Sv_f_mean, ABC_f and NASC_f
This page describes the calculation of Sv_f_mean and the derived quantities ABC_f and NASC_f, where:
and
R (m) is the mean range extent of the analysis domain.
These analysis variables are calculated from echograms with the data type Pulse compressed complex Sv and are based on the latest published research (Andersen et al. 2023; Levine et al. 2025). Levine et al. (2025) propose that Sv_f_mean derived from wideband echosounder data is equivalent to Sv_mean derived from narrowband echosounder data and can therefore be used to estimate scatterer density by echo integration.
Results are displayed for onscreen integration and are optional for integration exports. Be aware that the Fourier calculations can take time, so if these quantities are not needed it is recommended to deselect them when exporting. This can be applied globally on the EV File Properties dialog box, Export page, Integration results section) or locally for an Sv integration exporter object on the Exporter Properties dialog box, Sv Integration page.
Supported analysis domains
The supported analysis domains are cells, regions, regions by cells, and transects. The calculation is viable only when all pings within the analysis domain for a given channel share the same calibration settings. Echoview calculations respect data exclusions due to transects, exclusion lines, thresholds and bad data regions.
Fourier window size and placement
The effective Fourier window, or data window, is the sequence of data samples selected from an echogram of data type Pulse compressed complex Sv and transformed with a Fast Fourier Transform (FFT). The window size Nw is specified in units of pulse lengths as Window size (pulse lengths) on the Analysis page of the Variable Properties dialog box. The default value is 2 pulse lengths, which is the minimum recommended window size (Andersen et al., 2023, p.9). Levine et al., (2025) use a value of Nw = 2 m.
Samples are indexed from the start of the window (i = 0, 1, ..., Nw-1). If the specified window size results in an even number of samples, Echoview adds a single sample with linear value 0 (i.e., 0 + j0) to the end of the sequence. Note that zero padding is not possible for these wideband integration variables.
The window placement method is identical to the method used for the Wideband Frequency Response graph. For each ping of the analysis domain, the effective Fourier window is placed so that the centre sample of the window corresponds to the first sample of the domain. The window is then slid in range increments corresponding to approximately 0.5 x Nw (i.e., 50 % overlap to the nearest sample) until the centre sample of the window is no longer located within the domain. Note that this placement method results in one or more effective Fourier windows that extend outside the domain. Levine et al. (2025) use a 0.5 m (75 %) overlap, while the exact window placement method is not described.
Exclusions
When the wideband integration statistic cannot be calculated Echoview records -9999.
Where valid samples are empty water or thresholded to -999, Echoview records -999 for Sv_f_mean, 0 for NASC_f and 0 for ABC_f.
Echoview utilises methods developed for the wideband frequency response graph. The sliding calculation window indexes samples from the top of the window. For further information refer to the graph's assumptions and notes.
Calculations
Sv_f_mean (dB re 1 m2/m3)
Sv_f_mean is the band-mean volume backscattering strength 
(dB re 1 m2/m3) of the domain. The calculation is performed for each domain as follows,
- For each ping in the domain, the volume backscattering strength spectrum (frequency response) Sv(f) of each effective Fourier window is calculated by FFT (after Andersen et al., 2023, Eqs. 31–37).
- For each ping, the ping-mean frequency response is calculated as the linear mean of the frequency responses of each window.
- The domain-mean frequency response is calculated as the linear mean of the ping-mean frequency responses.
- The band-mean volume backscattering strength of the domain is then the linear mean Sv across the bandwidth of the domain-mean frequency response.
ABC_f (m2/m2)
ABC_f is the band-mean area backscattering coefficient Overline.svg){kind=small}
(m2/m2 over R) of the domain
ABC_f is calculated as:
where:
R (m) is the Thickness mean of the analysis domain. For more information refer to Thickness_mean.
NASC_f (m2/nmi2)
NASC_f_mean is the band-mean nautical area scattering coefficient Overline.svg){kind=small}
(m2/nmi2 over R ) of the domain.
NASC_f is calculated as:
