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The method.
There are 2 types of sensors being used: precision sensor and nonprecision sensors. Precision sensor is called quantum fluxgate meter and nonprecision one is called nonprecision fluxgate meter. Unlike nonprecision fluxgate meter, quantum fluxgate meter measures a vector. Accuracies are approximately 10.4 and 10.8. So, we need to measure magnetic field at a certain point, while flying above it by plane. At the same time, magnetic field of the Earth is approximately 50000 nt (its magnitude changes from the pole to equator and varies 2 times) and magnetic field of the plane is approximately 10 nt. Generally, influence of the plane consists of 3 components. First component is the magnetic field of the plane, considered as a constant magnet, second one is softcomponent and third one is dynamic component – influence of Foucault's current. The second component is smaller than first one, the third component is negligible small. The only way to calculate these components is to make a trial flight. The problem is that magnetic field is attached to certain points and changes in time – socalled variations. Magnetic field maps do not give absolute values. At the same time, magnetic exploration requires very high degree of accuracy, because it is used to explore the structure of rock, which is absolutely nonmagnetic in the ordinary sense. The task is to compute influence of the plane on a precision sensor, based on the data, obtained from one flight. Generally, this flight consists of 4 routes in different directions. After that it is possible to fly over area and to draw maps
 History
It was early 90es, when I first met this problem. There was international tender for the magnetic survey. I don't exactly remember whether it was about oil or gas and I'm not sure which of Sakhalin projects it was related with. We had some data from it. So I quickly prepared a program – something like leastsquares method. The only thing is that I optimized not values itself, but first differences. Program did work, but the result varied, depending on how the routes were entered – one by one or all together. In other words, such a result could not be called satisfactory. In addition, there was already a program, considered as industry standard. When we bought that program, to our great surprise, it turned out, that optimization is made separately for different directions, and there was no assumption for equality of equations in different directions. Such divergence is called deviation. Geophysicists fight with this special equation by flying counterroutes and transverse routes. If you visit http://search.yahoo.com/search?p=AEROMAGNETIC+COMPENSATOR,
You will find that today there is one more alternative AADCII – allegedly crafty algorithm, designed in 60es for submarines. There is right conclusion, that for compensation it is necessary to take all data. The point is that amendment can be imagined as a function on a sphere and if you keep going in one direction, it is possible to determine exact inclination of surface and curvature. Suspicious part of that program is neglect of altitude allegedly of no use, although differences in altitude during maneuvering of plane can reach 100 m, that correspond to 1 nT on equator. All coefficients are kept in onboard compensator and its contents are even not described. There are no means ofpostprocessing and control because of "uselessness". Number of parameters is 30 and this amount seems to me excessive. The more is the number of parameters, the higher is approximation accuracy, but interpolation accuracy is less.
The influence of side evolutions and velocity changes is less than vertical evolutions, but they also make influence. In other words: if magnitude of flexure is less than 1 nT, then to determine the fault it is necessary to know lapse rate and see magnetic field map. Improvement Ratio (IR) is the result of division of fault by starting magnetization of plane. It is more related to noise of planeboard than to compensation program. Pico Envirotec doesn't use this term at all.
 The program.
I developed a program in which I used 2 filters of different length. First filter separates spatial component of magnetic field, caused by plane maneuvering. Second filter must be used when there is correlated highfrequency noise on fluxgate meter and quantum sensor. The lengths of filters are measured in readings. The program is absolutely insensitive to constant gradients in 3 directions. If we take probable magnetic fields, i.e. 12 bends of magnetic field through the route with similar amplitudes and if we take the trajectory from real flight, then as a result of mathematic modeling by using of optimal filters, the fault is going to be 0.001 nT. It is also possible to use shorter filters and get accuracy equal to zero, but in this case, the conditionality of the system will decrease. In other words though accuracy is higher, interference susceptibility is higher, it's not recommended to decrease the length of the filter. I.e. fault is determined by irregularity of surrounding field and doesn't depend on the most rigid vector, so the term "improvement coefficient "in this case becomes useless.
Input data and output data may be in variable dimension. I.e. it is possible to register not only vertical gradients, but also horizontal gradients. It's clear, that initial values of gradients are not needed, only coordinates are assigned. Output dimension is also variable. Output can contain only rigid component, rigid and soft component or all three of them. All combinations are available: at the input 0, 1 and 3 coordinates, at the output 3 choices. Vertical gradient is provided for statistics.
 The results.
The program has been used for 2 years on 5 different boards. There are already maps built by this program. Standard maneuvering was used for compensation. Compensation accuracy was checked according to improvement coefficient and deviation. Deviation is standard criteria for external gondola and sensors' manufacturers also guarantee absolute accuracy. Residual deviation in all cases was less than 1 nT. In all cases the complete model was used, it included 3coordinates and dynamic component (which was negligible). The vertical gradient, which was obtained satisfied the true value. We installed very powerful equipment on one (magnetometry was not main method ) of the boards and flights were conducted at night with the equipment turned on. In spite of this, compensation worked good. On one of our boards we examined the influence of rudder on parking. Full turn of rudder made influence ± 0.4 nT. In spite of that, in opinion of geophysicist, maps were made better than with gondola. Though accuracy is 100 times less than on samples, it's clear, that this also corresponds to accuracy of rigid vector, but not to faults itself. The rudder is almost not used on the route. And this means, that it's possible to use magnetic exploration with rigid fastening.