# Interpolation of multidimensional data: some domains are lost

I am trying to make a reasonable interpolation of a dataset having the form dataset = {{x1,x2,x3,f[x1,x2,x3]},...}. I to the interpolation in the following way:

interpolation[x_,y_,z_]=Interpolation[{Log10[#[[1]]], Log10[#[[2]]], Log10[#[[3]]], #[[4]]}&/@dataset][Log10[x],Log10[y],Log10[z]]


After the interpolation, I tried to compare the initial dataset for the fixed x1 with the interpolated function using Plot3D and ListPlot3D. It turned out that the interpolation has "eaten" some data:

Moreover, if I restrict myself only on particular values of x1 (which is possible since there are only few values) and interpolate 2D function of x2,x3, the same issue remains. Is there any way to fix this issue?