Parametric Decomposition of Pulsed Lidar Signals with Noise Corruption Using FRFT Spectrum Analysis

The parametric decomposition of full-waveform Lidar data is challenging when faced with heavy noise scenarios. In this paper, we report a fractional Fourier transform (FRFT)-based approach for accurate parametric decomposition of pulsed Lidar signals with noise corruption. In comparison with other joint time-frequency analysis (JTFA) techniques, FRFT is found to present a one-dimensional Lidar signal by a particular two-dimensional spectrum, which can exhibit the mathematical distribution of the multiple components in Lidar signals even with a heavy noise interference. A FRFT spectrum-processing solution with histogram clustering and moving LSM fitting is designed to extract the amplitude, time offset, and pulse width contained in the mathematical distribution. Extensive experimental results demonstrate that the proposed FRFT spectrum analysis method can remarkably outperform the conventional Levenberg–Marquardt-based method. In particular, it can accurately decompose the amplitudes, time offsets, and pulse widths of the pulsed Lidar signal with a −10-dB signal-to-noise-ratio by mean deviation ratios of 4.885%, 0.531%, and 7.802%, respectively.

Wavefield separation for borehole acoustic reflection survey using parametric decomposition and waveform inversion

We have developed a wavefield separation filter for borehole acoustic reflection surveys (BARS) that uses parametric decomposition and waveform inversion, which we call the PWI filter. A BARS survey uses a sonic logging tool in a fluid-filled borehole to image near-borehole structure. Signals from a monopole or dipole source are reflected from geologic interfaces and recorded by arrays of receivers of the same tool. Because amplitudes of direct head waves and borehole modes are significantly larger than those of the event signals, wavefield separation to extract the event signals is crucial for BARS processing. The PWI filter estimates the direct head waves and borehole modes using the parametric decomposition, which is based on a 1D wave propagation model in the frequency domain. The wave-propagation model is calibrated using waveform inversion, which solves for the slowness and attenuation of the waves. The inversion is regularized using the assumption that the slowness and attenuation smoothly vary with frequency; the nonlinear system of equations is iteratively solved using the Newton method. An example of wavefield separation is shown for field data for a very fast formation for a monopole source. After using the PWI filter to separate the S-waves and direct and reflected Stoneley waves, we obtain the final filtered waveforms by further applying a median filter to separate the residual waveforms, which are not separated by the PWI filter.

Non-Parametric Wavelet Functional Analysis for Horizontal and Vertical displacements Derived from GPS Stations in Western Alaska during the Year 2012

In order to analyze the dynamic processes of the Earth interior and the effect of the propagation of the seismic waves to the surface, a comprehensive study of the Earth crust kinematics is necessary. Although the Global Positing System (GPS) is a powerful method to measure ground displacements and velocities both horizontally and vertically as well as to infer the tectonic stress regime generated by the subsurface processes (from local fault systems to huge tectonic plate movements and active volcanoes), the complexity of the deformation pattern generated during such movements is not always easy to be interpreted. Therefore, it is necessary to work on new methodologies and modifying the previous approaches in order to improve the current methods and better understand the crustal movements. In this paper, we focus on western Alaska area, where many complex faults and active volcanoes exist. In particular, we analyze the data acquired each 30 seconds by three GPS stations located in western Alaska (AC31, AB09 and AB11) from January 1, 2012 to December 31, 2012 in order to compute their displacements in horizontal and vertical components by vectorial summation of the average daily and annual velocities components. Furthermore, we design non-parametric DMeyer and Haar wavelets for horizontal and vertical velocities directions in order to identify significant and homogenous displacements during the year 2012. Finally, the non-parametric decomposition of total horizontal and vertical normalized velocities based on level 1 and level 2 coefficients have been applied to compute normal and cumulative probability histograms related to the accuracy and statistical evolution of each applied wavelet. The results present a very good agreement between the designed non-parametric wavelets and their decomposition functions for each of the three above mentioned GPS stations displacements and velocities during the year 2012.