Wood Anderson response simulation in obspy.signal.invsim

Usage Questions
1

Hi there,

I wanted to clarify a few things in the estimate_wood_anderson_amplitude_using_response function in obspy.signal.invsim.
In the function, the response is removed with an output of velocity, and then the poles and zeroes of the Wood Anderson instrument are applied to simulate WA response:

response = response.get_evalresp_response_for_frequencies(
[freq], output=“VEL”, start_stage=None, end_stage=None)[0]
response_amplitude = np.absolute(response)
wa_ampl /= response_amplitude
wa_ampl *= paz_2_amplitude_value_of_freq_resp(WOODANDERSON, freq) *
WOODANDERSON[‘sensitivity’]

Where WOODANDERSON is defined as:
WOODANDERSON = {‘poles’: [-6.283 + 4.7124j, -6.283 - 4.7124j],
‘zeros’: [0 + 0j], ‘gain’: 1.0, ‘sensitivity’: 2080}

However, these poles and zeroes seem to come from New Manual of Seismological Observatory Practice (2002). I can’t find that exact version, but in the revised version published in 2009 they state on page 570:

Note that the poles and zeros given in Tabs. 11.3 and 11.4 are valid only if the input signal to
the considered seismographs is ground displacement (amplitude Ad).

Where Table 11.3 contains the poles and zeroes for WA.

I’m confused here - perhaps this is just me misunderstanding what they wrote - but doesn’t this suggest that the input to the wood anderson simulation should be displacement and not velocity?
Why do we use the velocity in obspy?
Any help you can give me would be much appreciated.

Edit: I note now that the obspy response has one less zero than the response in the paper. I assume this is allowing us to translate directly from velocity into displacement?

2

Based on the above analysis, I also have a question. If the data I input is velocity, is it automatically assumed to be in meters per second? After simulating with WOODANDERSON, is the resulting displacement measured in millimeters?

3

You want to convert to displacement and then convolve with a Wood-Anderson. So replace VEL with DISP in your call to evalresp. This will turn wa_ampl to displacement.

The difference between velocity, displacement, and acceleration are all just one difference in a zero at zero. This is a property of the Fourier transform.

Note that your end result will be in m with the gain adjustment you are using of x2080. Usually people want a normalized gain, but check which magnitude type you are estimating.