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8.9 Instrument correction and magnitudes Ml, mb and Ms

The correction for instrument response is done by taking the spectrum of the selected window of the trace, dividing with the response function and converting back to the time domain. Any filtering specified is done in the time domain. Filtering is needed in most cases. The steps are:

Optionally filter in time domain

Remove DC

Apply sine taper on 10 percent of the signal in each end do FFT

If data has been high pass filtered in time domain at frequency flow, then Frequency domain 4 pole low pass Butterworth filter is added at frequency flow/5. This is for stability.

Correct for response

Do inverse FFT

Ground motion

Option g(Groun) removes the effect of the instrument and displays a ground motion seismogram. After selecting g and the zoom window, there is a question of which type of seismogram to calculate: Displacement (d), Velocity (v) or Acceleration (a). The corrected trace is shown below in nanometers(nm), nm/sec or nm/(sec*sec) (if response information is available). Note that this might produce strange seismograms, since e.g. a SP seismograph has very low gain at low frequencies so noise might be amplified very strongly. It is therefore recommended to also do some filtering when using the g option.

Amplitude for determining Ml

For the w(WA)-option (Wood Anderson), the trace is corrected for the instrument to produce displacement. The displacement trace is then multiplied with the response of the Wood-Anderson instrument to produce a signal to look exactly like it would have been seen on a Wood-Anderson seismograph. The maximum amplitude (nm) is read and saved to the S-file with name IAML. The Wood-Anderson response (PAZ) is hardwired in SEISAN and it is similar to a 2 pole Butterworth high-pass filter at 3 Hz. In SEISAN versions prior to 8.3, a fixed 8 pole bandpass filter was used (1.25 Hz - 20 Hz). Filtering is done in the frequency domain. For noisy traces it might also be required to put a filter at the high end. This can be specified in the MULPLT.DEF file. Unfortunately, the correct low cut filter with 2 poles will often result in the seismogram blowing up at low frequencies and might be quite useless for earthquakes with magnitude below 2.0 - 2.5 So in addition to the PAZ filter, a fixed bandpass filter can be added (see MULPLT.DEF). In the standard distribution of SEISAN, this additional filter is not set A filter 1.25 - 20 Hz is recommended. In all cases where an additional filter is used, the read amplitude is corrected for the filter gain and the true ground motion written in the S-file will be larger than the amplitude seen on the screen. The additional default filter probably only makes a difference for very large events (Ml \bgroup\color{black}$ >$\egroup 5). Other filters at a higher frequency should only be used for small events (M \bgroup\color{black}$ <$\egroup 1) . NOTE: In SEISAN version 7.1.1 and earlier, the low cut filter was set by mistake to 0.8 Hz. Repicking amplitudes with the correct filter might change magnitudes of larger events slightly.

Displaying response information

The response function for the current channel can be shown with option `:' (Resp), see Figure 8.11. If no response function is given, a message is shown. If the response function is taken from the waveform file header instead of from the CAL directory, a message is given.

Amplitude for determining mb:

Determining mb assumes that the maximum amplitudes are measured on classical 1 Hz WWSSN instruments having a peak gain around 1.5 Hz. This in reality means a band limited measurement. To pick ground amplitudes for determining Mb on instruments with a broader or more narrow frequency band, like most high frequency SP instruments, some filtering must first be done. Using the j(mb)-option, the trace is corrected for the instrument to produce displacement. The displacement trace is then multiplied with the response of the SP WWSSN instrument to produce a signal to look exactly like it would have been seen on a SP WWSSN seismograph. The unit of the amplitudes seen on the screen is nm, however the amplitude will only represent the ground motion correctly at the frequency of the maximum gain at 1.5 Hz and for all other frequencies, the true ground motion will be larger than seen on the screen. The maximum amplitude is now picked and displayed below the trace, corrected for the gain relative to the gain at 1.5 Hz and written to the S-file with name IAmb. This means that the amplitude written to the S-file generally will be larger than the amplitude displayed on the plot. The SP WWSSN response (PAZ) is hardwired in SEISAN and cannot be modified with filters.

In SEISAN version to 8.2.1, the default filters used to simulate SP WWSSN were, by mistake, in the band 0.9 (2 pole) to 1.8 Hz (3 poles). This will result in slightly wrong magnitudes unless the user had put in correct new filter contants... Prior to SEISAN version 8.2, the default filters used were 0.5 Hz (8 pole) and 5.0 Hz (8 pole filter), which was close to the correct values. No correction for relative gain was used in SEISAN versions prior to 8.3.. All of these changes could have resulted in smaller errors in mb, which only can be corrected by repicking the amplitudes.

Amplitude for determining mB

Amplitude for mB is defined as the maximum velocity on a wide band instrument (0.2 -30 sec or 0.033 - 5 Hz). The maximum amplitude Vmax is measured on a velocity trace. Using the J(mB) option, a velocity trace (nm/s) in the frequency band 0.033 - 5 Hz is displayed. The maximum amplitude in nm/s (irrespective of frequency) is picked and displayed below the trace. This amplitude is now written to the S-file with phase name IVmB_BB. In principle, mB can be calculated using any instrument, but in practice it can only be used if the P-signal is seen clearly on an unfiltered broad band velocity record. The Butterworth filter 0.033 - 5 Hz , 8 poles, is hardwired and it cannot be modified with additional filters.

Amplitude for determining Ms:

The attenuation function for determining Ms assumes that the amplitudes are measured on classical LP WWSSN instruments having a peak gain around 15 second. To pick ground amplitudes for determining Ms on instruments with a broader or more narrow frequency band, like most broad band instruments, some filtering must first be done. Using the k(Ms)-option, the trace is corrected for the instrument to produce displacement. The displacement trace is then multiplied with the response of the LP WWSSN instrument to produce a signal to look exactly like it would have been seen on a LP WWSSN seismograph. The unit of the amplitudes seen on the screen is nm, however the amplitude will only represent the ground motion correctly at the frequency of the maximum gain at 15 seconds and for all other periods, the true ground motion will be larger than seen on the screen. The maximum amplitude is now picked and displayed below the trace. This amplitude is then corrected for the gain relative to the gain at 15 seconds and written to the S-file with name IAMs_20. This means that the amplitude written to the S-file generally will be larger than the amplitude displayed on the plot. The LP WWSSN response (PAZ) is hardwired in SEISAN and no additional filters can be used.

The attenuation function for determining Ms assumes that the amplitudes are measured in the period range 18 - 22 sec and it is up to the user to make sure that the the amplitude is in the correct range..

For SEISAN 8.2.1, the default filters used were in the band 0.038 (2 pole) to 0.1 Hz (1 pole). Prior to SEISAN 8.2 default filters were 0.042 to 0.063 Hz (8 pole filter). No correction for relative gain was used in SEISAN versions prior to 8.3. These changes might have resulted in small errors ins Ms and can only be corrected by repicking the amplitudes.

Amplitude for determining MS

Amplitude for MS is defined as the maximum velocity on a wide band instrument (3 -60 sec or 0.017 - 0.3 Hz). Using the K(MS) option, a velocity trace (nm/s) in the frequency band 0.017 - 0.3 Hz is displayed. The maximum amplitude in nm/s (irrespective of frequency) is picked and displayed below the trace and written to the S-file with phase name IVMs_BB. In principle, MS can be calculated using any instrument, but in practice it can only be used if the surface wave is seen clearly on an unfiltered broad band velocity record. The big advantage with using MS is to avoid the 18-22 s limitation needed for Ms. The Butterworth filter 0.017 - 0.3 Hz , 8 poles, is hardwired and cannot be modified with additional filters.

Problem: If a long trace (large number of samples) is used, the instrument correction might fail (funny result seen) due to numerical overflow in the spectral conversion. Choose a shorter window.


next up previous contents index
Next: 8.10 Determine azimuth of Up: 8. Trace plotting, phase Previous: 8.8 Theoretical arrival times   Contents   Index
Peter Voss : Wed Aug 9 08:16:56 UTC 2017