflect the mineral composition of rocks, but not reflect the texture of volcanic rocks (Li, 2005).…”

Fractal dimension of well logging curves associated with the texture of volcanic rocks

“…The Earth experienced several geological processes can be viewed as a non-linear process, has led to strong heterogeneity in rock lithology, permeability and porosity distribution. The heterogeneity provides premise and feasibility that the study of fractal theory is applied to geophysics [5,6]. In an attempt to solve the problems in geology, many scholars investigate the fractal characteristics of well logging data, and make a great progress [7].…”