Decomposition of acquisition curves of isothermal remanent magnetization

Drebushchak M.V.

A.A. Trofimuk Institute of Petroleum Geology and Geophysics SB RAS, Novosibirsk, Russia

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Rock magnetism is a powerful tool for analysis of magnetic minerals in various rocks, especially in very low concentrations. Such rock-magnetic studies should provide information concerning concentration, composition, structure and origin of magnetic minerals, which is required for correct paleomagnetic interpretation of natural remanent magnetization components. Also, rock-magnetic concepts and techniques are become more popular for studies of environmental magnetism, as even subtle changes in sedimentary environment can be well monitored, for instance, through various degrees of oxidation.

One of the more commonly applied methods is the determination of acquisition curves of the isothermal remanent magnetization (IRM). Robertson and France [4] observed experimentally that the SIRM acquisition curves of particular minerals conform with a cumulative log-Gaussian (CLG) curve because of the logarithmic distribution of magnetic grain-size. In case of mixture of magnetic grains of different sizes, individual distributions add linearly to yield a cumulative curve, provided that interaction of magnetic grains is negligible.

Based on the assumption that an IRM acquisition curve corresponds to a CLG function, two transformations can be performed: magnetic induction values are converted to their logarithmic values and the linear ordinate scale is converted to a probability scale, which is achieved by standardizing the acquisition curve. After these transformations, unimodal distribution is represented by a straight line. Transformation of the IRM acquisition curve in this way is useful for estimating the number of components. Representation of acquisition curve on the linear ordinate scale is referred to as LAP (linear acquisition plot), as GAP (gradient acquisition plot) if it is a gradient curve, and as SAP (standardized acquisition plot) if it is a probability scale [3].

Since in real rocks magnetic grain assemblages are usually represented by grains of different sizes and composition, the major goals in the analysis of IRM acquisition curve are: 1) separation of this assemblage into the groups (components) of relatively homogeneous grains, each of which is represented by lognormal distribution; 2) estimation of the contribution of each of these components into the cumulative IRM acquisition curve.

Fig.1. Experimental and modeled curves and values of parameters for each component.

To solve this problem, different approaches have been used [2; 1]. This paper represents the method of processing a range of coercive spectra, based on the IRM acquisition curve similarity to the lognormal distribution. Moreover, it is possible to calculate magnetic distribution, even if it is far from saturation. Experimental curve can thus be represented as a sum of the cumulative lognormal curves, where each curve can be characterized with its SIRM (saturation magnetization), B_1/2 (field value, on which the half of saturation magnetization is achieved) and DP (dispersion parameter). The experimental data contains the IRM acquisition curves of the 113 samples obtained from the Siberian trap geological cross-section of the Permo-Triassic age, exposed in the borehole 59xc in the Kharaelakh synclinal fold on the north-west of the Siberian platform. To process such data, we created a program that provides approximation of experimental data with the modeled curves. In contrast to previously applied technic [2], that used the EM-algorithm, in this paper, we use Nelder-Mead method [3].

During the processing, the obtained IRM acquisition curves were represented in three different ways: LAP, GAP and SAP. These plots allow to estimate the number and initial characteristics of the components (SIRM, logB_1/2 and dispersion parameter), which are used as the starting approximation for the program. After approximation, model LAP, GAP and SAP are compared with the experimental data. Convergence of the model is estimated by the sum of squared residuals for each type of plots. The values of SIRM, logB_1/2 and dispersion parameter are optimized by minimizing of squared residuals. Second procedure is carried out with a slightly modified initial data to test the stability of the solution. Samples of model curves are shown on Fig.1.

In accordance with the ranges of values of B_1/2 in all experimental IRM curves has been allocated four components (grain groups) with their characteristic values of B_1/2: for the first component the range of values of B_1/2 varies from 2 to 13 mT, for the second – from 13 to 100 mT, for the third – from 100 to 316 mT and for the fourth – from 316 to 3162 mT. Component 2 is presented in all studied samples and gives major contribution to the total SIRM. The percentage contribution of different components in the resulting value of SIRM is shown in Fig.2. Furthermore, we obtained correlations between the component percentage and different magnetic parameters, such as magnetic susceptibility, saturation magnetization, coercivity etc. The revealed correlations are in a good agreement with each other and are easily interpreted in the frame of the existing concepts in theory, demonstrating the applicability of the method.

Fig.2. Distribution of the percentage contribution of the components to the total value of SIRM.

References

1. Утёмов Э.В., Нургалиев Д.К «Естественные» вейвлет-преобразования гравиметрических данных: теория и приложения // Физика Земли, 2005, №4, С. 88-96.

2. Kruiver P.P., Dekkers M.J., Heslop D. Quantification of magnetic coercivity components by the analysis of acquisition curves of isothermal remanent magnetization //Earth Planet Sci. Lett., 2001, 189, P. 269-276.

3. Nelder J.A., Mead R., A simplex method for function minimization // The Computer Journal, 1965, 7(4), P. 308-313.

4. Robertson D.J., France D.E., Discrimination of remanence-carrying minerals in mixtures, using isothermal remanent magnetization acquisition curves // Phys. Earth Planet. Inter., 1994, 89, P. 223-234.

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