Fast sparsity-promoting least-squares migration with multiples in the time domain

2017 ◽  
Author(s):  
Mengmeng Yang ◽  
Emmanouil Daskalakis ◽  
Felix Herrmann
Keyword(s):  
Least Squares ◽  
Time Domain ◽  
The Time Domain ◽  
Least Squares Migration

scholarly journals A New Method for Time Series Filtering near Endpoints

2008 ◽  
Vol 25 (4) ◽  
pp. 534-546 ◽  
Author(s):  
Anthony Arguez ◽  
Peng Yu ◽  
James J. O’Brien
Keyword(s):  
Time Series ◽  
Least Squares ◽  
Time Domain ◽  
Southern Oscillation ◽  
Fundamental Property ◽  
Great Promise ◽  
Constraint Forces ◽  
Variance Method ◽  
Equal Variance ◽  
The Time Domain

Abstract Time series filtering (e.g., smoothing) can be done in the spectral domain without loss of endpoints. However, filtering is commonly performed in the time domain using convolutions, resulting in lost points near the series endpoints. Multiple incarnations of a least squares minimization approach are developed that retain the endpoint intervals that are normally discarded due to filtering with convolutions in the time domain. The techniques minimize the errors between the predetermined frequency response function (FRF)—a fundamental property of all filters—of interior points with FRFs that are to be determined for each position in the endpoint zone. The least squares techniques are differentiated by their constraints: 1) unconstrained, 2) equal-mean constraint, and 3) an equal-variance constraint. The equal-mean constraint forces the new weights to sum up to the same value as the predetermined weights. The equal-variance constraint forces the new weights to be such that, after convolved with the input values, the expected time series variance is preserved. The three least squares methods are each tested under three separate filtering scenarios [involving Arctic Oscillation (AO), Madden–Julian oscillation (MJO), and El Niño–Southern Oscillation (ENSO) time series] and compared to each other as well as to the spectral filtering method—the standard of comparison. The results indicate that all four methods (including the spectral method) possess skill at determining suitable endpoints estimates. However, both the unconstrained and equal-mean schemes exhibit bias toward zero near the terminal ends due to problems with appropriating variance. The equal-variance method does not show evidence of this attribute and was never the worst performer. The equal-variance method showed great promise in the ENSO project involving a 5-month running mean filter, and performed at least on par with the other realistic methods for almost all time series positions in all three filtering scenarios.

Deconvolving the ghost effect of the water surface in marine seismics

Geophysics ◽  
2000 ◽  
Vol 65 (6) ◽  
pp. 1831-1836 ◽  
Author(s):  
Santi Kumar Ghosh
Keyword(s):  
Least Squares ◽  
Time Domain ◽  
Water Surface ◽  
Inverse Filtering ◽  
Autocorrelation Matrix ◽  
Common Time ◽  
Unit Impulse ◽  
The Time Domain ◽  
Sampling Instant ◽  
Selection Of

The ghost filters arising from the effect of the water surface on both source and receiver sides have a common time domain representation that consists of a unit impulse followed by its ghost, which is a delayed, negative unit impulse. The origin of the difficulties of deghosting lies in the zeroes in the spectrum of the ghost filter, which render incorrect any deghosting through least‐squares inverse filtering in the time domain. Another shortcoming of the time domain approach is that the digital description of the ghost filter is inexact when a sampling instant does not coincide with the instant of the onset of the ghost impulse. A frequency domain approach, on the other hand, is straightforward and accurate because it can avoid the zeroes of the filter either by explicitly choosing a recording band that excludes the zeroes or by recording at two depths. These two depths should be selected according to the criterion that their highest common measure is small enough to prevent zeroes at a common frequency of the two recordings. As the source‐side and the receiver‐side ghost filters have the same form, the criterion derived for the selection of the depths of the receivers would also hold for the selection of the depths of two sources whose aggregate signature is desired to have no zeroes in the spectrum, within the operative band. An important ramification of the analysis consists of the disproof of a prevalent conjecture that the zeroes in the spectrum of a wavelet make its autocorrelation matrix singular; actually, the zeroes cause an inexact and unacceptable least‐squares inverse, although the matrix itself is well conditioned.

Time-domain least-squares migration using the Gaussian beam summation method

2018 ◽  
Vol 214 (1) ◽  
pp. 548-572 ◽  
Author(s):  
Jidong Yang ◽  
Hejun Zhu ◽  
George McMechan ◽  
Yubo Yue
Keyword(s):  
Least Squares ◽  
Gaussian Beam ◽  
Time Domain ◽  
Summation Method ◽  
Least Squares Migration

An accelerated sparse time-invariant Radon transform in the mixed frequency-time domain based on iterative 2D model shrinkage

Geophysics ◽  
2013 ◽  
Vol 78 (4) ◽  
pp. V147-V155 ◽  
Author(s):  
Wenkai Lu
Keyword(s):  
Least Squares ◽  
Frequency Domain ◽  
Time Domain ◽  
Radon Transform ◽  
Real Data ◽  
Mixed Frequency ◽  
The Time Domain ◽  
Domain I ◽  
Time Invariant ◽  
2D Model

I have developed an accelerated sparse time-invariant Radon transform (RT) in the mixed frequency-time domain based on iterative 2D model shrinkage in the time domain. I denote it as SRTIS. In the traditional sparse time-invariant RT in the mixed frequency-time domain, the sparse RT is modeled as a sparse inverse problem that is solved by the iteratively reweighted least-squares (IRLS) algorithm in the time domain, and the forward and inverse RTs are implemented in the frequency domain. In this method, IRLS is replaced by iterative 2D model shrinkage, i.e., the sparsity of the Radon model is promoted by some simple 2D model shrinkage operations in the time domain. Synthetic and real data demultiple examples using the parabolic RTs are given to demonstrate the better performance of the SRTIS when compared with the least-squares-based RT, the frequency domain sparse RT, and the traditional time-domain sparse RT in the mixed frequency-time domain.

Direct determination of deuterium in untreated water and urine by NMR: application to DLW analysis

1995 ◽  
Vol 268 (5) ◽  
pp. E1018-E1026 ◽  
Author(s):  
J. T. Brenna ◽  
K. E. Yeager
Keyword(s):  
Least Squares ◽  
Time Domain ◽  
Fourier Transforms ◽  
Tap Water ◽  
Direct Determination ◽  
Average Error ◽  
Experimental Conditions ◽  
Wide Range ◽  
The Time Domain

Determination of deuterium (D) concentration in tap water and urine is demonstrated to average error approximately 0.5% (coefficient of variation) using a 400-MHz nuclear magnetic resonance (NMR) instrument. Time domain data are obtained using 0.75-ml samples in a broadband probe. Peak areas derived from absorption and magnitude mode Fourier transforms and least-squares fitting of the time domain free induction decays (FIDs) are all investigated as means to derive D concentrations from raw data. Least-squares fits using a sum of exponentially damped sinusoids, which yields estimates for the amplitude, damping constant (relaxation time), wavelength (resulting from mixing of precession and reference frequencies), and phase for each of the two components, are shown to provide the best precision for unfiltered FID. Amplitudes are proportional to the number of spins at each frequency, as analysis of untreated urine from doubly labeled water experiments yield highly linear washout data (r2 > 0.99998) for baseline-corrected log-transformed data. The procedure is general and should extend to other body fluids with minimal modifications. These data show that least-squares curve fitting is the most precise method of quantitative NMR data reduction for a wide range of experimental conditions.

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