# Statistical combination operator algorithm

The Statistical combination operator is used to create a virtual line by applying a statistical operation to operand lines.

## Algorithm terms

 Term Definition Line segment The join between adjacent time/depth coordinates of a line. In Echoview, line segments have a line status. Operands Operand 1 is a user selected acoustic variable that specifies the ping geometry for the Statistical combination line. Operand 2, 3 ... are the user selected lines used as input lines for the Statistical combination operator. The algorithm uses the Divergence limit to determine eligible line segments from the operands. Statistic A statistical operation applied to Operands. Available Statistics are: Minimum depth - the minimum depth from the line segments is chosen for the output line. Maximum depth - the maximum depth from the line segments is chosen for the output line. Median depth - the median depth of line segments is chosen for the output line. Mean depth - the linear average depth of line segments is calculated and is the result for the output line. Note: The median depth of an odd number of lines is determined using the median of the (odd number of) depths. Where there is an even number of depths (lines) the median is the arithmetic mean of the two middle depths. Choice operation The Statistics: Minimum depth, Maximum depth or Median depth. Combination operation The Statistic: Mean depth. Divergence limit The allowable distance that a line segment can deviate from the mean of all the eligible line segment depths.

## Before you begin

A typical use for the Statistical combination line operator is to combine sounder-detected bottom lines (or Echoview-generated lines) from a range of frequencies. When using multiple frequency data, frequency dependent effects need to be accounted for.

Simmonds and MacLennan1 discuss the implications of the increase of absorption coefficient with frequency in sea water and fresh water. For sea water, a factor of ten increase in frequency results in an approximate factor of ten increase in acoustic absorption coefficient. Such increases in absorption coefficient lead to an increase in TVG and an increase in the deterioration of the signal to noise ratio. It follows that each frequency has some range limit beyond which the acoustic signal can not be detected.

An example of this is seen for higher frequencies used in surveys in deep water. It is common for the range limit of the data to occur before the bottom depth. As a result sounder-detected bottom lines become erratic as data is swamped by noise (beyond the range limit).

To address this problem and to allow you to pre-process lines for the Statistical combination line operator, Echoview offers a Crop operator. This operator allows you to apply range limits to lines.

## Statistical combination operator algorithm

For the:

• Operands selected on the Operand page of the Line Properties dialog box of the virtual line.
• Statistic selected on the Statistical combination page of the Line Properties dialog box of the virtual line.
• Optional Divergence limit selected on the Statistical combination page of the Line Properties dialog box of the virtual line.

The algorithm considers the line segment start points of all the input lines in time sequence. To avoid absurdly short line segments, start points that are less than a half of the current minimum segment length after the previous point are ignored.

The Statistical Combination line operator will start a new output line segment when any of its input lines starts a new line segment.

1. Each input line segment start point depth is compared to the depths of the other input lines at that time. These are called the current depths.
2. The line status of the output line is the highest current status. Discard any current depths that do not have this status.
3. If a Divergence limit is set then:
1. take the mean of the current depths
2. find the depth that diverges most from the mean
3. if this depth is more than the Divergence limit from the mean then remove it from the current depths and go to step a.
4. end
4. Finally the selected Statistic is applied to the current depths.

Notes:

• Operand 1 specifies the ping geometry of the statistical combination line.
• A line segment with line status other than Good initiates a new output line segment. However this can only become the output depth if there are no other current line segments with a higher line status.
• An unexpected line may be due to too few or irregular coordinate points in the operand lines. Refer to the note for this operator for more information.