Operand 1
Cell statistic variable
The Cell statistic operator accepts gridded Sv data and outputs a virtual variable with the same grid; each cell's samples are set to a selected cell statistic.
The Cell statistic (single targets) operator accepts two operands. Operand 1 provides the gridded single target data. Operand 2 provides the ping geometry. The output is a virtual variable with the same grid and a specified ping gemorty; each cell's samples are set to a selected cell statistic.
Cell statistic settings specified on the Cell statistic page of the Variable properties dialog box. When required, Cell statiistics are converted to the linear domain for intermediate calculations with output values reconverted to the dB domain. Excluded and thresholded samples affect the calculations of the cell statistic.
About the Cell statistic operator discusses uses of these Cell statistic operator.
The diagram below shows gridded input operand samples and the output cell statistic.
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Operand 1
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Cell statistic variable
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Where:
i is the index for pings in Operand 1. I is the index for the pings in the Cell statistic variable. The number of pings is unchanged by the operator i.e.i = I. j is the index for samples in an Operand 1 ping := {0 ... n-1} J is the index for samples in a Cell statistic output ping := {0 ... m-1}
n is the number of samples in an Operand 1 ping m is the number of samples in the Cell statistic ping
When Operand 1 is Sv m = n When Operand 1 is Single target
m = the ping geometry from Operand 2
A is the set af all samples in an Operand 1 cell. Samples in set A can be referred as sample s and denoted as
s i,j. Eligible samples from set A are specified by the algorithms (below). The set for eligible samples is referred to as A'.Y is the set of all samples in the Cell statistic cell. Samples in this set are denoted by yI,J (cell). Separation of time/distiance Grid is the separation displayed under Show time/dist grid on the Grid page of the Variable Properties dialog box of Operand 1. Cells for the Cell statistic variable are defined by the Grid for Operand 1.
Separation of depth/range Grid is the separation displayed under Show depth/range/line-referenced grid on the Grid page of the Variable Properties dialog box of Operand 1. Cells for the Cell statistic variable are defined by the Grid for the Operand 1.
Operations
The operations available can be divided into two groups, mean statistics and sampled statistics . They are described individually below:
Mean
Samples within Operand 1's cells contribute to the Mean for each cell. In the Cell statistic variable the samples, yi,J (cell), are set to the associated Mean from Operand 1.
Let A be the set of samples s, in the Operand 1 cell, over which the (Sv or TS) Mean is calculated.
The sample values in the output cell are set to:
yI,J (cell) = 10 log (sv (Operand 1 cell))
Calculations are performed in the linear domain not the decibel domain. See Conversions for details.
This calculation is used for calculating the Mean for each cell of the input operand:
Where:
= the value of sample J in output ping Iin a cell of the Cell statistic variable = the linear mean Sv for all samples or the linear mean TS for all single targets in A (m2/m3) - see Conversions. = the set of all eligible samples in the Operand 1 cell.
- No-data samples are ignored.
- Thresholded samples are ineligible and are not used for the Mean calculation.
svs = the linear Sv value for sample s (m2/m3) or the linear TS value for sample s - see Conversions. N = the number of eligible samples in the Operand 1 cell Sampled statistics
Minimum
In the Cell statistic variable the samples, yI,J (cell), are set to the corresponding cell's Minimum value from Operand 1.
yI, J (cell) = W0
Where:
yI, J (cell) = the value of sample J in output ping Iin a cell of the Cell statistic variable = the value for Sv minimum - or - the value for TS minimum
Where W is the ordered list of sample values si, j for all i,j in set A, being (W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1
and N is the number of samples in the list.
Such that:
- Thresholding is ignored and those samples' values are part of set A.
- No-data samples are ignored.
Refer to the introductory diagram above for definitions of any remaining symbols.
Maximum
In the Cell statistic variable the samples, yI,J (cell), are set to the corresponding cell's Maximum value from Operand 1.
yI, J (cell) = W0
Where:
yI, J (cell) = the value of sample J in output ping Iin a cell of the Cell statistic variable W0 = the value for Sv maximum - or - the value for TS maximum
Where W the ordered list of sample values si, j for all i,j in set A, being (W0, W1, W2, .... WN-1) such that Wi ≥ Wi+1
and N is the number of samples in the list.
Such that:
- Thresholding is ignored and those samples' values are part of set A.
- No-data samples are ignored.
Refer to the introductory diagram above for definitions of any remaining symbols.
Median
In the Cell statistic variable the samples, yI,J (cell), are set to the corresponding cell's Median value from Operand 1.
yI, J (cell) = Wk if N is odd (W k+Wk+1)/2 if N is even Where:
yI, J (cell) = the value of sample J in output ping I in a cell of the Cell statistic variable. Wk = the value of sample k in the list W — (defined below) k = ëN/2û * N = the number of eligible samples in the list W A' = the set of all eligible samples in the Operand 1 cell.
- No-data samples are ignored.
- Thresholded samples are ineligible and are not used for the Median calculation.
W = the ordered list of sample values si, j for all i,j in set A', being (W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1
Refer to the introductory diagram above for definitions of any remaining symbols.
Percentile
In the Cell statistic variable the samples, yI,J (cell), are set to the corresponding cell's Percentile value from Operand 1.
yI, J (cell) = Wk + (Wk+1 - Wk) (k' - k)
Where:
yI, J (cell) = the value of sample J in output ping I in a cell of the Cell statistic variable. The operand's data type outputs Sv cell percentile or Single target cell percentile. Wk = the value of sample k in the list W — (defined below) k = ëk'û * k' = N x P/100 N = the number of eligible samples in the list W. P = the Percentile entered on the Cell statistic page of the Variable properties dialog box A' = the set of all eligible samples in the Operand 1 cell.
- No-data samples are ignored.
- Thresholded samples are ineligible and are not used for the Percentile calculation.
W = the ordered list of sample values si, j for all i,j in set A', being (W0, W1, W2, .... WN-1) such that Wi ≤ Wi+1 Refer to the introductory diagram above for definitions of any remaining symbols.
In the Cell statistic variable, the samples yI,J (cell) are set to the corresponding cell's No. of samples or No. of single targets from the input operand.
| The algorithm | Eligible samples for the Number calculation: |
| No. of samples is calculated in a way similar to the Integrate Cell feature for Sv data. |
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| No. of single targets is calculated in a similar way to the Analyze Cell feature for single target data. |
About virtual variables
Cell statistic operator
Cell statistic settings
About the Cell statistic operator
Footnote:
*Floor function ëxû, gives the largest integer less than or equal to x.
