[S-EM14] Electric, magnetic and electromagnetic survey technologies and scientific achievements

[SEM14-09] Analyzing the distribution pattern “Symmetry and Spread” of Normalized Residual of Magnetotelluric Data

*Roshan Kumar Singh¹, Yoshiya Usui¹, Kiyoshi Baba¹, Marion Jegen² (1.Earthquake Research Institute,The University of Tokyo, 2.GEOMAR, Helmholtz Centre of Ocean Research Kiel)

Keywords:marine magnetotellurics, three-dimensional inversion, normalized residuals

3-D inversion of magnetotelluric (MT) data are widely used these days owing to the recent developments in computational facilities. Several 3D inversions codes have been proposed by researchers globally. 3D inversion technique is strongly ill-posed and non-unique problem where the outcome of the technique are dependent on several inversion parameters such as grid size, initial half-space resistivity, data errors, data weighting, model regularization etc. One of the important parameter which effects the inversion outcomes in many cases is the handling of data errors which are handled very differently by various researchers. In many cases, percentage of absolute values of respective components are used for error floors while in many cases percentage of product of off-diagonal components of impedance data is assigned to all the components of impedance data. The values of percentage applied also varies which in most of the cases depend upon level of expertise. These strategies have their own advantages and disadvantage. Most of the times obtaining a good overall RMS misfit and analyzing the misfit between the sounding curves for observed and predicted data is proved to be meaningless/misleading because there can be a large number of different 3-D models, mapping different conductivity structures and having similar values of RMS and misfits of sounding curves. Therefore, a systematical assessment of each of these inversion parameters which can affect the outcome of the inversion process becomes very important to obtain a robust and meaningful 3-D models which truly reflects the geology of area is obtained. In this paper attempt has been made to analyze the performance of an inversion based on the symmetry and spread of the distribution of residual obtained by normalizing the difference between observed and predicted data for impedance and vertical magnetic transfer function data by the natural error of the dataset. This strategy also helps in selecting the optimized values of various inversion parameter. Symmetry is one of the most important characteristic used for data analysis. Symmetrical distribution which is also known as normal distribution which is preferred over a non-symmetrical dataset. A symmetrical distribution is a continuous probability distribution that is symmetrical around its mean (mean, median and mode lies at the same point), and most of the data lies around the central peak, and approximately 68.2% of values lies within 1 standard deviation of the mean. Symmetry is often measured by the skewness of the dataset. A perfect symmetrical dataset has no skewness but a dataset with zero skewness is not obtained in geophysical observations. Geophysical data errors are either right skewed (majority of dataset lies left to the median) or left skewed (majority of dataset lies right to the median). The other important parameter which should be considered while analyzing a dataset is the spread of the dataset. A series which is less spread and lies within region close to median is preferred than the series with a wider spread. A series which is more symmetrical and distributed in a small region around the central median is always preferred. Symmetry and the spread of the dataset can be very well understood by plotting the Box and Whisker plot for the dataset. Box and Whisker presentation of data has its advantage over the histograms or other mode of representation of data distribution. Symmetry of dataset in a box and whisker plot is explained by the location of median with respect to the length of the box (difference between the 25 % (Q1) and 75 % (Q3) quartile of dataset) and the length of the whiskers ( maximum and minimum values in the dataset). The spread of the dataset is explained by the size of the boxes which is measured as the interquartile range (difference between the Q1 and Q3) and also by the difference between the maximum and minimum values. Therefore, on a visual inspection a series with a small box, Q2 located close to zero, Q2 located at the center of the box, box located at the center of the maximum and minimum values of the dataset is preferred. This method of analyzing MT data based on symmetry and spread of the normalized residual analysis has been applied on MT dataset from Trista de Cunha (TDC) island which is a volcanic hotspot responsible for volcanic activity in the South Atlantic Ocean.