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2-‐2
i. Basic trace opera-ons and resampling
ii. Trace rota-ons
iii. Frequency domain opera-ons and filtering
Pre-‐processing
• Seismic data is rarely recorded in a form where it is directly (sensibly) analysable
• Instrumental factors, long period noise, temperature varia-ons and electronic interference all leave their mark on seismic data (especially from field deployments)
• Data may be recorded at different sampling rates at different sta-ons in the network, or at unnecessarily high rates (genera-ng unprocessable amounts of data)
• Finally, ALL real data contains noise which masks, to some degree or another, the signal of interest
• This lesson is an overview of SAC’s facili-es with dealing with these annoyances
Basic clean-‐up
• There are several commands which are run as a pre-‐processing step before most other processing task
• These are de-‐meaning and de-‐trending data, and removing glitches like -ming chirps or tears
• This essen-ally removes noise outside the frequency range of the data
• The commands for these are: rmean, rtrend and rglitches
• They have some op-ons (especially rglitches), but are generally run well with the default for most data
Example:
SAC> rglitches
SAC> rtrend
Resampling data
• A common processing step is up/down sampling data
• This might be for a variety of reasons (reduce file bloat, match other data)
• Primary command for upsampling is interpolate
• This uses ‘Wiggins’ interpola-on (Wiggins, BSSA, 1976) • Easiest is to specify a new DELTA • Note that this can turn unevenly spaced data into evenly
spaced (thus allowing spectral analysis, for example)
SAC> help interpolate
SUMMARY: Interpolates evenly or unevenly spaced data to a new sampling rate.
SYNTAX: INTERPOLATE {DELTA v} {EPSILON v} {BEGIN v|OFF} {NPTS n|OFF}
Resampling data • Upsampling
• Note that no new informa-on is gained: an upsampled trace is just a smoother version with more points
SAC> interp delta 2
SAC> interp delta 0.05
Downsampling data
• Unlike upsampling, downsampling can introduce ar-facts, through aliasing
• This can be mi-gated by pre-‐filtering the data to the target bandwidth before resampling (an(-‐aliasing)
• This is done by the command decimate • Decimate can reduce the sampling by a
factor n between 2-‐7
• Other factors can be achieved by chaining decimate commands
SAC> help decimate
SUMMARY: Decimates (downsamples) data, including an optional anti-aliasing FIR filter.
SYNTAX: DECIMATE {n} {FILTER {ON|OFF}}
Resampling data
• Example: decima-ng data
SAC> r example.sac SAC> lh delta npts b e
FILE: example.sac ----------------- delta = 0.10E-01 npts = 4096 b = 0.0 e = 40.950 SAC> decimate 2; decimate 5 SAC> lh delta npts b e
FILE: example.sac ----------------- delta = 0.10 npts = 410 b = 0.0 e = 40.90
2-‐2
i. Basic trace opera-ons and resampling
ii. Trace rota-ons
iii. Frequency domain opera-ons and filtering
Rota-ons • Some-mes, seismograms are not
recorded in the orienta-on most convenient to a par-cular processing method; either by accident or design
• However, with 3-‐component sensors we (theore-cally) record full vector displacement
• Any 3 orthogonal components can be rotated to form any other 3 with no loss of informa-on; this is equivalent to a frame of reference rota-on
Radial – Transverse reference frame
• A common rota-on in global seismology is to rotate horizontal components to radial-‐transverse reference frame
• The radial direc-on is in the direc-on of the great circle path between the earthquake and sta-on; transverse (or tangen(al) is perpendicular to that
• This separates the SH wavefield from the (coupled) P-‐SV wavefield, making interpreta-on of S-‐phases easier
Rota-ons in SAC
• Command to rotate SAC traces is rotate
• Only 2D rota-ons are available in SAC (but these can be chained together)
• Rotate operates on pairs of traces, these must be the same length, and have the same sample rate
• There are two kinds of rota-on …
SAC> help rotate
SUMMARY: Rotates a pair of data components through an angle.
SYNTAX: ROTATE {TO GCP | TO v | THROUGH v} {NORMAL|REVERSED}
Rotate THROUGH
• With the through op-on, either 2 horizontal traces, or 1 horizontal and 1 ver-cal are rotated through X degrees clockwise from their current orienta-on
• Rota-ons require the cmpinc and cmpaz headers to be set (and modify them)
SAC> r SWAV.BHZ SWAV.BHR SAC> lh cmpinc
FILE: SWAV.BHZ -------------- cmpinc = 0.0
FILE: SWAV.BHR -------------- cmpinc = 90.0 SAC> rotate through 30 SAC> lh cmpinc
FILE: SWAV.BHZ -------------- cmpinc = 30.0
FILE: SWAV.BHR -------------- cmpinc = 120.0
DEMO
Rotate TO
• With the to op-on, horizontal traces (only) are rotated to a specified azimuth (degrees c’wise from North) …
• or to the great circle path azimuth
• This generates the radial-‐transverse components
SAC> rotate to 45
SAC> rotate to gcp
DEMO
2-‐2
i. Basic trace opera-ons and resampling
ii. Trace rota-ons
iii. Frequency domain opera-ons and filtering
Frequency domain for seismology
• Fourier analysis represents a uniformly sampled signal as a weighted summa-on of sine-‐waves of different frequencies and phases (i.e., delays)
• Any signal, however complex (such as a seismic wave) can be perfectly represented by such a summa-on
• The set of coefficients which describe the amplitudes and phases of the sine waves at each frequency is called the frequency domain
• A -me variant signal like a seismic trace can, in principle, be transferred to and from the frequency domain losslessly
• Many opera-ons which are complex or impossible in the -me domain become trivial in the frequency domain
Amplitude spectra
• The frequency domain representa-on of a signal can be used to iden-fy dominant frequencies in a seismic trace; these might be signal, noise or both
Fast Fourier Transforms
• The Fast-‐Fourier Transform (FFT) allows rapid transforma-ons to (and from) the frequency domain.
• In SAC, the command fft computes the FFT of the current trace(s) in memory
• This creates a frequency domain representa-on of the traces
• The spectra can be plofed with the command plotsp
SAC> help fft
SUMMARY: Performs a discrete Fourier transform.
SYNTAX: FFT {WOMEAN|WMEAN} {RLIM|AMPH}
SAC> help plotsp
SUMMARY: Plots spectral data in several different formats.
SYNTAX: PLOTSP {type} {mode}
plotsp
• By default plotsp plots the amplitude spectrum and the phase, using logarithmic scales, however ogen just interested in the amplitude spectrum:
plots the amplitude spectrum only, using linear scales for both axes
SAC> plotsp am linlin
Reading and wri-ng spectral files
• Once FFT has been run on a trace, it is converted to a SAC spectral file. This can be saved and read using the normal SAC read/write commands.
• However, the amplitude or phase part of a spectral file can also be wrifen out as a normal SAC file, using the writesp command:
• will write out two normal SAC files, one called myfile.sac.AM containing the amplitude data, and one called myfile.sac.PH containing the phase data
• This can be useful for handling or plohng spectral data in a way not normally allowed in SAC
• The readsp command can be used to create a spectral file from two normal SAC files
SAC> writesp myfile.sac
Filtering
• If, using spectral analysis, we can determine what frequencies present in our seismogram represent noise, and which signal, we can filter out unwanted frequencies to improve our observa-on of the phases we are interested in.
• Filtering covers a very broad range of theory and methodology
• Filtering involves convolving a filter spectrum with the seismogram spectrum
• SAC has implements several filter spectra – most commonly employed is the Buferworth filter:
where f is frequency, fc is the cut-‐off frequency, and np is the number of poles (essen-ally the sharpness of the cut-‐off)
Example: 2-‐pole low-‐pass Buferworth filter
Filtering in SAC
• Main filter commands in SAC are highpass, lowpass and bandpass
• The filter type, corner frequencies, poles and number passes (1-‐2)are specified, e.g.:
Filters the current trace(s) with a 2-‐pole Buferworth filter, with corner frequencies at 0.02 Hz (50 seconds) and 0.1 Hz (10 seconds)
SAC> help bandpass
SUMMARY: Applies an IIR bandpass filter.
SYNTAX: BANDPASS {BUTTER|BESSEL|C1|C2} {CORNERS v1 v2} {NPOLES n} {PASSES n} {TRANBW v} {ATTEN v}
SAC> bp bu co 0.02 0.1 n 2 p 2
Tes-ng the response func-on of a filter
• To test what the amplitude spectra of a filter looks like: SAC> funcgen impulse delta 0.05 npts 4096 SAC> bp bu co 0.02 0.1 n 2 p 2 SAC> fft (10.6e)FFT default change: not removing the mean DC level after DFT is 0.10802E-04 SAC> plotsp am loglin
Shortcut is the filterdesign command …
SAC> fd bp bu co 5 25 n 2 p 2 delta 0.01 Note: Phase and group delays for single pass.