Seismic observatory processing is tuned to detect and locate the majority of earthquakes which are characterized by well observed body wave arrivals. However there is a class of events which are often missed because of their low frequency signals. While the body waves may not be observed, the surface waves generated may permit detection and location. These events may be due to "slow earthquakes", landslides or other phenomena.
This tutorial focuses on the use of the surface wave to detect an event through a set of examples.
A review of the Fourier transform and its properties, the Hilbert transform and the Discrete Foourier Transform are given in Theory.pdf.
This review gave the background for applying time shifts, removing the effects of dispersion and the creation on the signal envelope. This tutorial focuses on the use of the surface-wave signal to detect and event. It will do this by compressing the signal and forming an envelope. Section_01 shows some characteristics of signals as a function of epicentral distance in a spherical Earth model.
Section_02 creates a sample data set to test the compression algorithm for the simple case of noise free observations. Thus the retults are independent of the event magnitude.
Section_03 uses the sample data set created oin Section_02 to prototype the operational use of the data compression. The distinguishing feature is that one would apply the detection in progressive time windows. This will also compare the performance without and with a windowing based on the origin time and group velocity range.
Section_05 shows the effect of changing the length of the waveform window.
Section_06 focuses on the effect of station noise on the stack as a function of the source moment magnitude.