Dear Subhendu Mondal, glad to meet you!

Your question is very useful to remember us some issues related with the gravity and magnetic interpretation.

First, it is tacit that gravity and magnetic data cannot be interpreted uniquely in terms of depth; even when the density or magnetic susceptibility contrast are strong or weak, a whole family of configurations can be found for the interface contrast, at various depths, and any one of which will satisfy the observed gravity / magnetic data.

I divide my answer in four parts, following your own words:

1) When you write: “…2D subsurface model…”. Please, you must remember that the real profiles from maps are not in 2D: they are 2.5D. This is an important concept. If you are working at GM-SYS modeling tool, you must to choice the gravity observation and / or magnetic observation profiles: the real data, and each one you change your model (density contrast, depth, shapes of the anomalies) the curves of your gravity model and / or magnetic model changes. The challenge is trying to do your best model for the convergence of the model with the observation data.

2) When you write: “…i am using residual anomaly…”. As a Geophysicist interpreter, I must say to you that nowadays, and in the past too, it is not possible to reach a whole discrimination of gravity / magnetic anomaly map / profile into the contribution of:

1- the regional

2- the residual

3- (plus, the noise)

because their power spectra overlapping.

If you are talking about residual data, therefore, you applied before an upward continuation, and also, a continuation distance of one grid cell is not uncommon, although you should be critical of how much resolution you are losing in the smoothed data when you choose the upward continuation distance. This is your choice, again, as a the better person who know the geology and target of your work.

3) When you write: “…which will be the maximum depth value for preparing the model with better accuracy?” As Interpreter, you can drive the maximum depth tolerance to allow (percentage) (default value is 15). Therefore, all depth-solutions with error estimate smaller than this tolerance will be accepted. A smaller tolerance will result in fewer but more reliable solutions.

I recommend trying to do before a spectral analysis (remember limitations that I said in point 2), and you will have an estimation of the shallower average sources of your zone of interest by measuring the slope of the energy spectrum and dividing it by 4pi. A typical energy spectrum for gravity / magnetic data may exhibit three parts – a deep source component, a shallow source component, and a noise component.

An additional argument: we do not escape the ambiguity: in fact, gravity and its derivatives are related by a result of Green’s theorem, that provides an analytical proof of ambiguity not only for gravity but also for magnetic as well.

Also, remember that there are a wide variety of gravity and magnetic surveys, as a function of the terrain clearances, sampling rates, line spacings … and your spectral analysis is reflecting not only these condition (acquisition) but also: the choice of your grid-cell-size (interpretation) e.g.: this should normally be ¼ to ½ the nominal data sample interval.

4) When you write: “…is there any thumb rule in this case?"

The best rule is trying to do

1- spectral analysis,

2- profiles in GM-SYS or similar;

3- inversion profiles, and

4- compare it with another solution, such as: Euler deconvolution, SPI, Werner, AS, and, of course, if you have: seismic and well-logs control.

It should be emphasized finally, that, regional - residual (local) separation that describe large-scale-deep structure and small-scale-shallow structure, respectively, you and me must be considered in terms of the scale of the survey; also, I recommend to you to define the regional as the effect in which you are not interested. Maybe for you the regional is different that my criteria.

Best regards, Mario E. Sigismondi

Dear Mario E. Sigismond Sir, First of all, i want to express my solely gratitude and thanks for your kind edifying comments and guide in this case. I am very glad to meet you.Hope you are doing fine. I have another question regarding this if you kindly consider it i will be great. What is the best method for regional and residual separation? Is it a applying a Gaussian residual regional separation filter or applying upward continuation approach with fixing a optimum continuation distance depending on the grid cell size and geological interest. Any suggestion or reference study material to understand Power spectral analysis of geopotential field and determine filter wavelength from it ?

Waiting for reply, Thanking you

Dear Subhendu, your question is not easy to response, due that for each Geophysicist / Geologist interpreter, a simple and secure way to manage the regional and residual solution in one study-case maybe is not the best on other project. Almost, it is a subjective process: it means, the result depends on the choice of the best fit by you. And your own experience.

The procedures used to arise the regional / residual respones are basically two: graphical and analytical methods.

In the first case (graphical) the foremost technique is usually done in 2D (profiles): you make a series of profile/s or transect/s along your maps (total component) over which you manually performed the separation between each profile. This process lets considering the adjustment is made by least squares, and both, regional and residual have a relative balance between positive and negative anomalies. Also, you can do this over a map, a little more complex but the same philosophy. The graphical methods are subjective process: The result depends on the choice of the best fit, and your experience.

Analytical methods, as you know, are a lot, for example:

1- upward simple continuation (Nettleton, 1954; Fuller, 1967), and the upward continuation distance is an arbitrary parameter (also: subjective parameter).

2- low-pass filtering to define the regional.

3- Gaussian filter, it is a smooth filter that is often used for low-pass or high-pass, and you define the Gaussian regional / residual.

4- bandpass-filter, I recommend that you use a tapered filter such as the Buttterworh filter

In my own experience, I use frequently the upward continuation, because it is a clean filter, and produces almost no side effects that may require the application of another filters or processes to correct. The upward continuation minimize the effects of the shallow sources, and also, the noise in the grids. The Butterworth bandpass filter is very good to me, too.

If you couldn´t find what you need above, please contact my by email, I will be happy to help you in the Geosoft environment, just write to me at: [email protected] / [email protected]

Let me share this paper "Separation of regional and residual magnetic field data" by Li and Oldenburg (Geophysics, 63, 2 (March-April 1998).

Best wishes, Mario E. Sigismondi

Dear Mario E. Sigismond Sir thank you for enlightening with your deep knowledge in the above fact, Please accept my gratitude. I have some little queries on potential field data analysis. I will be happy to contact you. Thank you.

Dear Subhendu Mondal

Here I may address some more things for this interpretation technique.

Regional and residual separation of potential field data is a bit tricky job to do. As explained by Dr Mario Emilio Sigismondi, both gravity and magnetic methods ought to give different spectral depths despite their dimensional unity. I could say the following things for the practical regional-residual separation of potential field data

1. Knowledge of dimensions (length and width) of the grid is an important parameter in the depth estimate. As the dimensions of the grid increases, we can see the change in the depth estimate for the deeper and shallow sources.

2. As a thumb rule for a 2D profile or gridded data, w.r.t maximum depth extent, the depth of the profile cannot go beyond 1/5th of its length.

3. The cell size is important, which will be in relation to the maximum cut-off wavenumber. Suppose that if you were taking a 2km sample interval, the maximum cut-off wavenumber would be 0.5.

4. It is important to pick the spectral peaks slope break while fixing cut-off wavenumber. An estimate of R-squared (Coefficient of determination), the standard error in slope, P-value, uncertainty should be computed in order to remove manual errors in interpreting depths.

5. Always, the depths from the spectral analysis is OVER-ESTIMATED. The depth is an average regional depth of the region and cannot be used in the regions where there is both land and oceanic zones are at place. In these cases, you may find the wrong interpretation.

The method adopted for spectrum computation is of prime importance for achieving reasonable depths. There are many spectral techniques available for the computation of Power Spectrum (Please go through MATLAB spectral toolbox).

And finally, I may also say that regional residual separation cannot be concluded with one technique, where we may address issues related to peeking of intermediate anomalies in to long and short wavelength component in wavelength filtering, geologically stable upward continuation has a problem with its depth thumb rule, finite element method gives good results for singular anomalies, polynomial trend gives long-wavelength component in to shallow features, etc. So, please go through two-three techniques, and based on the geological trends, one needs to interpret the possibility of handling the separated anomalies

Also many thanks to Dr Mario Emilio Sigismondi for giving us a good view of Gravity and Magnetic anomaly separation.

Best wishes,

KND.

Dear K.N.D Prasad , wish you a very good morning with best wishes for your prosperous life. Thanks a lot for giving a constructive additional contribution in this discussion. I am agree with your opinion and information you have provided but here, i would like to request you to provide some available literature in supporting your point 2 and POINT 3 related to thumb rules. It will be good to know the base of the conceptual source of these Thumb rules. Thanking you again.

Dear Subhendu Mondal ,

Please go through the book written by Blakely (1996) entitled "Potential theory in Gravity and Magnetic Applications". And also go through the literature of Prof. Maurizio Fedi. I have learned some basics with the above-said references

Dear K.N.D Prasad,

Thank you. Best wishes

The best technique is to used the spectral method for your grid for estimate your deep causative sources. So you can delimit the max depth. Generally, depth in 2D model is about 1/4 to 1/6 length of the profile.

Respected Taher Zouaghi Sir,

Thank you sir for your kind reply and suggestion. I would like to request you to provide some publications supporting the theory of depth =1/4 OR 1/6 of profile length so that i can cite it.