DECONVOLUTION AND SPECTRAL ESTIMATION USING FINAL PREDICTION ERROR

Geophysics ◽  
1975 ◽  
Vol 40 (3) ◽  
pp. 411-425 ◽  
Author(s):  
Gerard J. Fryer ◽  
Mark E. Odegard ◽  
George H. Sutton
Keyword(s):  
Time Series ◽  
Prediction Error ◽  
Spectral Estimation ◽  
Stationary Time Series ◽  
Multiple Time ◽  
Ocean Bottom ◽  
Ocean Bottom Seismometer ◽  
Spectral Estimates ◽  
Predictive Deconvolution ◽  
Final Prediction Error

Least‐squares, zero‐lag inverse filters may be used for predictive deconvolution of stationary time series and for obtaining autoregressive or maximum entropy spectral estimates. The greatest problem in finding such an inverse filter is determining the optimum operator length for a given finite length of data. The identical problem of determining the correct order of an autoregressive model for the data has been solved by Akaike, whose final prediction error (FPE) statistic is a minimum for the optimum length model. This minimum FPE criterion may be applied to both single and multiple time series. The FPE procedure has been used successfully on simultaneous three‐component seismometer and hydrophone data for the detection of refracted arrivals from explosions up to 1350 km away and for estimation of spectra of microseismic noise observed at the time of each shot. The data were recorded with an ocean bottom seismometer.

Characteristics of Current-Induced Harmonic Tremor Signals in Ocean-Bottom Seismometer Records

2021 ◽  
Author(s):  
David Essing ◽  
Vera Schlindwein ◽  
Mechita C. Schmidt-Aursch ◽  
Celine Hadziioannou ◽  
Simon C. Stähler
Keyword(s):  
Time Series ◽  
Fundamental Frequency ◽  
Volcanic Tremor ◽  
Mode Locking ◽  
Spectral Amplitude ◽  
Bottom Current ◽  
Ocean Bottom ◽  
Ocean Bottom Seismometer ◽  
Natural Sources ◽  
Bottom Currents

Abstract Long-lasting harmonic tremor signals are frequently observed in spectrograms of seismological data. Natural sources, such as volcanoes and icebergs, or artificial sources, such as ships and helicopters, produce very similar harmonic tremor episodes. Ocean-bottom seismometer (OBS) records may additionally be contaminated by tremor induced by ocean-bottom currents acting on the OBS structure. This harmonic tremor noise may severely hinder earthquake detection and can be misinterpreted as volcanic tremor. In a 160-km-long network of 27 OBSs deployed for 1 yr along the Knipovich ridge in the Greenland Sea, harmonic tremor was widely observed away from natural sources such as volcanoes. Based on this network, we present a systematic analysis of the characteristics of hydrodynamically induced harmonic tremor in OBS records to make it distinguishable from natural tremor sources and reveal its generation processes. We apply an algorithm that detects harmonic tremor and extracts time series of its fundamental frequency and spectral amplitude. Tremor episodes typically occur twice per day, starting with fundamental frequencies of 0.5–1.0 Hz, and show three distinct stages that are characterized by frequency-gliding, mode-locking, and large spectral amplitudes, respectively. We propose that ocean-bottom currents larger than ∼5  cm/s cause rhythmical Karman vortex shedding around protruding structures of the OBS and excite eigenvibrations. Head-buoy strumming is the most likely source of the dominant tremor signal, whereas a distinctly different tremor signal with a fundamental frequency ∼6  Hz may be related to eigenvibrations of the radio antenna. Ocean-bottom current velocities reconstructed from the fundamental tremor frequency and from cross correlation of tremor time series between stations match observed average current velocities of 14–20  cm/s in this region. The tremor signal periodicity shows the same tidal constituents as the forcing ocean-bottom currents, which is a further evidence of the hydrodynamic nature of the tremor.

Ergodicity of stationary white Gaussian processes

Geophysics ◽  
1998 ◽  
Vol 63 (6) ◽  
pp. 2091-2092
Author(s):  
Santi K. Ghosh
Keyword(s):  
Time Series ◽  
Signal Processing ◽  
Decomposition Theorem ◽  
Seismic Signal ◽  
Stationary Time Series ◽  
Stationary Time ◽  
Predictive Deconvolution ◽  
Minimum Delay ◽  
Seismic Signal Processing ◽  
Noise Models

Stationary time series is an important concept in seismic signal processing. According to Robinson (1967), the method of predictive deconvolution is the minimum‐delay interpretation of the decomposition theorem of Wold (1938) for stationary time series. Stationary noise models have found use in geophysics as well (Robinson and Treitel, 1980).

scholarly journals Nonparametric and parametric methods of spectral analysis

2019 ◽  
Vol 283 ◽  
pp. 07002 ◽  
Author(s):  
Hangfang Zhao ◽  
Lin Gui
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
High Resolution ◽  
Spectral Estimation ◽  
Estimation Method ◽  
Parametric Estimation ◽  
Stationary Time Series ◽  
Estimation Methods ◽  
Practical Applications ◽  
Small Variance

Spectral Analysis is one of the most important methods in signal processing. In practical application, it is critical to discuss the power spectral density estimation of finite data sampled from some stationary time series. A spectral estimator is expected to have good statistical properties such as consistency, high resolution and small variance. For one spectral estimation method, there exists a trade-off between high resolution and small variance. The paper provides a comparison of several popular spectral methods from both theoretical properties and practical applications. We first address several basic nonparametric methods, whose statistical characters are analysed. Then we explain the connections and differences between temporal windowing and lag windowing. Thereafter, the confidence intervals of both windows are given and used to evaluate the estimated results. Besides, several different parametric estimation methods of autoregressive time series are compared, and whose properties and effects are also introduced. Building on our understanding of these studies, we then apply parametric and nonparametric spectral estimation methods on the data of ocean surface wave height.

SEVERAL FUNDAMENTAL PROPERTIES OF DCCA CROSS-CORRELATION COEFFICIENT

Fractals ◽  
2017 ◽  
Vol 25 (02) ◽  
pp. 1750017 ◽  
Author(s):  
XIAOJUN ZHAO ◽  
PENGJIAN SHANG ◽  
JINGJING HUANG
Keyword(s):  
Time Series ◽  
Correlation Coefficient ◽  
Cross Correlation ◽  
Stationary Time Series ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Linear Measure ◽  
Fundamental Properties ◽  
Cross Correlation Analysis ◽  
Synthetic Time Series

The (detrended cross-correlation analysis) DCCA cross-correlation coefficient was proposed to measure the level of long-range cross-correlations between two non-stationary time series on multiple time scales. It has been applied to diverse areas of interest, although many properties of this method are not clear. In this paper, we theoretically study several fundamental properties of the DCCA cross-correlation coefficient, which contributes to acquiring more statistical characteristics of this measure. We resort to a synthetic time series that is followed by the integration and the detrending procedures of the DCCA cross-correlation coefficient, which divide the steps to estimate the coefficient into two portions. The former portion, including the integration and the detrending, is proved to be a linear transformation. The second portion is devoted to measuring Pearson’s [Formula: see text] between two synthetic time series. We confirm that the DCCA cross-correlation coefficient is also a linear measure by definition. The simulations including the ARFIMA processes and the multifractal binomial measures are numerically analyzed, which confirm the theoretical analysis.

DETECTION OF P‐WAVES FROM WEAK SOURCES AT GREAT DISTANCES

Geophysics ◽  
1964 ◽  
Vol 29 (2) ◽  
pp. 197-211 ◽  
Author(s):  
Jon F. Claerbout
Keyword(s):  
Time Series ◽  
Prediction Error ◽  
P Wave ◽  
Pass Band ◽  
Multiple Time ◽  
Multiple Time Series ◽  
P Waves ◽  
Short Period ◽  
Band Pass ◽  
Detection Of Signals

Optimum (Wiener sense) filters for suppression of noise in multiple time series are computed by a new method due to E. A. Robinson. Filters for prediction error and interpolation error have been used to detect P‐wave signals from three teleseismic events. These filters facilitate detection of signals in noise with low signal‐to‐noise ratios. The instrumentation consists of short‐period Benioff seismometers, both three‐component stations and surface arrays of verticals. It was found that microseismic noise in the pass band of these instruments is more accurately termed “Brownian motion of a surface” than “random waveforms with characteristic direction(s) of propagation.” Thus, single time‐series filters work almost as well as multiple time‐series matrix filters. Prediction‐error filters gave results substantially more satisfactory than simple band‐pass filters.

Optimal reorientation of geophysical sensors: A quaternion-based analytical solution

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. F19-F30 ◽  
Author(s):  
Lars Krieger ◽  
Francesco Grigoli
Keyword(s):  
Time Series ◽  
Time Series Data ◽  
A Priori ◽  
Synthetic Data ◽  
Optimal Solution ◽  
Seismic Profile ◽  
Series Data ◽  
Ocean Bottom ◽  
Full Time ◽  
Ocean Bottom Seismometer

One of the most critical problems affecting geophysical data acquisition procedures is related to the misorientation of multicomponent sensors with respect to a common reference system (e.g., geographic north). In many applications, misoriented sensors affect data analysis procedures, leading to errors in results and interpretations. These problems generally occur in applications where the orientation of the sensor cannot be actively controlled and is not known a priori, e.g., geophysical sensors deployed in borehole installations or on the seafloor. We have developed a quaternion-based method for the optimal reorientation of multicomponent geophysical sensors. In contrast to other approaches, we took into account the full time-series record from all sensor components. Therefore, our method could be applied to all time-series data and was not restricted to a certain type of geophysical sensor. Our method allows the robust calculation of relative reorientations between two-component or three-component sensors. By using a reference sensor in an iterative process, this result can be extended to the estimation of absolute sensor orientations. In addition to finding an optimal solution for a full 3D sensor rotation, we have established a rigorous scheme for the estimation of uncertainties of the resulting orientation parameters. We tested the feasibility and applicability of our method using synthetic data examples for a vertical seismic profile and an ocean bottom seismometer array. We noted that the quaternion-based reorientation method is superior to the standard approach of a single-parameter estimation of rotation angles.

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