Adaptive Grid Sampling

This method of sample placement covers the site with rectangular grids and places samples at an offset within the grids.

Method for applying Adaptive Grid Sampling in VSP

This method is used to place samples on the map observing the following constraints:

The exact number of samples will be specified
Every location on the map has an equal probability of being selected
Sample Areas that are in close proximity to each other will be gridded together as a group
The group of sample areas will be covered with equally-sized rectangular grids
Each grid will contain no more than one sample
A sample is located only within selected areas of the map (i.e. in selected Sample Areas)

The method of placing samples proceeds as follows:

1. Sample Areas are collected into groups. A sample area is considered in the vicinity of a group if it is within the extents plus 10%.

2. The total surface area of all the selected sample areas is computed ( $A_T$ ).

3. The number of samples is allocated to each group based on the proportion of the group area ( $A_G$ ) compared to the total area ( $A_T$ )

4. The assigned samples are then placed in each group as follows:

a. The area of one grid ( $A_g$ ) is computed by dividing $A_G$ by the number of samples ( $n$ ) allocated to the group.

b. The aspect ratio ( $T$ ) is computed by dividing the width of the group by the height of the group.

c. The length of the grid side ( $L_g$ ) is found by computing the square root of $A_g * T$ .

c. The entire group is covered by grid rectangles that are $L_g$ wide by $L_g / T$ tall, beginning at the minimum x, minimum y of the group extents. If the triangular pattern is selected, every 2nd row is shifted left by $L_g / 2$ . Note that VSP also supports rotating the entire grid at an angle.

d. The proportion of each grid ( $P_g$ ) that is inside of selected Sample Areas is computed ( $0 \leq P_g \leq 1$ ). Grids where $P_g = 0$ are discarded. The total number of remaining grids is $N$ .

e. The total $P_g$ of all grids is equal to the total number of samples allocated to the group:

$n= \displaystyle\sum_{i=1}^N P_g(i)$

f. The probability that a grid will contain a sample is $P_g$ .

g. All grids where $P_g = 1$ are selected for sampling.

h. $r$ is the number of grids where $P_g < 1$ . $R$ is the sum of all $P_g$ where $P_g < 1$ .

i. $R$ grids are selected for sampling from the remaining $r$ grids. The probability that a grid is selected for sampling is $P_g$ .

j. A random horizontal offset ( $H_o$ ) and vertical offset ( $V_o$ ) is chosen.

k. For each grid, the offset location in the grid is checked.. If the location falls inside a selected Sample Area it is accepted, otherwise:

i. Another random horizontal offset ( $H_r$ ) and vertical offset ( $V_r$ ) is chosen.

ii. If the location at offset ( $H_o$ , $V_r$ ) falls inside a selected Sample Area it is accepted.

iii. If the location at offset ( $H_r$ , $V_o$ ) falls inside a selected Sample Area it is accepted.

iv. If the location at offset ( $H_r$ , $V_r$ ) falls inside a selected Sample Area it is accepted.

v. Steps i through iv are repeated until a location is accepted.

l. A sample is placed at the accepted location.