Instantaneous Frequency Attribute Comparison

NASA Astrophysics Data System (ADS)

The instantaneous seismic data attribute provides a different means of seismic interpretation, for all types of seismic data. It first came to the fore in exploration seismology in the classic paper of Taner et al (1979), entitled " Complex seismic trace analysis". Subsequently a vast literature has been accumulated on the subject, which has been given an excellent review by Barnes (1992). In this research we will compare two different methods of computation of the instantaneous frequency. The first method is based on the original idea of Taner et al (1979) and utilizes the derivative of the instantaneous phase of the analytic signal. The second method is based on the computation of the power centroid of the time-frequency spectrum, obtained using either the Gabor Transform as computed by Margrave et al (2011) or the Stockwell Transform as described by Stockwell et al (1996). We will apply both methods to exploration seismic data and the DPRK events recorded in 2006 and 2013. In applying the classical analytic signal technique, which is known to be unstable, due to the division of the square of the envelope, we will incorporate the stabilization and smoothing method proposed in the two paper of Fomel (2007). This method employs linear inverse theory regularization coupled with the application of an appropriate data smoother. The centroid method application is straightforward and is based on the very complete theoretical analysis provided in elegant fashion by Cohen (1995). While the results of the two methods are very similar, noticeable differences are seen at the data edges. This is most likely due to the edge effects of the smoothing operator in the Fomel method, which is more computationally intensive, when an optimal search of the regularization parameter is done. An advantage of the centroid method is the intrinsic smoothing of the data, which is inherent in the sliding window application used in all Short-Time Fourier Transform methods. The Fomel technique has a larger CPU run-time, resulting from the necessary matrix inversion. Barnes, Arthur E. "The calculation of instantaneous frequency and instantaneous bandwidth.", Geophysics, 57.11 (1992): 1520-1524. Fomel, Sergey. "Local seismic attributes.", Geophysics, 72.3 (2007): A29-A33. Fomel, Sergey. "Shaping regularization in geophysical-estimation problems." , Geophysics, 72.2 (2007): R29-R36. Stockwell, Robert Glenn, Lalu Mansinha, and R. P. Lowe. "Localization of the complex spectrum: the S transform."Signal Processing, IEEE Transactions on, 44.4 (1996): 998-1001. Taner, M. Turhan, Fulton Koehler, and R. E. Sheriff. "Complex seismic trace analysis." Geophysics, 44.6 (1979): 1041-1063. Cohen, Leon. "Time frequency analysis theory and applications."USA: Prentice Hall, (1995). Margrave, Gary F., Michael P. Lamoureux, and David C. Henley. "Gabor deconvolution: Estimating reflectivity by nonstationary deconvolution of seismic data." Geophysics, 76.3 (2011): W15-W30.

Yedlin, M. J.; Margrave, G. F.; Ben Horin, Y.

2013-12-01