Time frequency of surface microseismic data recorded during two-hour stimulation job
Microseismic signals are actually non-stationary signals. In non-stationary signal processing field, the
- Short-Time Fourier Transform(STFT)
- Continuous Wavelet Transform(CWT) and
are the most common way to derive the time frequency representation for the non-stationary signals. The popular methods of STFT and Wavelet analysis have limitations in representing close frequencies and dealing with fast varying instantaneous frequencies and this is often the nature of microseismic signals.
The S-transform, which is first proposed by R.G. Stockwellin 1996, is unique in that it provides frequency-dependent resolution while maintaining a direct relationship with the Fourier spectrum. It is an extension of the ideas of the STFT and is based on a moving and scalable localizing Gaussian window. It proves to have a good performance of noise reduction as well as desirable characteristics that are absent in CWT. Therefore, the S-transform is a more preferable tool to track resonant frequencies and provide a detailed time frequency representation.Watch Full Movie Online Streaming Online and Download
Here we present time frequency spectra of one downhole microseismic data derived by use of the 3 methods mentioned above. The following are some Matlab codes/libraries will be used in following tutorial series, you can download them at will.
Here are the tutorials: