## 回顾

• [7]：Quantization bit rate of A/D conversion
• [8]：Sensor sensitivity (in V/unit_of_input)
• [9]：Unit of input
• [10]：Nature period of the sensor
• [11]：Damping constant of the sensor
• [12]：Amplification factor applied to sensor output prior to A/D conversion (in dB)
• [13]：LSB value of A/D conversion

## 流程

• 输入：波场振幅（[9]）
• 输入增强：对输入波场进行放大（[12]）
• Analog Stage：将连续的波场振幅转换为连续电压信号（[10]、[11]、[8]）
• Analog-Digital Conversion：将连续电压信号转换为离散电压信号（[7]、[13]）
• Digital Stage：对离散数据进行处理

### 输入

[9] 给出了输入波场振幅的单位，一般来说，其值为 m/s，即 Hi-net 是速度地震仪。

### 输入增强

$$L{dB} = 20 \log{10}\left(\frac{A_o}{A_i}\right)$$

$$10^{\frac{L_{dB}}{20}}$$

### Analog Stage

$$G \frac{s^2}{s^2+2 h \omega s + \omega^2}$$

• $G$：Sensor sensitivity，即 $G$= [8]
• $h$：damping constant， 即 $h$= [11]
• $\omega$： natural angular frequency，即 $\omega=\frac{2\pi}{[10]}$

### Analog-Digital Conversion

bit rate 与 LSB value 之间的关系如下：

$$\frac{V{high}-V{low}}{2^{bitrate}}$$

LSB value 的倒数 $\frac{1}{[13]}$，其单位为 $counts/V$，即单位电压所对应的离散值得变化量，也就是这一阶段的增益 $S_d=\frac{1}{[13]}$。

### Digital Stage

In all response files for Hi-net data, sensor sensitivity is set to the case of 200 V/(cm/s). Actual sensitivity of each channel is shown at the 8th column of the channel table file. This means that the values at 37th line from the top and 4th line from the bottom should be modified from the response file in this web page, considering this point.

Response of Observation Equipment 中给出的三种仪器响应 RESP 文件，仅仅只是示例，每个 RESP 文件的前 37 行和后 4 行（PS：此处行号并不包括注释行）必须根据 channel table 中的值进行修改，而其余行则不需要修改。看看 RESP 文件的内容可知，不需要修改的行恰好对应 Digital Stage（stage number 为 3 或 4），这暗示着 **Hi-net 的所有 channel 的 Digital Stage 部分是完全相同的 **。

## 总结

• 检查 [9] 确认输入波场为速度场
• 由 [12] 计算波场放大系数
• 由 [10]、[11] 构造增益为 1 的 transfer 函数，计算其零点和极点，并计算 transfer 函数在自然频率处的振幅，以得到归一化因子 $A_0$
• [8] 为增益，可直接使用
• 对 [13] 列取倒数得到增益（[7]没有用）

## 附录

### 官方回复邮件

Question1: Apr 24, 2014 09:32 (UT) +0900(JST)

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 ?

Best Regards.


Answer1: May 07, 2014 08:30 (UT) +0900(JST)

Thank you for accessing our website.
This is the NIED Hi-net/F-net/V-net administrator.

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
literature, such as,

Scherbaum, F., Of Poles and Zeros: Fundamentals of Digital Seismology,
#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