Probably kriging is the best. most software for spatial interpolation include kriging.

Dear Selvakumar:

Thank you for quarry. I think it is depends on data variable and spatial distance of data points. Generally,   kriging is the best method for spatial interpolation in GIS software.

With best regards,

Pravat

Thank you Berndtsson sir for your kind suggestion,,,

Dear Pravat ji, pls clarify how kriging method is best in compared to IDW

Fallow the paper: Comparison of GIS-based interpolation methods for spatial distribution of soil organic carbon (SOC)

http://www.sciencedirect.com/science/article/pii/S1658077X15300825

Well among the wnown methods of spatial maping I think that kringing is the best as it may gives the accuracy of the interpolation, given the data density. Still I guess that you have to remain the master of your map, by comparing and logically give some convergence to the available parameters such as the water table movement, geology...

The same for any extension towards the poorly covered borders in data... 

Many techniques give similar interpolation if you have an even grid network. However, at the edges with few and uneven observations, kriging is most probably the best.

I agree with the other contributors that krigging is better.

In many of the papers Krigging interpolation has been reported to perform better over IDW. However, this is highly dependant on the variability in the data, distance between the data points and number of data points available in the study area. Better approach would be, I think, to use both the methods and look at the performance parameters vis RSS, RMSE, R2 of the prediction etc. This will give an idea of the prediction accuracy and selection will be easy and appropriate. If you have geo-referenced data points, trialling both methods would not be giant task. You can use any of the GIS package for that.

Kriging is more versatile than IDW.  For example, kriging can be setup as either an exact interpolator (precisely match measured values, as IDW does), or an in-exact interpolator that limits "bulls eyes" if there is high uncertainty associated with measurements.  There are several forms of kriging as well (simple, ordinary, universal, etc.), which provides flexibility in terms of the expected condition (expected average concentration) where measurements are scarce.  Here's a Stack Exchange example for a case in which the back-ground concentration is zero:  http://gis.stackexchange.com/questions/107285/kriging-with-expectation-of-0-beyond-the-data-supports/122933#122933

Peter Kitanidis's book is a thorough reference:

Kitanidis, P.K., 1997, Introduction to Geostatistics: Applications in Hydrogeology. Cambridge University Press, Cambridge, UK, 249 p.

I have tried both and found that krigging shows better what I see in the field. IDW somehow leaves outlayers as such. best you try both and decide

Krigging will give better results. 

Geostatistical interpolation techniques are in general more suitable for estimating variables at unknown locations than deterministic methods (IDW). The advantage of geostatistical interpolation  is true especially in the presence of a spatial structure where observations close to each other are more alike than those that are far apart (spatial autocorrelation). This behavior is typical of environmental and Earth data. The autocorrelation  can be verified by the construction of the variogram, that in the case of IDW technique is not required.

Furthermore, as the groundwater quality data may include  a large number of parameters (i.e., major and minor ions), most of them are often statistically correlated, in this case the application of  cokriging method by using a primary variable to estimate a correlated auxiliary variable  has higher accuracy than others for estimating spatial distribution of groundwater data. Finally, the use of indicator and disjunctive kriging can provide the calculation of risk maps, known the law limits of some of these parameters. 

Before conducting your analyses, make sure to test the data for normalcy. Fluid concentration data are often lognormally distributed and you may need to transform the data.

Neither are better. Visual analysis of the data in light of the underlying variable of geology, hydrogeology, land use and depth etc make the contouring of numbers a much more robust issue than these computer programs are capable of addressing.

Spend some time with the data in light of all that surround it. You will then be contouring the numbers with real earth concepts. 

It depends on distribution of the data (spatial as well as frequency). If you have good number of known points (samples) with normal distribution then Kriging may be preferred. However, better results could be obtained only after multiple iterations of testing/changing the parameters (trial and error basis).

The program Surfer is good.

Лучше всего карту качества подземных вод строить на основе геоморфологической или ландшафтной карт, поскольку они отражают аспект формирования качества подземных вод. Но в любом случае такую карту должен строить опытный гидрогеолог.

Всего наилучшего!

I think that it is necessary to consider the lithology and the state of fracturing of the rock before choosing the interpolator

Depends on Spatial distribution of data(Numbers of samples points ) and data variability (Range of data structure). Basically Kriging or IDW models are used for spatial distribution.

Pravat Kumar Shit 

It depends on your data distribution over the study area (i.e. number of observations and uniformity of data distribution) and normality of data frequency distribution. In fact kriging may work better in presence of a good spatial uniformity and density of data (not too skewed). Otherwise, Kriging and IDW may work similar in univariate cases. 

Kriging is more preferable. Indeed, Kriging provides a more reliable interpolation because it examines specific sample points to obtain a value for spatial autocorrelation that is only used for estimating around that particular point, rather than assigning a universal distance power value

Yep, kringing seems to be preferable as stated by Raphael, but most important is the quality, accuracy and density of the data network... and more important is to verify possibly with some points as control of the obtained result... be aware too of the risk of the exagerated extrapolation, which could be misleading...

Interesting discussion by all. Kriging was developed for the mining industry to help direct economic mining development plans on the basis of relatively closely spaced core hole data. Predictable results depend on assuming and evaluating stationarity of mineral rock matrix concentration data by comparing statistical results of data along horizontal transects at differing core sampling intervals. As is hinted by some of the excellent comments provided to you so far, mapping groundwater is a horse of a different color. Groundwater is not only mobile, but there are many factors that affect both the vertical and horizontal distribution of groundwater quality parameters. This is particularly true of shallow groundwater data wherever the influence of vertical tranmissivity increases with decreasing depth. Increasingly relaxed horizontal earth stresses with decreasing depth allow increased rates of vertical and horizontal groundwater mixing through vertical fractures and bedding contacts. Consider, for example, regional groundwater discharge into alluvial aquifers, or, how aquitard thickness and depth might influence cross flow between unconfined, semi-confined, and confined aquifers. Furthermore, groundwater flow is dynamic and, depending on aquifer depth and confinement, results of any given data set might be expected to change based on recharge rates and seasonality. If your data are based on water wells and not monitor wells then the problem becomes even more complex because the domestic water well environment is in itself a mixing zone. Bottom line is, you will be hard pressed to assume stationarity. Accordingly, arguments regarding the contouring method, such as kirging vs. IDW, becomes less relevant.