Multidimensional arrays allocated through calloc

Are the first two ways of defining the array equivalent in memory?

Not quite. In the second type they are almost certainly contiguous, while in the first type this is not sure.

Type 1: in-memory representation will look like this:

          +---+---+---+---+---+---+---+---+---+---+
    double| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |   
          +---+---+---+---+---+---+---+---+---+---+ 
            ^
            |------------------------------------                                     
                .   .   .   .   .   .   .   .   |    // ten rows of doubles
                                                -
          +---+---+---+---+---+---+---+---+---+--|+
    double| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0||   
          +---+---+---+---+---+---+---+---+---+--|+
            ^   .   .   .                       -
            |   ^   ^   ^   .   .   .   .   .   |
            |   |   |   |   ^   ^   ^   ^   ^   |
          +-|-+-|-+-|-+-|-+-|-+-|-+-|-+-|-+-|-+-|-+
array1[ii]| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | // each cell points to ten doubles
          +---+---+---+---+---+---+---+---+---+---+
            ^
            |
            |
          +-|-+
    array1| | |
          +---+

Type 2: in-memory representation will look like this:

          +---+---+---+---+---+---+---+---+---+---+     +---+
    double| 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | ... | 0 |  
          +---+---+---+---+---+---+---+---+---+---+     +---+
            ^   ^   ^   ^   ^   ^   ^   ^   ^   ^         ^
            |   |   |   |   |   |   |   |   |   |         |
            |   |   |   |   |   |   |   |   |   |         |
          +-|-+-|-+-|-+-|-+-|-+-|-+-|-+-|-+-|-+-|-+     +-|-+
array1[ii]| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | ... |99 | // each cell points to one double
          +---+---+---+---+---+---+---+---+---+---+     +---+
            ^
            |
            |
          +-|-+
    array1| | |
          +---+

Simple Example

#include<stdio.h>
#include<stdlib.h>

int **d ;
int sum();

//----------------------------------------------  
int main(){

    d = (int **)calloc(3,sizeof(int*));
    printf("\n%d",sum());     
}

//-----------------------------------------------
int sum(){
   int s = 0;
   for(int i = 0; i < 3; i++)
       d[i] = (int *) calloc (3,sizeof(int));

   for(int i = 0; i < 3; i++){ 
       for(int j = 0; j < 3; j++){
           d[i][j] = i+j;
           s += d[i][j];
           printf("\n array[%d][%d]-> %d",i,j,d[i][j]);
        }
   }
   return s;
}