# Instrumental Response

## Input

The unit of Hi-net input is determined by column [9], ususally m/s.

## Analog Stage

The moving coil velocity type seismometer is used in Hi-net and its transfer function in the Laplace domain is given as:

$\frac{Gs^2}{s^2 + 2hws + w^2}$

where,

• $$G$$: gain factor, given as column [8] in V/unit_of_input

• $$h$$: damping constant, given as column [11]

• $$w$$: natural angular frequency, given as column [10]

Roots of the numerator and the denominator correspond to the zeros and the poles, respectively, and the A0 normalization factor is the inverse of the absolute value of the above equation except G at the normalization frequency ($$f_n$$). The normalization frequency of Hi-net seismometer is always 20 Hz.

It’s easy to know that the instrumental response has two poles and two zeros. It’s also easy to calculate A0, with $$s=i*2*\pi*f_n$$.

## Preamplification

The sensor ouput is amplified prior to A/D conversion. The amplification factor is determined by column [12] in dB.

According to the definition of decibel of field quantities:

$L_{F}=20\log _{10}\left({\frac {F}{F_{0}}}\right)\!~\mathrm {dB} .$

Thus, the “sensitivity” in this stage is $$10^{\frac{[12]}{20}}$$ .

## Analog-Digital Conversion

The gain in this stage is given by $$\frac{1}{[13]}$$, in counts/V.

## Digital Stage

The gain in this stage is 1.0, according to the three RESP files provided on Hi-net website.

## Summary

The total sensitivity is:

$G = \frac{[8]*10^{\frac{[12]}{20}}}{[13]}$

The CONSTANT in SAC PZ file should be:

$CONSTANT = A0 * G = A0 * \frac{[8]*10^{\frac{[12]}{20}}}{[13]}$

Important

HinetPy uses win2sac_32 to do the conversion from win32 to SAC format. win2sac_32 always remove total sensitivity (G) from waveform and multiply by 1.0e9 to convert unit from meter to nanometer.

Thus, the extracted SAC files are velocity in nm/s or acceleration in nm/s/s. The total sensivitity G is also omitted when generating PZ files.

## Q&A

My question:

Hi,

I am using Hi-net data and am confused with the instrumental response even after I have looked through all pages of Hi-net website.

In the page of ‘For Registered Users’ -> ‘Response of Observation Equipment’, only three RESP files are given. It seems that I have to rewrite a new RESP or SAC_PZ file for each channel.

So I have to confirm that I understand details of response, which are very important for correct data processing.

1. Do all channels have the same zeroes and poles?

2. At line 19, do all channels have the same A0 Normalization factor (0.999953)?

3. In the FAQ Q08, one equation is given to convert the A/D value from an WIN32 file to the corresponding physical quantity. It is

v = I * [13] / ([8] * 10 ^ ([12] / 20 ) )

If I want to generate a SAC PZ file, the CONSTANT will be

CONSTANT = [8]*10^([12]/20) / [13] * A0 ?

In the “Response of Observation Equipment” page, sample RESP files are provided and you need to modify them according to your purposes, as you wrote. The explanation in this page assumes that the parameters of the seismometer other than the gain factor do not change. Strictly speaking, the zeros, the poles, and the A0 normalization factor can change depending on the parameters of the seismometer. The moving coil velocity type seismometer is used in Hi-net and its transfer function in the Laplace domain is given as:

Gs^2/(s^2 + 2hws + w^2)

where G, h and w are the gain factor, the damping constant, and the natural angular frequency, respectively. Roots of the numerator and the denominator correspond to the zeros and the poles, respectively, and the A0 normalization factor is the inverse of the absolute value of the above equation except G at the normalization frequency. Detailed explanation about this type of seismometer is available in many literature, such as,

Scherbaum, F., Of Poles and Zeros: Fundamentals of Digital Seismology, Kluwer Academic Publishers, 1996. #see chapter 4

The gain factor, the damping constant, and the natural period are provided in the channels table file as explained in the Q&A08. Note that the gain factor is measured at its natural frequency. http://www.hinet.bosai.go.jp/faq/?LANG=en#Q08