SUMMARY The method of rectangular polynomial analysis (RPA) is developed and refined to represent a curl‐free potential field of internal origin. It is applied to annual mean values of the geomagnetic field from 42 European observatories. RPA is found to be an efficient means of representing the regional field, though less suitable for modelling the anomaly field.

Alldredge's method of rectangular harmonic analysis has been reexamined. After correction of errors, it is found to give improbable values between the data points and wild values outside them. A much more realistic model has been obtained by (1) determining only the most significant coefficients (those that exceed their standard deviations, obtained by an iterative process), (2) introducing new parameters to allow for a linear trend across the region, and (3) increasing the scaling factors so that the sinusoids start and finish outside the region. Modification 1 is the most important for improving the interpolative qualities of the model. Modifications 2 and 3 reduce, but do not entirely eliminate, the wild values near the edges.

Transforming multi-dimensional datasets, containing measurements of different physical parameters recorded at the same location, into a single composite imagery is quite important and frequently used in geophysical analysis as well as other scientific disciplines. This study focuses on the application of several different integration approaches for archaeo-geophysical data with a purpose of achieving complementary and improved information about the buried archaeological target by generating a single data set from multiple geophysical methods. An extensive geophysical survey using ground penetrating radar (GPR) and differential magnetic methods was made in different parts of the Aizanoi archaeological site (Cavdarhisar, Kutahya, Turkey) to locate and enhance subsurface archaeological structures. However, in this article, the outputs of graphical, mathematical and statistical integration approaches, which are applied both on synthetic images and real field case data, are presented and discussed. Comparing these results and experimental applications, mathematical and statistical integration approaches provide more useful and practicable information than just the single distinct datasets from each geophysical parameter studied.