Study on construction of local marine geomagnetic field model based on curve-surface interpolation

There are many methods in building local geomagnetic field, such as polynomial method, interpolation method, Spherical Cap Harmonic Analysis and Rectangular Harmonic Analysis. Curve Surface Spine Function and Multi-surface Function are two interpolation methods. The model based on interpolation passes each node compared with fitting method. It can be proved that the interpolation method can get more accurate result compared with polynomial fitting method in building the local marine geomagnetic field model. The issue which should be researched in multi-surface function are quality control of geomagnetic data, kernel function choice, choice of the smoothing factor, model node selecting and zoning modeling method. The quality control of geomagnetic data is very important in building local marine geomagnetic field, here we introduce a kind of trend-surface methods for the quality control. The method establishes a function relative to location and uses 2sigma/3sigma principle to remove the gross error of geomagnetic data. It is proved to be very efficient in the filtering. The kernel function normally used are hyperboloid function and inverted hyperboloid function. Which one adopted in building the model needs to be verified in actual application. By experiment, we found that the accuracy of the model is higher using hyperboloid function than using inverted hyperboloid function. Smoothing factor is another important parameters in building local geomagnetic field model. Smoothing factor can improve the curvature of the model surface. Optimum smoothing factor is also required to be verified and determined in actual applications. We can find that the model´s accuracy improving with the smoothing factor change from 0 to 100. We can also find there is an inflexion in the change of model accuracy. The hyperboloid function model´s accuracy changes little with smoothness factor, but for the inverted hyperboloid function, corresponding model accuracy is very sensitive to smoot- hness factor. The model´s accuracy is improved with the increase of node number. But the computational complexity will be increased with the node number increasing, and at the same time will lead to the unstable solution in building geomagnetic field model. Thus the node number should be appropriate in building the model. Generally, we only need small number of geomagnetic data in building the local geomagnetic field model with uniform change. However, a large number of geomagnetic data is required when geomagnetic change is more complicated. Character node is very important in building precise local geomagnetic field model. Character node represents its´ surrounding geomagnetic field change. By experiment, we found that the accuracy of model constructed with selected the character node was better than that built with random geomagnetic data, especially in which geomagnetic field changes sharply. Zoning modeling method can avoid the problem, which too large nodes number lead to computational complexity in large area. The model´s accuracy can be improved distinctly if we use enough and high-quality geomagnetic data. Because the model surface passes each node in building the model using Multi-surface Function, thus it can guarantee the smoothness and continuity in the common area of two adjoin modeling zones. Geomagnetic data of a marine area with 11-kilometer length and 1-kilometer width is used for the study of building local marine geomagnetic field model. In the study, we adopt above research methods and achieve the model accuracy with 8.09 nT of root mean square (RMS) in whole area. We also implement a zoning modeling experiment. In the experiment, we divide the whole area into 5 subsections, build models in these subsections, and achieve the model´s accuracy with 5.29 nT in the whole area. Comparing above statistic parameters, we can find that the zoning modeling method is a kind of ideal methods in building high-accuracy local marine geomagnetic field model