A sound exposure level is defined as the integral of squared pressures, over a defined time-period and frequency range, and it is reported with units of dB re: 1 µPa^2s (for water-borne acoustics). My understanding is that a sound exposure level is supposed to be an integral, not a sum, with the major difference being that an integral incorporates the distance between each value (e.g. the "dt"), which is dependent on the sample rate.

In my discussions with a few scientists on this topic, I’m finding inconsistent methods in the way that sample rates are (or are not) included in the calculation of sound exposure levels. This is particularly concerning because sound exposure levels are often used in management contexts, like the US National Marine Fisheries Marine Mammal Acoustic Technical Guidance and Southall et al 2019 Marine Mammal Noise Exposure Criteria.

Here's a snippet of R-code which demonstrates how I think the SEL should be calculated

#Calculate a SEL over 100 ms window, from 20 Hz - 1000 Hz 

library(tuneR)
library(seewave)

clip<-readWave(wavfile)
WavClip<-clip@left - mean(clip@left) #Account for DC offset
fs<[email protected]

#Calibration
cal=177 #full system calibration  
cal = 10^(cal/20) #convert from dB to linear
Nbit <- clip@bit
WavBit <- WavClip/(2^(Nbit-1))
WavCal<-WavBit*cal

#Limit frequence range with bandpass filter
WavFilt<- bwfilter(WavCal, f = fs, n =4, from = 20, to=1000, output = "Sample",bandpass = TRUE)

#Limit time range 
winLen_sec<-0.1*fs 
Wav100ms<-WavFilt[1:winLen_sec]

#Integrate squared pressures, divide by sample rate, convert to dB
SEL<-10*log10(sum(Wav100ms^2)/fs) 

A sound exposure level is defined as the integral of squared pressures, over a defined time-period and frequency range, and it is reported with units of dB re: 1 µPa$^2$s (for water-borne acoustics). My understanding is that a sound exposure level is supposed to be an integral, not a sum, with the major difference being that an integral incorporates the distance between each value (e.g. the "dt"), which is dependent on the sample rate.

In my discussions with a few scientists on this topic, I’m finding inconsistent methods in the way that sample rates are (or are not) included in the calculation of sound exposure levels. This is particularly concerning because sound exposure levels are often used in management contexts, like the US National Marine Fisheries Marine Mammal Acoustic Technical Guidance and Southall et al 2019 Marine Mammal Noise Exposure Criteria.

Here's a snippet of R-code which demonstrates how I think the SEL should be calculated

#Calculate a SEL over 100 ms window, from 20 Hz - 1000 Hz 

library(tuneR)
library(seewave)

clip<-readWave(wavfile)
WavClip<-clip@left - mean(clip@left) #Account for DC offset
fs<[email protected]

#Calibration
cal=177 #full system calibration  
cal = 10^(cal/20) #convert from dB to linear
Nbit <- clip@bit
WavBit <- WavClip/(2^(Nbit-1))
WavCal<-WavBit*cal

#Limit frequence range with bandpass filter
WavFilt<- bwfilter(WavCal, f = fs, n =4, from = 20, to=1000, output = "Sample",bandpass = TRUE)

#Limit time range 
winLen_sec<-0.1*fs 
Wav100ms<-WavFilt[1:winLen_sec]

#Integrate squared pressures, divide by sample rate, convert to dB
SEL<-10*log10(sum(Wav100ms^2)/fs) 

A sound exposure level is defined as the integral of squared pressures, over a defined time-period and frequency range, and it is reported with units of dB re: 1 µPa^2s. My understanding is that a sound exposure level is supposed to be an integral, not a sum, with the major difference being that an integral incorporates the distance between each value (e.g. the "dt"), which is dependent on the sample rate.

In my discussions with a few scientists on this topic, I’m finding inconsistent methods in the way that sample rates are (or are not) included in the calculation of sound exposure levels. This is particularly concerning because sound exposure levels are often used in management contexts, like the US National Marine Fisheries Marine Mammal Acoustic Technical Guidance and Southall et al 2019 Marine Mammal Noise Exposure Criteria.

Here's a snippet of R-code which demonstrates how I think the SEL should be calculated

#Calculate a SEL over 100 ms window, from 20 Hz - 1000 Hz 

library(tuneR)
library(seewave)

clip<-readWave(wavfile)
WavClip<-clip@left - mean(clip@left) #Account for DC offset
fs<[email protected]

#Calibration
cal=177 #full system calibration  
cal = 10^(cal/20) #convert from dB to linear
Nbit <- clip@bit
WavBit <- WavClip/(2^(Nbit-1))
WavCal<-WavBit*cal

#Limit frequence range with bandpass filter
WavFilt<- bwfilter(WavCal, f = fs, n =4, from = 20, to=1000, output = "Sample",bandpass = TRUE)

#Limit time range 
winLen_sec<-0.1*fs 
Wav100ms<-WavFilt[1:winLen_sec]

#Integrate squared pressures, divide by sample rate, convert to dB
SEL<-10*log10(sum(Wav100ms^2)/fs) 

A sound exposure level is defined as the integral of squared pressures, over a defined time-period and frequency range, and it is reported with units of dB re: 1 µPa^2s (for water-borne acoustics). My understanding is that a sound exposure level is supposed to be an integral, not a sum, with the major difference being that an integral incorporates the distance between each value (e.g. the "dt"), which is dependent on the sample rate.

In my discussions with a few scientists on this topic, I’m finding inconsistent methods in the way that sample rates are (or are not) included in the calculation of sound exposure levels. This is particularly concerning because sound exposure levels are often used in management contexts, like the US National Marine Fisheries Marine Mammal Acoustic Technical Guidance and Southall et al 2019 Marine Mammal Noise Exposure Criteria.

Here's a snippet of R-code which demonstrates how I think the SEL should be calculated

#Calculate a SEL over 100 ms window, from 20 Hz - 1000 Hz 

library(tuneR)
library(seewave)

clip<-readWave(wavfile)
WavClip<-clip@left - mean(clip@left) #Account for DC offset
fs<[email protected]

#Calibration
cal=177 #full system calibration  
cal = 10^(cal/20) #convert from dB to linear
Nbit <- clip@bit
WavBit <- WavClip/(2^(Nbit-1))
WavCal<-WavBit*cal

#Limit frequence range with bandpass filter
WavFilt<- bwfilter(WavCal, f = fs, n =4, from = 20, to=1000, output = "Sample",bandpass = TRUE)

#Limit time range 
winLen_sec<-0.1*fs 
Wav100ms<-WavFilt[1:winLen_sec]

#Integrate squared pressures, divide by sample rate, convert to dB
SEL<-10*log10(sum(Wav100ms^2)/fs)