Smoothing imaging condition for shot-profile migration

Geophysics ◽  
2007 ◽  
Vol 72 (3) ◽  
pp. S149-S154 ◽  
Author(s):  
Antoine Guitton ◽  
Alejandro Valenciano ◽  
Dimitri Bevc ◽  
Jon Claerbout
Keyword(s):  
Time Domain ◽  
Signal To Noise Ratio ◽  
Wiener Filter ◽  
Window Size ◽  
Trial And Error ◽  
Data Set ◽  
Smoothing Operator ◽  
Imaging Condition ◽  
Damping Parameter ◽  
The Time Domain

Amplitudes in shot-profile migration can be improved if the imaging condition incorporates a division (deconvolution in the time domain) of the upgoing wavefield by the downgoing wavefield. This division can be enhanced by introducing an optimal Wiener filter which assumes that the noise present in the data has a white spectrum. This assumption requires a damping parameter, related to the signal-to-noise ratio, often chosen by trial and error. In practice, the damping parameter replaces the small values of the spectrum of the downgoing wavefield and avoids division by zero. The migration results can be quite sensitive to the damping parameter, and in most applications, the upgoing and downgoing wavefields are simply multiplied. Alternatively, the division can be made stable by filling the small values of thespectrum with an average of the neighboring points. This averaging is obtained by running a smoothing operator on the spectrum of the downgoing wavefield. This operation called the smoothing imaging condition. Our results show that where the spectrum of the downgoing wavefield is high, the imaging condition with damping and smoothing yields similar results, thus correcting for illumination effects. Where the spectrum is low, the smoothing imaging condition tends to be more robust to the noise level present in the data, thus giving better images than the imaging condition with damping. In addition, our experiments indicate that the parameterization of the smoothing imaging condition, i.e., choice of window size for the smoothing operator, is easy and repeatable from one data set to another, making it a valuable addition to our imaging toolbox.

scholarly journals Application of Laplace Domain Waveform Inversion to Cross-Hole Radar Data

2019 ◽  
Vol 11 (16) ◽  
pp. 1839
Author(s):  
Xu Meng ◽  
Sixin Liu ◽  
Yi Xu ◽  
Lei Fu
Keyword(s):  
Time Domain ◽  
Waveform Inversion ◽  
Radar Data ◽  
Dominant Frequency ◽  
Data Set ◽  
Laplace Domain ◽  
Full Waveform ◽  
Highly Nonlinear ◽  
The Time Domain ◽  
Ground Penetrating

Full waveform inversion (FWI) can yield high resolution images and has been applied in Ground Penetrating Radar (GPR) for around 20 years. However, appropriate selection of the initial models is important in FWI because such an inversion is highly nonlinear. The conventional way to obtain the initial models for GPR FWI is ray-based tomogram inversion which suffers from several inherent shortcomings. In this paper, we develop a Laplace domain waveform inversion to obtain initial models for the time domain FWI. The gradient expression of the Laplace domain waveform inversion is deduced via the derivation of a logarithmic object function. Permittivity and conductivity are updated by using the conjugate gradient method. Using synthetic examples, we found that the value of the damping constant in the inversion cannot be too large or too small compared to the dominant frequency of the radar data. The synthetic examples demonstrate that the Laplace domain waveform inversion provide slightly better initial models for the time domain FWI than the ray-based inversion. Finally, we successfully applied the algorithm to one field data set, and the inverted results of the Laplace-based FWI show more details than that of the ray-based FWI.

scholarly journals A SFTD Algorithm for Optimizing the Performance of the Readout Strategy of Residence Time Difference Fluxgate

Sensors ◽  
2018 ◽  
Vol 18 (11) ◽  
pp. 3985 ◽  
Author(s):  
Siyu Chen ◽  
Yanzhang Wang ◽  
Jun Lin
Keyword(s):  
Residence Time ◽  
Time Domain ◽  
Signal To Noise Ratio ◽  
Low Frequency ◽  
Transformation Method ◽  
Time Difference ◽  
Single Frequency ◽  
Time Frequency ◽  
Frequency Magnetic Field ◽  
The Time Domain

Residence time difference (RTD) fluxgate sensor is a potential device to measure the DC or low-frequency magnetic field in the time domain. Nevertheless, jitter noise and magnetic noise severely affect the detection result. A novel post-processing algorithm for jitter noise reduction of RTD fluxgate output strategy based on the single-frequency time difference (SFTD) method is proposed in this study to boost the performance of the RTD system. This algorithm extracts the signal that has a fixed frequency and preserves its time-domain information via a time–frequency transformation method. Thereby, the single-frequency signal without jitter noise, which still contains the ambient field information in its time difference, is yielded. Consequently, compared with the traditional comparator RTD method (CRTD), the stability of the RTD estimation (in other words, the signal-to-noise ratio of residence time difference) has been significantly boosted with sensitivity of 4.3 μs/nT. Furthermore, the experimental results reveal that the RTD fluxgate is comparable to harmonic fluxgate sensors, in terms of noise floor.

scholarly journals Transmission compensated primary reflection retrieval in the data domain and consequences for imaging

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. Q27-Q36 ◽  
Author(s):  
Lele Zhang ◽  
Jan Thorbecke ◽  
Kees Wapenaar ◽  
Evert Slob
Keyword(s):  
Thin Layer ◽  
Time Domain ◽  
Velocity Model ◽  
Original Data ◽  
Transmission Losses ◽  
Multiple Reflections ◽  
Data Set ◽  
Numerical Examples ◽  
The One ◽  
The Time Domain

We have developed a scheme that retrieves primary reflections in the two-way traveltime domain by filtering the data. The data have their own filter that removes internal multiple reflections, whereas the amplitudes of the retrieved primary reflections are compensated for two-way transmission losses. Application of the filter does not require any model information. It consists of convolutions and correlations of the data with itself. A truncation in the time domain is applied after each convolution or correlation. The retrieved data set can be used as the input to construct a better velocity model than the one that would be obtained by working directly with the original data and to construct an enhanced subsurface image. Two 2D numerical examples indicate the effectiveness of the method. We have studied bandwidth limitations by analyzing the effects of a thin layer. The presence of refracted and scattered waves is a known limitation of the method, and we studied it as well. Our analysis indicates that a thin layer is treated as a more complicated reflector, and internal multiple reflections related to the thin layer are properly removed. We found that the presence of refracted and scattered waves generates artifacts in the retrieved data.

Predictive processing of array acoustic waveform data

Geophysics ◽  
1997 ◽  
Vol 62 (6) ◽  
pp. 1710-1714 ◽  
Author(s):  
Xiao Ming Tang
Keyword(s):  
Time Domain ◽  
Predictive Processing ◽  
Multiple Wave ◽  
Data Set ◽  
Waveform Data ◽  
Array Data ◽  
Wave Data ◽  
Minimization Procedure ◽  
The Time Domain ◽  
Wave Modes

Estimation of wave velocity (or slowness) from array waveform data is a basic and very important process in acoustic logging and seismic processing. A predictive method is developed to process array waveform data containing multiple wave modes. These wave modes may overlap in both time and frequency and are inseparable using conventional techniques. In this new technique, the waveform at a receiver is modeled by a combination of wave data at other receivers using a time‐domain prediction theory. It is assumed that the array data contain a number of propagating modes. A minimization procedure is formulated to optimize the match between the predicted and measured waveforms, yielding slowness estimates of the wave modes across the array. Most important, the optimization is performed directly in the time domain using the entire array wave data set, including all possible data combinations. This strategy effectively reduces the noise effects and enhances the robustness of the estimation. Furthermore, the estimated slowness values can be used in formulating a procedure to split the array data into individual wave modes, allowing their behavior to be analyzed. Examples are shown to demonstrate the ability of the technique to extract wave slowness from multiple wavemode data.

Viscoacoustic waveform inversion of velocity structures in the time domain

Geophysics ◽  
2014 ◽  
Vol 79 (3) ◽  
pp. R103-R119 ◽  
Author(s):  
Jianyong Bai ◽  
David Yingst ◽  
Robert Bloor ◽  
Jacques Leveille
Keyword(s):  
Finite Difference ◽  
Time Domain ◽  
Field Data ◽  
Wave Equations ◽  
Finite Difference Methods ◽  
Waveform Inversion ◽  
Data Set ◽  
Velocity Models ◽  
Difference Methods ◽  
The Time Domain

Because of the conversion of elastic energy into heat, seismic waves are attenuated and dispersed as they propagate. The attenuation effects can reduce the resolution of velocity models obtained from waveform inversion or even cause the inversion to produce incorrect results. Using a viscoacoustic model consisting of a single standard linear solid, we discovered a theoretical framework of viscoacoustic waveform inversion in the time domain for velocity estimation. We derived and found the viscoacoustic wave equations for forward modeling and their adjoint to compensate for the attenuation effects in viscoacoustic waveform inversion. The wave equations were numerically solved by high-order finite-difference methods on centered grids to extrapolate seismic wavefields. The finite-difference methods were implemented satisfying stability conditions, which are also presented. Numerical examples proved that the forward viscoacoustic wave equation can simulate attenuative behaviors very well in amplitude attenuation and phase dispersion. We tested acoustic and viscoacoustic waveform inversions with a modified Marmousi model and a 3D field data set from the deep-water Gulf of Mexico for comparison. The tests with the modified Marmousi model illustrated that the seismic attenuation can have large effects on waveform inversion and that choosing the most suitable inversion method was important to obtain the best inversion results for a specific seismic data volume. The tests with the field data set indicated that the inverted velocity models determined from the acoustic and viscoacoustic inversions were helpful to improve images and offset gathers obtained from migration. Compared to the acoustic inversion, viscoacoustic inversion is a realistic approach for real earth materials because the attenuation effects are compensated.

EXACT WAVE‐SHAPING WITH A TIME‐DOMAIN DIGITAL FILTER OF FINITE LENGTH

Geophysics ◽  
1976 ◽  
Vol 41 (4) ◽  
pp. 659-672 ◽  
Author(s):  
R. F. Mereu
Keyword(s):  
Time Series ◽  
Time Domain ◽  
Symmetric Functions ◽  
Wiener Filter ◽  
Region Of Interest ◽  
Number Of Zeros ◽  
Series Of Experiments ◽  
Optimum Filter ◽  
The Time Domain ◽  
Spike Sequence

When the signs of alternate terms of a symmetric discrete time series are reversed and the newly created series is then convolved with the original series, the resultant time‐series will have alternate values equal to zero. This property of symmetric functions may be exploited to design a new deconvolution and wave‐shaping time‐domain filter which is capable of transforming a given wavelet into an output made up of a sequence of spikes separated by zeros, or a sequence of wavelets, whose shapes are identical to that of any desired wavelet. In its design, no Z-transform polynomials are factored or divided and no equations are solved. The weights are derived entirely in the time domain from a series of successively derived subfilters ([Formula: see text], [Formula: see text], [Formula: see text] ⋯ [Formula: see text]) which, when convolved with the original wavelet, creates the spike sequence output. These subfilters may be conveniently grouped into a symmetric component which is derived from the autocorrelation function, a component which depends upon the characteristics of the original wavelet and a component which depends upon the desired wavelet. The number of zeros separating the spike outputs may be controlled by increasing the number of sub‐filters N according to the formula [Formula: see text]. The Wiener filter is an optimum filter in the least‐squares sense but its errors occur across the output. The new filter is an optimum filter in an “error‐distribution” sense. Its errors are in reality the noncentral spikes of the spike sequence. By choosing the length properly, the errors may be moved away from the region of interest leaving that region effectively “error‐free”. A limitation to this procedure is the computational round‐off error which increases as the filter length is increased. In a series of experiments with various types of wavelets it was found that the spike position always occurs at the center of the filter, with the anticipation and memory components automatically falling into place. A very important property of the filter is the fact that the input parameters required for its design are identical to those needed for the normal equations of the Wiener filter. Initial tests with a noisy time‐series showed that the new filter could be effectively employed using the statistical properties of the noise in the same manner that the Wiener filter is applied.

scholarly journals Amplifier Noise Based Optical Steganography with Coherent Detection

2014 ◽  
Vol 2 (1) ◽  
Author(s):  
Ben Wu ◽  
Matthew P. Chang ◽  
Naomi R. Caldwell ◽  
Myles E. Caldwell ◽  
Paul R. Prucnal
Keyword(s):  
Time Domain ◽  
Short Range ◽  
Review Paper ◽  
Signal To Noise Ratio ◽  
Random Phase ◽  
Coherent Detection ◽  
The Public ◽  
Key Space ◽  
Optical Delay ◽  
The Time Domain

AbstractWe summarize the principle and experimental setup of optical steganography based on amplified spontaneous emission (ASE) noise. Using ASE noise as the signal carrier, optical steganography effectively hides a stealth channel in both the time domain and the frequency domain. Coherent detection is used at the receiver of the stealth channel. Because ASE noise has short coherence length and random phase, it only interferes with itself within a very short range. Coherent detection requires the stealth transmitter and stealth receiver to precisely match the optical delay,which generates a large key space for the stealth channel. Several methods to further improve optical steganography, signal to noise ratio, compatibility with the public channel, and applications of the stealth channel are also summarized in this review paper.

scholarly journals Time-Domain Multidimensional Deconvolution: A Physically Reliable and Stable Preconditioned Implementation

2021 ◽  
Vol 13 (18) ◽  
pp. 3683
Author(s):  
David Vargas ◽  
Ivan Vasconcelos ◽  
Matteo Ravasi ◽  
Nick Luiken
Keyword(s):  
Inverse Problem ◽  
Time Domain ◽  
Body Wave ◽  
Complex Salt ◽  
Iterative Solvers ◽  
Physical Constraints ◽  
Damping Parameter ◽  
Band Limited ◽  
The Time Domain ◽  
Multiple Elimination

Multidimensional deconvolution constitutes an essential operation in a variety of geophysical scenarios at different scales ranging from reservoir to crustal, as it appears in applications such as surface multiple elimination, target-oriented redatuming, and interferometric body-wave retrieval just to name a few. Depending on the use case, active, microseismic, or teleseismic signals are used to reconstruct the broadband response that would have been recorded between two observation points as if one were a virtual source. Reconstructing such a response relies on the the solution of an ill-conditioned linear inverse problem sensitive to noise and artifacts due to incomplete acquisition, limited sources, and band-limited data. Typically, this inversion is performed in the Fourier domain where the inverse problem is solved per frequency via direct or iterative solvers. While this inversion is in theory meant to remove spurious events from cross-correlation gathers and to correct amplitudes, difficulties arise in the estimation of optimal regularization parameters, which are worsened by the fact they must be estimated at each frequency independently. Here we show the benefits of formulating the problem in the time domain and introduce a number of physical constraints that naturally drive the inversion towards a reduced set of stable, meaningful solutions. By exploiting reciprocity, time causality, and frequency-wavenumber locality a set of preconditioners are included at minimal additional cost as a way to alleviate the dependency on an optimal damping parameter to stabilize the inversion. With an interferometric redatuming example, we demonstrate how our time domain implementation successfully reconstructs the overburden-free reflection response beneath a complex salt body from noise-contaminated up- and down-going transmission responses at the target level.

scholarly journals Accelerating linear system solvers for time-domain component separation of cosmic microwave background data

2020 ◽  
Vol 638 ◽  
pp. A73
Author(s):  
J. Papež ◽  
L. Grigori ◽  
R. Stompor
Keyword(s):  
Cosmic Microwave Background ◽  
Time Domain ◽  
Component Separation ◽  
Microwave Background ◽  
Data Set ◽  
Background Data ◽  
Cosmic Microwave Background Data ◽  
Subspace Recycling ◽  
The Time Domain ◽  
Sampling Procedures

Component separation is one of the key stages of any modern cosmic microwave background data analysis pipeline. It is an inherently nonlinear procedure and typically involves a series of sequential solutions of linear systems with similar but not identical system matrices, derived for different data models of the same data set. Sequences of this type arise, for instance, in the maximization of the data likelihood with respect to foreground parameters or sampling of their posterior distribution. However, they are also common in many other contexts. In this work we consider solving the component separation problem directly in the measurement (time-) domain. This can have a number of important benefits over the more standard pixel-based methods, in particular if non-negligible time-domain noise correlations are present, as is commonly the case. The approach based on the time-domain, however, implies significant computational effort because the full volume of the time-domain data set needs to be manipulated. To address this challenge, we propose and study efficient solvers adapted to solving time-domain-based component separation systems and their sequences, and which are capable of capitalizing on information derived from the previous solutions. This is achieved either by adapting the initial guess of the subsequent system or through a so-called subspace recycling, which allows constructing progressively more efficient two-level preconditioners. We report an overall speed-up over solving the systems independently of a factor of nearly 7, or 5, in our numerical experiments, which are inspired by the likelihood maximization and likelihood sampling procedures, respectively.

3D prestack plane-wave, full-waveform inversion

Geophysics ◽  
2008 ◽  
Vol 73 (5) ◽  
pp. VE135-VE144 ◽  
Author(s):  
Denes Vigh ◽  
E. William Starr
Keyword(s):  
Plane Wave ◽  
Data Acquisition ◽  
Time Domain ◽  
Waveform Inversion ◽  
Back Propagation ◽  
Synthetic Data ◽  
Full Waveform Inversion ◽  
Data Set ◽  
Full Waveform ◽  
The Time Domain

Prestack depth migration has been used for decades to derive velocity distributions in depth. Numerous tools and methodologies have been developed to reach this goal. Exploration in geologically more complex areas exceeds the abilities of existing methods. New data-acquisition and data-processing methods are required to answer these new challenges effectively. The recently introduced wide-azimuth data acquisition method offers better illumination and noise attenuation as well as an opportunity to more accurately determine velocities for imaging. One of the most advanced tools for depth imaging is full-waveform inversion. Prestack seismic full-waveform inversion is very challenging because of the nonlinearity and nonuniqueness of the solution. Combined with multiple iterations of forward modeling and residual wavefield back propagation, the method is computer intensive, especially for 3D projects. We studied a time-domain, plane-wave implementation of 3D waveform inversion. We found that plane-wave gathers are an attractive input to waveform inversion with dramatically reduced computer run times compared to traditional shot-gather approaches. The study was conducted on two synthetic data sets — Marmousi2 and SMAART Pluto 1.5 — and a field data set. The results showed that a velocity field can be reconstructed well using a multiscale time-domain implementation of waveform inversion. Although the time-domain solution does not take advantage of wavenumber redundancy, the method is feasible on current computer architectures for 3D surveys. The inverted velocity volume produces a quality image for exploration geologists by using numerous iterations of waveform inversion.

Sign in / Sign up

Export Citation Format

Share Document