Application of butterworth high pass filter as an approximation of wood anderson seismometer frequency response to earthquake signal recording

ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 379

ACTA IMEKO
ISSN: 2221-870X
December 2020, Volume 9, Number 5, 379 - 382

APPLICATION OF BUTTERWORTH HIGH PASS FILTER AS AN

APPROXIMATION OF WOOD ANDERSON SEISMOMETER FREQUENCY

RESPONSE TO EARTHQUAKE SIGNAL RECORDING

Hamidatul Husna Matondang1, Endra Joelianto2, Sri Widiyantoro3

1 BMKG, Jakarta, Indonesia, hamidatul.husna@bmkg.go.id

2 ITB, Bandung, Indonesia, ejoel@tf.itb.ac.id
3 ITB, Bandung, Indonesia, sriwid@geoph.itb.ac.id

Abstract:

The method for generating maximum amplitude

and signal to noise ratio values by using second

order high pass Butterworth filter on local seismic

magnitude scale calculations is proposed. The test

data are signals from local earthquake that have

been occurred in Sunda Strait on April 8th 2012.

Based on the experimental results, a 8 Hz cutoff

frequency and a gain of 2200 of second order

Butterworth high pass filter as an approach to

simulating the frequency response of Wood

Anderson seismometer can provide maximum

amplitude value, SNR, and the magnitude better

than simulated Wood Anderson frequency

response.

Keywords: High Pass Butterworth Filter; Wood

Anderson Seismometer; Frequency Response

Simulation; Instrument Correction

1. INTRODUCTION

Initially, the calculation of the local seismic

magnitude scale was based on the calculation of the

magnitude scale obtained from Wood Anderson's

seismometer recordings. However, the Wood

Anderson seismometer is a short period instrument

that has analog recording, in which, the analog

recording speed on paper is limited. This resulted in

an earthquake recording on the recording station

that was close to the location of the earthquake

experiencing clipping. Therefore, recording

earthquake signals from the Wood Anderson

seismometer is no longer used in the calculation of

local magnitude scales. Thus, the study of local

magnitude has been shifted to the use of digital

recording. In order to produce digital recordings as

if coming from a Wood Anderson seismometer, the

digital recordings are processed to simulate the

Wood Anderson seismometer frequency response.

The recording of the Wood Anderson frequency

response simulation provides more accurate data

from the original instrument, because there is no

clipping on earthquake recordings [1]. However, in

practice, the Butterworth filter application is still

used to eliminate microseismic noise [2].

Considerable research has been done on

simulating seismometer responses. Among them,

designing a simulation of the frequency response of

Wood Anderson seismometer from recursive filters

with differential equations has been considered in

[3]. The seismometer frequency response is

considered as a second order high pass filter. If the

filter is applied to an earthquake signal, the 2nd order

Butterworth high pass filter with a cutoff frequency

of 2 Hz can approximate the local magnitude in 0.1

magnitude units [1]. The seismometer frequency

response approach can also be obtained from a 5th

order Butterworth low pass filter cascaded with a 3rd

order Butterworth high pass filter [4]. These filters

are used to correct short period and broadband

seismometer responses. Pole and zero

determination was provided for recursive filters

used as a correction for seismometer instruments

[5].

Different from previous studies, this paper tests

earthquake signals using a second order

Butterworth high pass filter with a cutoff frequency

of 0.1 to 12 Hz. The test data used in this paper are

local earthquake signals and noise signals recorded

by four earthquake recording stations. The Do the
authors mean to correct short period and broadband

seismometer responses recording stations are Cigelis

Jawa Indonesia (CGJI), Lembang (LEM), Cisompet

(CISI) and Karang Pucung Jawa Indonesia (KPJI).

Local earthquake recorded signals used are the ones

related to the earthquake that have occurred in the

Sunda Strait on 8th April 2012 at 08: 06: 47.1 am

UTC+07.00 with a strength of 4.6 magnitudes, at

coordinates longitude 105.859998 and latitude -6.94

with depth of 100 km. While noisy signals were

taken in the morning at 03.00 am UTC+07.00, noon

at 12.00 pm UTC+07.00 and at night at 10.00 pm

UTC+07.00 [6].

http://www.imeko.org/
mailto:hamidatul.husna@bmkg.go.id
mailto:ejoel@tf.itb.ac.id
mailto:sriwid@geoph.itb.ac.id

ACTA IMEKO | www.imeko.org December 2020 | Volume 9 | Number 5 | 380

From the test results, the gain value and cut off

frequency of the filter are configured considering

the recorded data characteristic. The filter is then

applied to the signal. The results of the filter

application are expected to produce higher

amplitude and signal to noise ratio (SNR) values

than the simulated Wood Anderson’s seismometer

frequency response. The Butterworth filtered results

are used as an approach to simulate earthquake

recordings that would be obtained from a typical

frequency response of a Wood Anderson's

seismometer.

2. PROPOSED METHODOLOGY

The design is based on the similarity of

responses between the Butterworth high pass filter

and the Wood Anderson seismometer which is a

second order system [7]. The filter is applied to

earthquake signals that have been used for local

seismic magnitude scale calculations. From the

filtered signal, the maximum amplitude is obtained

in the S signal phase and signal to noise ratio (SNR).

For comparison, the maximum amplitude and

SNR of filtered earthquake signals are compared

with the maximum amplitude and SNR of the

earthquake signal on a simulated Wood Anderson

seismogram. The research flow chart is shown in

Figure 1.
Start

Data Collection

Catalogue Data of BMKG

Waveform Data

conversion of

seed to sac

Resampling

Determination of the

butterworth highpass

filter coefficient

Application of High Pass

Butterworth Filter Frequency

Response Design Results

Component

Rotation

Readings of Maximum

Amplitude and SNR

Calculation

Component

Rotation

Finished

Application of High Pass

Butterworth Filter Frequency

Response Design Results

Readings of Maximum

Amplitude and SNR

Calculation

Reference

Figure 1: Flowchart of the Method

3. ANALYSIS

The results of the Butterworth filter test applied

to BMKG data show an almost similar amplitude

value for each earthquake recording station. The

average maximum amplitude value for the four

recording stations is 24,000,000 nm, produced by

the Butterworth filter with a gain of 3000 and a cut-

off frequency of 0.1 Hz. While the minimum

amplitude is obtained from the gain with a value of

1000 and the cut-off frequency around 0.1 Hz. See

Figure 2.

Figure 2: Cut off frequency, gain and maximum

amplitude curves

It is also known that the frequency response of

second order Butterworth Filter with gains of 2000,

2200, and 2300 have similarities with frequency

response of Wood Anderson’s Seismometer.

However, the second-order Butterworth filter

frequency response with a gain of 2200 and an 8 Hz

cut-off frequency that is close to the maximum

amplitude of Wood Anderson's seismometer.

The second-order Butterworth filter frequency

response with a gain of 1000 has a magnitude

smaller than the magnitude generated by the Wood

Anderson seismometer. Whereas the second order

Butterworth filter frequency response with a gain of

3000 has a magnitude greater than the seismic

magnitude generated by the Wood Anderson

seismometer. See Figure 3.

Table 1: Signal to noise ratio of Wood Anderson

Seismometer and Butterworth Filter Simulated

The largest maximum amplitude value of each

recording station is obtained from the Butterworth

filter simulation results, while the results from the

Station

Simulated Wood

Anderson

Butterworth Filtered

signal