Linear Mathematical Methods Research Articles

Numerical relationships between magnetic parameters measured in Quaternary sediments and global paleoclimatic proxies

The complexity of most geological and geophysical problems prompts sometimes the use of non linear mathematical methods to handle them. An adaptive neuro fuzzy inference system (ANFIS) that combines fuzzy logic with neural networks, is applied here to study a paleoclimate section from the Quaternary sedimentary fill of the Lake Mucubaji (western Venezuela). The purpose of this work is to find a set of numerical relationships that could predict the possible connections between oxygen isotope (δ18O) values from two different locations in the northern hemisphere (Ammersee in southern Germany and an ice core from the Greenland Ice Core Project — GRIP) and rock-magnetic parameters measured in Mucubaji samples (i.e. mass-specific magnetic susceptibility — χ, magnetic remanence S-ratio, mass-specific saturation isothermal remanent magnetization — SIRM and anhysteretic remanent magnetization — ARM). The best inferences in terms of coefficient of determionation R2 and the Root Mean-Square Error (RMSE) are obtained using those magnetic data as input that include information about magnetite grain size distributions, e.g., SIRM and ARM in FIS structures [1χ, 4ARM] and [4ARM, 1SIRM]. A comparison between Ammersee and GRIP actual data, as well as their corresponding inferences for the FIS structure [4ARM, 1SIRM], reveals a reasonable good inference of global trends for both records, overlooking the regional and/or local paleoclimate forcings that might have affected Ammersee. A better correlation between global isotope paleoclimate records and magnetic proxies, is perhaps prevented by the role played by local and regional paleoclimate and tectonism in Mucubaji. We also argue that the ratio of ARM over SIRM appears to be related in a complex way to the onset and to the end of the Younger Dryas. Our novel approach to the assessment of a specific paleoclimate case study shows the potential of the ANFIS technique in solving problems where traditional univariate and multivariate linear regression methods could prove inadequate.

Complexity and Productivity Differentiation Models of Metallogenic Indicator Elements in Rocks and Supergene Media Around Daijiazhuang Pb–Zn Deposit in Dangchang County, Gansu Province

With the help of complexity indices, we quantitatively studied multifractals, frequency distributions, and linear and nonlinear characteristics of geochemical data for exploration of the Daijiazhuang Pb–Zn deposit. Furthermore, we derived productivity differentiation models of elements from thermodynamics and self-organized criticality of metallogenic systems. With respect to frequency distributions and multifractals, only Zn in rocks and most elements except Sb in secondary media, which had been derived mainly from weathering and alluviation, exhibit nonlinear distributions. The relations of productivity to concentrations of metallogenic elements and paragenic elements in rocks and those of elements strongly leached in secondary media can be seen as linear addition of exponential functions with a characteristic weak chaos. The relations of associated elements such as Mo, Sb, and Hg in rocks and other elements in secondary media can be expressed as an exponential function, and the relations of one-phase self-organized geological or metallogenic processes can be represented by a power function, each representing secondary chaos or strong chaos. For secondary media, exploration data of most elements should be processed using nonlinear mathematical methods or should be transformed to linear distributions before processing using linear mathematical methods.