Characterization of polarization attributes of seismic waves using continuous wavelet transforms Mamadou S. Diallo 1 , Michail Kulesh 1 , Matthias Holschneider 1 , Frank Scherbaum 2 , and Frank Adler 3 ABSTRACT Complex-trace analysis is the method of choice for ana- lyzing polarized data. Because particle motion can be repre- sented by instantaneous attributes that show distinct fea- tures for waves of different polarization characteristics, it can be used to separate and characterize these waves. Tradi- tional methods of complex-trace analysis only give the in- stantaneous attributes as a function of time or frequency. However, for transient wave types or seismic events that overlap in time, an estimate of the polarization parameters requires analysis of the time-frequency dependence of these attributes. We propose a method to map instantaneous po- larization attributes of seismic signals in the wavelet do- main and explicitly relate these attributes with the wavelet- transform coefficients of the analyzed signal. We compare our method with traditional complex-trace analysis using numerical examples. An advantage of our method is its pos- sibility of performing the complete wave-mode separation/ filtering process in the wavelet domain and its ability to pro- vide the frequency dependence of ellipticity, which contains important information on the subsurface structure. Further- more, using 2-C synthetic and real seismic shot gathers, we show how to use the method to separate different wave types and identify zones of interfering wave modes. INTRODUCTION Multicomponent seismic recording provides increased informa- tion for subsurface characterization, particularly in the estimation of the polarization states of seismic arrivals. The processing of such data sets is computationally expensive and requires sophisti- cated techniques in order to infer the physical properties and struc- ture of the subsurface from the bulk of available information. With multicomponent data, usually one is confronted with the issue of separating seismic events of different polarization characteristics. For instance, one would like to distinguish between the body waves P- and S-waves that are linearly polarized from elliptically polarized Rayleigh waves. Polarization analysis is also used to identify shear-wave splitting Rene et al., 1986; Li and Crampin, 1991. Given a signal from three component recordings, with S x  t, S y  t, and S z  t representing the seismic traces recorded in three or- thogonal directions, any combination of two orthogonal compo- nents can be selected for the polarization analysis. Within the con- text of Rayleigh-wave characterization, one can select a combina- tion of the vertical component S z  t with the inline horizontal com- ponent either S x  t or S y  t. Note that sometimes obtaining the in- line horizontal component requires an appropriate rotation of S x  t and S y  t. Polarization analysis also can be carried out for all com- ponents simultaneously Morozov and Smithson, 1996. Use of in- stantaneous attributes as defined by Taner et al. 1979 allows us to quantify the polarization of shear waves. Because Rayleigh waves are strongly dispersive in heterogeneous media, their polarization attributes are both frequency and mode dependent Shieh and Herr- mann, 1990. In the context of seismic-hazard assessment using ambient vibrations, the characterization of this frequency depen- dence is of enormous practical interest. Particularly in connection with dispersion measurements, the frequency dependence of the polarization of Rayleigh-wave packages in ambient vibration records can be used to help predict the shakeability of the corre- sponding subsurface structure Scherbaum et al., 2003; Ohrnberger et al., 2003. In exploration seismology, however, Rayleigh-wave arrivals are considered to be coherent noises that must be filtered in order to enhance reflection events of interest. René et al. 1986 proposed a method for multicomponent seis- Manuscript received by the Editor July 4, 2003; revised manuscript received May 10, 2005; published online May 26, 2006. 1 University of Potsdam, Applied and Industrial Mathematics, Am Neuen Palais 10, 14469, Potsdam, Germany. E-mail: mamadou.s.diallo@exxonmobil. com. 2 University of Potsdam, Faculty of Geoscience, Karl-Liebnecht-Strasse 24-25, 14414 Potsdam, Germany. E-mail: fs@geo.uni-potsdam.de. 3 University of Potsdam, Applied and Industrial Mathematics, am Neuen Palais 10, 14469, Potsdam, Germany. E-mail: adler@rz.uni-potsdam.de. © 2006 Society of Exploration Geophysicists. All rights reserved. GEOPHYSICS, VOL. 71, NO. 3 MAY-JUNE 2006; P. V67–V77, 7 FIGS., 2 TABLES. 10.1190/1.2194511 V67