Magnetotelluric Array and Magnetic Magnetotelluric Surveys

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1 Magnetotelluric Array and Magnetic Magnetotelluric Surveys Dr. Wen J Whan JTech Co., Ltd.; wwj@jtech.com.tw Abstract. Surveys using synchronous MT array could further reduce the local noise. Multi variance analysis (Egbert and Booker) transforms the array data into two large eigenvalue, which corresponding to nearly uniform source fields and comes out with a multivariate transfer function. Synchronous MT array at three or more sites ensure removal of galvanic distortions in MT apparent resistivity curves (V. Plotkin). Using MT Array, we also proposed a magnetic MT (MMT) survey, where the electric field is calculated by the change of vertical magnetic field. The method would be convenient for area where the reasonable spacing for electrodes is difficult to be located. MT Array Exploration The variance technique is applied to remove un-correlated noise (Karl Kappler) for,,,,,.,.,.,.sps multiple simultaneously recorded time series. The time series for each frequency band is pre-processed with a zero phase band pass filter in order to remove the frequencies which is not in the band. It then uses other clean data window to design the Wiener filter and predict/ remove the noisy window. Examples for uncorrelated noise removal for SPS frequency band is show in Figure and Figure. Figure has the time series span of about four seconds while Figure has the time series span of about, seconds. The two figures show clearly the un-correlated noise are removed. Figure : Red line: original; Green: noise removed; Span: ~ seconds Figure : Red line: original; Green: noise removed; Span: ~, seconds

2 Magnetic Magnetotelluric (MMT) Surveys Figure below represents the notations for calculating the electrical field from the vertical component of electromagnetic field. From Maxwell Equations, we get E.dx = -dφn,s / dt Equation () states that the sum of the electrical field along a closed path equals to the negative change rate of the vertical components of the magnetic flux through the surface enclosed by the closed path. Assuming E i,j is the circular electrical field on the Cell[I,j] and BZ i,j is the vertical component of the magnetic field through the cell, also assuming the cell size is small enough so that both E i,j and BZ i,j are uniform, we get E i,j = - (dl * dbz i,j / dt ) / where dl is the distance between the grids. The X component of the electrical field is then EX i,j = E i,j - E i,j-, while the Y component of the electrical field is EY i,j = E i-,j - E i,j EY i-,j- () () EX i-,j- BZ i-,j-/e i-,j- EX i,j- BZ i,j-/e i,j- EX i+,j- BZ i+,j-/e i+,j- EY i+,j- Y X EY i-,j BZ i-,j /E i-,j Br im /E i,j BZ i+,j /E i+,j EY i+,j Cell [ I, j ] EY i-, j+ BZ i-,j+/e i-,j+ BZ i,j+/e i,j+ BZ i+,j+/e i+,j+ EY i+,j+ EX i-,j+ EX i,j+ EX i+,j+ Figure : Cells used for calculating the E field from the change of vertical magnetic field.

3 JTech and National Taiwan Ocean University (NTOU) together has carried out a MT array survey in south I-Lan, Taiwan. There are arrays. Each array has stations and one remote reference. Between each adjacent array, there are two overlapped stations. The data will be used for array processing and MMT verification in the near future. The follows show a numerical modeling effort to prove the concept of MMT first. Figure : Every Polygon representing an array of MT stations recorded simultaneously. Every array is overlapped with stations from the adjacent array D Numerical Modeling for MMT Creating earth model Numerical experiments are carried out for D model of the medium shown in Figure. The system of coordinates is chosen with the OX axis directed to the north and the OY axis directed to the east located on the Earth s surface Z =. The axis of OZ is directed deep into the medium. The sizes of the polygon make L = km along each of horizontal axes. The model of the medium consists of three laterally non-uniform layers lying on the conductivity basis with the specific resistivity of Ohm. The.7 km top layer with the specific resistivity of Ohm containing two small-scale heterogeneity with the specific resistivity of Ohm models geological noise (Figure a). The second layer (thickness of km, specific resistivity of Ohm) and the third layer (thickness of 7 km, specific resistivity Ohm) contain the conductivity channel with the specific resistivity of Ohm modeling a fault. Horizontal sections of this fault in the second and third layers are presented in Figure b and c (depths of these sections are specified over each of them). Vertical section of the fault along the OX axis is given in Figure d at y =. km. White points on horizontal sections of specific resistivity have shown grid nodes in which fields are defined. Their numbering for marking of possible points of data logging is shown in Figure e. For display of three-dimensional structure of the medium model, horizontal sections of specific resistivity in different depths are given in Figure f. All sections are received by means of graphic procedures of MATLAB. Calculate Ex and Ey from Numerical Modeling For calculation of an electromagnetic MT-field the numerical model realized based on Treffts's method is used [Plotkin & Gubin, ]. Each of several lateral non-uniform layers is represented set of parallelepipeds with uniform conductivity. In these numerical calculations the quantity of parallelepipeds along horizontal axes was selected equal. In parallelepipeds as basic functions are used exact solutions of the Maxwell equations in the form of plat waves on all three axes of coordinates. Boundary conditions are set taking into account excitement of spatial field harmonicas inside lateral non-uniform layers. For the top boundary conditions on a terrestrial surface and the lower boundary conditions on border with the layered medium, it is used two-dimensional Fourier transformation of electric and magnetic fields. The lower boundary conditions consider occurrence of TM-mode and spatial harmonicas inside lateral non-uniform layers and their attenuation deep into of horizontally layered medium lying below. The top boundary conditions similarly

4 consider attenuation of spatial field harmonicas deep into of the atmosphere. On external sides of non-uniform layers periodic boundary conditions are set. Distributions of amplitudes of the vertical component of the magnetic field on the Earth s surface are shown in Figure. Appropriate distributions of amplitudes of horizontal components of the electric field on the Earth s surface calculated by means of the numerical model and on formulas of the vortex field are provided for two time periods in Figure 7-. In the left column in all figures fields in cases of polarization of primary wave with the index are shown, in the right column fields are shown in cases of polarization of primary wave with the index. The selected components and methods of their calculation are specified over each amplitude distribution. The fields calculated by data on the vertical component of the magnetic field using formulas for the vortex part are received by two methods. In first method one-sided numerical approximations for spatial derivatives (designation is side differences) of components of fields are used: E E E E ( E E ). x ij ij, y ij i j In other method, computations are executed by means of more exact central differences (designation is central differences) for spatial derivatives: E E E )/, E ( E E )/. x ( ij ij y i j i j Discussion and conclusion Comparing the horizontal components of the electric field received on the numerical model and by data on the vertical components of the magnetic field it is possible to conclude that fields of the TE-mode and fields calculated by the central differences on the vertical component of the magnetic field are closest. The level of compliance depends on the direction of polarization of primary wave relative to lateral non-uniformity (along or across the fault). Perhaps, calculations with finer mesh of nodes of the numerical model will result in bigger clarity and the best compliance of the discussed fields. However use in practice of too close located points of registration requires the increased accuracy of measurements and is complicated by presence of noises. Another improvement for numerical modeling for verifying the MMT is to smooth the spatial distribution of the change of vertical magnetic field ACKNOWLEDGMENTS The MT array field project at I-Lan South was partially supported by National Taiwan Ocean University. We would like to thank those students who contribute the field work in the extreme hot weather in the summer vacation. We would also like to thank Dr. Plotkin for working on the numerical modeling for D MMT verification. REFERENCES. Gary D. Egbert, 997. Robust multiple-station magnetotelluric data processing, Geophys. J. Int., pp V. V. Plotkin,, Synchronous MT surveys with laterally inhomogeneous excitation, Russian Geology and Geophysics 7 (). Wen J Whan, etc., Electromagnetic and its Combined Surveying Apparatus and Method, US Patent: US79 A.. Karl Kappler,, A Data-Variance Technique for Despiking Magnetotelluric Data, IAGA WG. on Electromagnetic Induction in the Earth, th Workshop Abstract, Giza, Egypt, September -,. Plotkin, V.V., Gubin, D.I.,. Accounting for near-surface inhomogeneities over a horizontally layered section in magnetotelluric sounding. Russian Geology and Geophysics (7), 9

5 OZ, km a b z= km lg, Om m z=. km lg, Om m z=9. km c lg, Om m d y=. km lg, Om m e - f Figure. D earth model: horizontal sections (a, b, c; white points shown grid nodes) at different depths specified over each of them, vertical section (d), numbering grid nodes (e) in which fields are defined and three-dimensional structure of the medium (f).

6 H z T=. s dl=.7 km H z H z H z T=. s T=97. s 7 dl=.7 km dl=.7 km 7 7 H z 7 7 H z 7 Figure. Vertical components of the magnetic fields on the Earth s surface for three time periods, white points shown grid nodes. At the left for polarization H x =, H y = and at the right for polarization H x =, H y =.

7 .... side differences E x side differences E x central differences E x. central differences E x TE-mode E x TE-mode E x full field E x full field E x Figure 7. Comparison of fields on the Earth s surface for time period of T=. s, dl=.7 km, white points shown grid nodes. At the left for polarization H, H and at the right for polarization H, H. x y x y

8 side differences E x side differences E x central differences E x central differences E x TE-mode E x TE-mode E x full field E x full field E x Figure. Comparison of fields on the Earth s surface for time period of T=. s, dl=.7 km, white points shown grid nodes. At the left for polarization H, H and at the right for polarization H, H x y x y