Inverse Filter for Seismic Sensors

I am an amateur seismographer, located in Locust Valley, NY. My station consists of home built sensors of rather short natural period. Out of necessity, I have developed a digital inverse filter, which allows extension of the natural period of the sensors to five or more times their natural period. It took a lot of grunting and straining to perfect this filter, and I want to share it with anybody who could benefit. It ended up being simple to code and use. All you need to set it up is the natural period and damping of the sensor, and the desired filter period. It can be used in real time or on completed files.

In case you have any need to enhance the performance of geophones or any other open loop sensor you operate, please refer to web page

"Period-extending filter algorithm and analysis"

This page describes the analog prototype of the filter and the pseudocode for its digital version. A mathematical analysis demonstrates that the filter's frequency response is correct.

This filter is implemented in my programs "WQFilter.exe" and "Heliplot.exe"

"WQFilter.exe" is a utility program for filtering WinQuake PSN Type 4 event files. "Heliplot.exe" is a program for filtering and displaying Dataq WQD format files. It would be easy for me to code these applications for other file formats, including Little Endian SAC binary files.

Dr. Alan Jones has also incorporated this filter into "AmaSeis.exe" for filtering SAC binary format event files. If you are using AmaSeis, please download the latest version.

All my applications are written using Visual Basic 6.0 for Windows. Alan is currently re-coding AmaSeis using Java, so that it can be compiled for other operating systems.

Please note that "WQFilter.exe" also includes Butterworth filters for lowpass and highpass filtering. Forward, backward, and forward-backward filtering can be selected. If you apply both my period extending filter and a second order highpass backward filter to the event data, you can end up with a broader bandwidth file which has no phase distortion and no time delay in the passband.

Typical impulse response test results:


Two events showing striking improvement in waveform detail:



You are invited to try out the filter for yourself. Download "". It contains the raw and filtered WinQuake event files illustrated above. Use "WQFilter.exe" to see if you can duplicate the filtered examples.

Bob McClure
April 2007