The Model Of Geo-electric Field Variation

The Taylor Polynomials and Surface Spline function are two-dimensional spational planar Mathematical Models, and they are applied to derive of the regional geo- magnetic field models widely. In this paper, the theory of the Taylor Polynomials and Surface Spline function are firstly applied them in building the time-variation daily geo-electric field models.Firstly, the geo-electric field observation data of channel NS and EW from 2008 to 2012 in regional geo-electric networks in Eastern and Northern C hina are collected, and the data with the similar geomagnetic index(Kp), the different years(or the same Loyd season in same years) and the same lunar date(or before and after the day) are classified. Then the daily time-varying models with geomagnetic index Kp=1 and 2, Kp=3 and 4, Kp=5 of the daily variation based on the Taylor Polynomials and Surface Spline function methods are fitted. And the daily geo-electric strom models are simulated by the geo-electric field observation data with geomagnetic index Kp>5.Then compare the geo-electric field model curves with the sample curves(the geo-electric field observation data which is used to build the models is called “sample value”, the curves are called “sample curves”), calculate the error between the model value and the sample value. Next, describ the daily variation described curves on the same lunar date(or before and after the day) in other years(or the same Loyd season in same years), with the similar geomagnetic index, using the two models(the model describ the same geo-electric field stations because the difference of the observation environment among different stations is great). In addition, the error between the geo-electric field model curves and the daily variation described curves is to be analyzed.Finally, we sum up and analyze the result of the model fitting and model Description, the conclusions are as follows:(1) Although the geo-electric field variation is complex, the models of the daily time- variation geo-electric field measured by the regional geo-electric observation networks fitted by the two methods are identical(both the models of the geo-electric daily variation and geo-electric storm by the two models), and the two model curves accorded with the measured sample curves in the variation with time. It prove that the modelling method is reliable, as well as the modeling process and the result.(2)The model curves of time-variation geo-electric field consistent with the sample curves, and the error between model curves and the sample curves is small, much less than the daily variation margin(about 2%-8% of the daily variation margin of the minute-value models, about 0.08%-4% of the hour- value models). It shows that, the fitted models are reliable, can reflect the sample curves in the variation with time, and it is feasible to fit the daily geo-electric field models in the similar condition.(3) The daily variation geo-electric field models by the minute-value and the average hour-value can reflect the features of the geo-electrical daily variation clearly, and the minute-value geo-electric field models based on the minute-value geo-electric field observation data is better than the hour- value geo-electric field models, the former can reflect clearly slight structural changes superimposed on the geo-electrical daily variation more clearly, also the changes of the observation environment and measurement system of the stations on this day.(4) The geo-electrical variation models of each channel based on the sample curves of same channel by each station in the same regional geo-electric observation networks reflect the own feature of the geo-electrical variation on each channel, also the common feature of the sample curves of same channel on this channel and in this region. The consistency between the model curves of each channel and the sample curves shows the own feature of the geo-electrical variation on each channel; the inversion process of solving linear equations in calculating the model coefficients, it is interrelated of the calculation of model coefficients for geo-electrical observation data on each channel, which can reflect the common feature of each channel in regional geo-electric observation networks, that is the common feature of the same channel in regional geo-electric observation networks.(5) When describing the measured daily geo-electric variation curves on the same lunar date in other years, in the similar geomagnetic index, using the model curves, it can be seen that the error between the model curves and the described measured curves is small(about 2%-16% of the daily variation margin of the minute- value models). It suggest that the two models could be well used to describe the measured daily variation on the same lunar date in other years(or in different months in the same year and the same Loyd season) the same season in the similar geomagnetic index.(6) When describing the daily variation curves on the same magnetic weather with the two models, the described result is that the model describing of the daily variation geo-electric field with the models in the low geomagnetic index is better than that in the high geomagnetic index, that is to say, the error in a low geomagnetic index is small, and the error in a high geomagnetic index is big.(7) When modeling the geo-electric storm models based on the geo-electric storm observation data, it can be seen that the error is much than that in a low geomagnetic index(Kp≤5). And, at present, it is difficult to describe geo-electric storm curves in other day by geo-electric storm models.(8) The average model curves based on multi-day sample curves more clearly show the geo-electric daily variation features such as: the day’s twice fluctuation waveform and its amplitude, phase and the peak-to-valley extreme value immediately before and after noon etc.It is an important thing to establish the geo-electric daily variatio n models according to the different magnetic weather(the different Kp index) and the same lunar date in the same season and the geo-magnetic index in each regional network. The models can be used to quantitatively evaluate the quality of observation data of regional geo-electric field networks, and the geo-electric field anomaly measured by the network can be picked up based on the models, which can be serviced to the monitoring and prediction for the disaster event like earthquake etc.