Yes OK is oldest one but it doesn't mean it has no pratical Applicabilty now. Nowadays it has been replaced by more robust machine learning algorithms which had increased the accuracy of interpolation and prediction. In case of no availability of machine learning and DSM OK is best option left.

You can use IDW or Inverse Distance Weighted for interpolation. It's the modern way. Adel Djellali

IDW

The IDW (Inverse Distance Weighted) tool uses a method of interpolation that estimates cell values by averaging the values of sample data points in the neighborhood of each processing cell. The closer a point is to the center of the cell being estimated, the more influence, or weight, it has in the averaging process.

Kriging

Kriging is an advanced geostatistical procedure that generates an estimated surface from a scattered set of points with z-values. More so than other interpolation methods, a thorough investigation of the spatial behavior of the phenomenon represented by the z-values should be done before you select the best estimation method for generating the output surface.

Kriging may be one of oldest technique of interpolation but still very useful and it's accuracy of interpolation is very accurate. I will also suggest that you try Least Squares Collocation. Is an advance form of Kriging, you only need to specify the decay distance, that's the distance within which the distances between the point sought for and nearest number of points will not have effect on the interpolated value.

Hi Adel,

In fact, each interpolation method is selected from the sample data in use, and the best result you will looking for.

"IDW is a linear method, a spatial interpolation method, a process for assigning a value to any point in a space from a set of known points.The choice of p is therefore a function of the degree of smoothing desired for the interpolation, the density and distribution of the interpolated samples, and the maximum distance beyond which an individual sample can influence surrounding points."

"For Kriging methods use kriging or Gaussian process regression. It's a method of interpolation for which the interpolated values are modeled by a Gaussian process governed by prior covariances.The basic idea of kriging is to predict the value of a function at a given point by computing a weighted average of the known values of the function in the neighborhood of the point. The method is mathematically closely related to regression analysis.The kriging estimation may also be seen as a spline in a reproducing kernel Hilbert space, with the reproducing kernel given by the covariance function." (Wikipedia)

For exemples : https://www.gisresources.com/types-interpolation-methods_3/#:~:text=Interpolation%20is%20the%20process%20of,noise%20levels%2C%20and%20so%20on.

Good read and research,

HP

Kriging as a technique creates a unique surface as a suitable tool for interpolation in the face of paucity or insufficient spatial data in any given domain.

The interpolation technique one selects must be suitable to answer the specific question being raised. Ordinary Kriging is robust under certain conditions, under different conditions it may not be the best technique. The data must support the technique employed as the "Garbage In, Garbage Out" or GIGO phrase holds true.

Thank you very much for your answers. It Is possible to develop a new method of interpolation to estimate geotechnical data.

Regards

"newest", "oldest" are meaningless terms. Nearest Neighbor and IDW were certainly used well before the work of Matheron (circa 1965).

Nearest neighbor was used because it is intuitive and doesn't require any computations. IDW is not based on any theory