Signal Processing

The following documentation explains, in chronological order, all the steps performed to construct the amplitude spectra used for the inversion.

Trace Processing

1. Traces are checked for gaps and overlaps. Traces with cumulative gap or overlap duration larger than gap_max or overlap_max, respectively, are skipped.

2. The trace mean is removed (only if the configuration parameter trace_units is set to auto, i.e., if the trace has not been preprocessed outside SourceSpec).

3. Gaps and overlaps are merged.

4. Traces with RMS smaller than rmsmin are skipped.

5. Traces are optionally checked for clipping (see Clipping Detection).

6. Instrumental response is removed and trace transformed in its physical units (e.g., velocity, acceleration).

7. Trace is filtered.

8. Signal to noise ratio is measured as the ratio between signal RMS in the P- or S-window (depending on the wave_type parameter) and the RMS of the noise window. Traces with signal to noise ratio smaller than sn_min are skipped.

See the source code of ssp_process_traces.process_traces() for implementation details.

Spectral Processing

1. A check is made to see if the signal window contains enough data. Traces with no data or more than 25% of zero values are skipped. This is typically due to a wrong specification of signal window (e.g., wrong P or S arrivals).

2. Traces are integrated to displacement in time domain, if time_domain_int is True.

3. Signal and noise windows are cut and tapered.

4. The noise window is checked. If the ratio between noise RMS and signal RMS is smaller than 1e-6, the noise is considered not significant and the trace is skipped.

5. The amplitude spectra of the signal and noise windows are computed, using numpy.fft.rfft(). If spectral_win_length is not None, the signal is zero-padded to this length before computing the Fast Fourier Transform.

6. Spectra are integrated to displacement in frequency domain, if time_domain_int is False.

7. Amplitude spectra are windowed (see config parameters freq1_broadb, freq2_broadb and similar).

8. Geometrical spreading is corrected (see Geometrical spreading).

9. Amplitude spectra are converted to seismic moment units (see Building spectra).

10. Amplitude spectra are resampled in \(log_{10}\) frequency spacing.

11. The resampled spectra are smoothed. The smoothing window width is defined in frequency decades (config parameter spectral_smooth_width_decades)

12. The spectral signal to noise ratio is checked. Amplitude spectra with signal to noise ratio smaller than spectral_sn_min are skipped.

13. The “H” component is built based on one or more spectral components, depending on the wave_type and ignore_vertical config parameters:

    • if wave_type is P or S:

      • if ignore_vertical is False, the two horizontals and the vertical components are combined;

      • if ignore_vertical is True, only the two horizontals components are combined;

    • if wave_type is SV:

      • if ignore_vertical is False, the radial and the vertical component are combined;

      • if ignore_vertical is True, only the radial component is used;

    • if wave_type is SH:

      • only the transverse component is used;

    Spectra are combined through the root sum of squares (see Overview).

14. All the amplitude spectra are converted to moment magnitude units (see Building spectra).

15. Station corrections are applied, if requested (see Station Residuals).

16. The weight spectrum is built, depending on the config option weighting.

See the source code of ssp_build_spectra.build_spectra() for implementation details.