solution based on second degree functions is relatively straightforward critical numbers may need to be generated from preselected criterion to help determine a satisfactory fit in choosing the proper solution for models with more complex functions such as those with higher degree polynomials or irrational numbers in a further stage polynomials of the third degree may be fitted offering the possibility of 34 cusps 34 such as those configurations found in overthrust folds such polynomials can afford more than two possible solutions and more elaborate criteria will be needed to choose the proper solution according to the geological configuration critical numbers may be generated from these criteria to help determine a satisfactory fit in selecting the proper solution in another stage exponential functions will be fitted for example wavy surfaces will be generated by circular functions these exponential functions should cover all possible folded configurations in fig2 and 3 an examkple of maps of the dip profile according to the mathematical model of the present invention are illustrated the data used to arrive at the numbers shown in fig2 was derived from a dipmeter survey of a hyperboloidal structure of revolution the apex of the structure was 4000 meters below sea level and at 2000 meters north and 650 meters west of a surface reference point the apex was penetrated by the well head for the wellbore at 555 meters north and 632 meters west of the surface reference point and 345 meters below sea level fitted functions of the present method were used to derive this data one manner of defining the dip of the plane of a geologic structure intersecting a borehole is by two characteristics of the a unit vector normal to that plane the dip magnitude and the dip azimuth the dip magnitude is the angle.