Michail Kulesh

Characterization of polarization attributes of seismic waves using continuous wavelet transforms

Complex-trace analysis is the method of choice for analyzing polarized data. Because particle motion can be represented by instantaneous attributes that show distinct features for waves of different polarization characteristics, it can be used to separate and characterize these waves. Traditional methods of complex-trace analysis only give the instantaneous 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 polarization attributes of seismic signals in the wavelet domain 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 possibility of performing the complete wave-mode separation/filtering process in the wavelet ...

Instantaneous polarization attributes based on an adaptive approximate covariance method

We introduce a method for computing instantaneous-polarization attributes from multicomponent signals. This is an improvement on the standard covariance method (SCM) because it does not depend on the window size used to compute the standard covariance matrix. We overcome the window-size problem by deriving an approximate analytical formula for the cross-energy matrix in which we automatically and adaptively determine the time window. The proposed method uses polarization analysis as applied to multicomponent seismic by waveform separation and filtering.

Polarization analysis of a Pi2 pulsation using continuous wavelet transform

In this contribution, we extend a series of previous works focused on an investigation of signal’s polarization attributes using the continuous wavelet transform, where we proposed a method to map instantaneous polarization attributes of multicomponent signals in the wavelet domain and explicitly relate these attributes with the wavelet transform coefficients of the analyzed signal. In this work, we applied our polarization method to an examination of characteristics of Pi2 pulsations. We have shown some merits of the use of the continuous wavelet transform for the Pi2 pulsations’ analysis. First, we used our polarization method for the geomagnetic field data from the MSR, KAK, GUA, SMA, BLM and LAQ observatories and showed some correlations between the polarization parameters of pulsation and the station’s position (nightside or dayside). Secondly, we considered the signal’s north components of a pair of stations and demonstrated a time-frequency variations of the phase difference between two stations during the pulsation.

Estimating polarization attributes with an adaptive covariance method in the wavelet domain

In this contribution we introduce a method of computing instantaneous polarization attributes from multicomponent signal recordings in the time-frequency domain using continuous wavelet transform (CWT). The proposed method is a twofold improvement of the standard covariance technique. Firstly the time-window for the covariance matrix computation is adaptively selected, which allows computation of the polarization parameters at each time point (no interpolation is required). Secondly the use of CWT allows the construction of filter to separate events overlapping in time but living in different frequency band.

Inverse Problems and Parameter Identification in Image Processing

Many problems in imaging are actually inverse problems. One reason for this is that conditions and parameters of the physical processes underlying the actual image acquisition are usually not known. Examples for this are the inhomogeneities of the magnetic field in magnetic resonance imaging (MRI) leading to nonlinear deformations of the anatomic structures in the recorded images, material parameters in geological structures as unknown parameters for the simulation of seismic wave propagation with sparse measurement on the surface, or temporal changes in movie sequences given by intensity changes or moving image edges and resulting from deformation, growth and transport processes with unknown fluxes. The underlying physics is mathematically described in terms of variational problems or evolution processes. Hence, solutions of the forward problem are naturally described by partial differential equations. These forward models are reflected by the corresponding inverse problems as well. Beyond these concrete, direct modeling links to continuum mechanics abstract concepts from physical modeling are successfully picked up to solve general perceptual problems in imaging. Examples are visually intuitive methods to blend between images showing multiscale structures at different resolution or methods for the analysis of flow fields.