Its actually not possible to achieve a complete separation of observed gravity into regional, local and noise value by any mathematical filter, because their power spectra overlap. So all such attempts (and there are very many variations on the theme) are doomed to failure. It can only ever be an approximation, often a poor one. The best you can do is remove the things you understand (which is what the standard corrections do), then realise that even the Bouguer correction is an interpretive step, because you're assuming constant density between ground surface and datum, and any modelling you do MUST take that into account. 

The concept of regional-residual separation arose in more qualitative times, when people just wanted to get an approximate "picture" of shallower vs deeper geology. You MUST NOT try to model data that have been subjected to this kind of filtering, unless you apply the same filters to the models. You are much better off modelling the "whole earth" and not trying to filter to separate. These days any decent PC has the power to do that.

We have tackled this problem in our own way, see papers on the Thuringian Basin and the Kolarovo gravity high on my page in Research Gate. We model the regional field as 2D harmonic function with the same values on the boundary of the area of investigation, as the observed field. It is the smoothest possible function with no artificial extrema inside the area. If you subtract such a function, the residual field would be zero on the boundary, which emphasizes the local anomaly inside. Then, we separate sources in depth based on upward and downward continuation (this step is not obligatory). A local anomaly is approximated with the field of several 3D line segments, it provides very stable estimates for mass and depth of the object sought. Finally, for a given set of line segments, we obtain a restricted object or a density interface with the same gravitational field.

How to know the gravitational field - is an integrated field. That is, it is made by the gravitational effect of numerous, diverse in their physical parameters and forms masses. And there are numerous methods (their number will undoubtedly grow) for the separation of the gravitational field. This number should not scare.

You must try to ensure that the methods used to determine the residual anomalies could give information appropriate to the specific geological conditions of the region. Necessarily it is necessary to proceed from the set of geological problems. If we are interested in the upper part of the Earth's crust (say up to a depth of 8-10 km) which can accumulate mineral recourses, it is advisable to remove the pieces of information that are related to depth factors. As usual, the underlying mass is recorded on a long stretch of observation, creating regional anomalies. Therefore, it is necessary to filter (remove) anomalies associated with deep masses and leave the local part (residual anomalies) gravitational field. To do this, there are methods: averaging averaged gradients, calculation of second derivatives of the potential, analytic continuation, approximation, etc.

For example, in the Middl Kura depression Azerbaijan on regional background gravitational field corresponds to the structure of the crystalline basement lies at a depth of 10-14 km. Structural features of the overlying Cretaceous sediments have high density displays excessive local anomalies of the second order.

Again, when determining the residual anomaly is necessary to apply the methodology, the results of which reflect more clearly the geological reality in the region.

The question is not correct>>>>>

The question may be : What are the methods of gravity separations and what are the advantages and disadvantages of each technique?????

There are numerous methods of separation; Traditional separation methods as graphical techniques and analytical separation methods > each technique has its advantages and disadvantages>

There are no best separation technique

there is no optimum gravity separation

Dear Husin Setia Nugraha and colleagues:

The gravity anomaly maps, go on straight signs of lateral contrasts in density between adjacent rock, in fact, the sum of all lateral density contrasts at all depths within the Earth´s rock “all of the features which is shows have their origin in horizontal discontinuities at any depth from the grass roots down”, in Nettleton´s words.

Data separation / filtering allows us to isolate portions of the gravity anomaly that are of our own attention in the interpretation step, but then again, these signatures require necessary be understood with additional geological and geophysical information to hypothesis a precise earth´s model. Earlier to the geological / geophysical interpretation phase, the data is reduced into a diverse form by filtering or enhancement methods, to facilitate comparison with additional data such as seismic, magnetic, well-logs, etc. Also, the improve or recovery of anomalies of our interest, source density contrast, by filtering techniques, is not only a reduction process, but also it is an interpretation technique, in cooperation with a whole dataset.

In other words: I been argued that the separations techniques are inside the interpretation. Even more importantly: intrinsically, the question that we are trying to solve, it is joint describing the gravity interpretation, and it is just one aspect of reductions that needs to be considered seriously is the FA´s / Bouguer´s / isostatic´s map interpretation. Also, I suggest you put the emphasis in the geological and geophysical aspect and add later the math technique, in a whole framework with other inaccuracies in reductions and uncertainties in the separation of regional and residual anomalies, fortunately, often small in comparison with density contrasts playing. I recommend reading “Errors in the total Bouguer reduction”, by M. Talwani, GEOPHYSICS, 63, 4 (1998).

“…The regional is what you take out to make what is left look like the structure…” is a valid sentence today, this remark points a way toward useful control on the selection of a regional, and thus, in the interpretation step. “The objective of gravity interpretation is to deduce the geological character of the subsurface from variations in the gravitational field”, wrote the landmark Nettleton´s paper. I attach and suggest reading “Comparison of some commonly used regional residual separation techniques”, by Keating, Pinet and Pilkington, ©The Society of Exploration Geophysicists and the Chinese Geophysical Society: International Workshop on Gravity, Electrical & Magnetic Methods and Their Applications Beijing, China. October 10-13, 2011.

Best regards, Mario E. Sigismondi