A frequency-approximated approach to Kirchhoff migration

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. S211-S218 ◽  
Author(s):  
Mark E. Vardy ◽  
Timothy J. Henstock
Keyword(s):  
Time Domain ◽  
Narrow Band ◽  
Frequency Bands ◽  
Kirchhoff Migration ◽  
Frequency Decomposition ◽  
Band Pass ◽  
Band Limited ◽  
The Time Domain ◽  
Ultimate Control ◽  
Kirchhoff Integral

The integral solution of the wave equation has long been one of the most popular methods for imaging (Kirchhoff migration) and inverting (Kirchhoff inversion) seismic data. For efficiency, this process is commonly formulated as a time-domain operation on each trace, applying antialiasing through high-cut filtering of the operator or pre-/postmigration dip filtering. Migration in the time domain, however, does not allow for velocity dispersion; standard antialiasing methods assume a flat reflector and tend to overfilter the data. We have recast the Kirchhoff integral in the frequency domain, enabling robust antialias filtering through appropriate dip limiting of each frequency and implicit accommodation of true dispersion. Full frequency decomposition of the input seismogram can be approximated by band-pass filtering (or correlation with band-limited source sweeps for Chirp/Vibroseisdata) into a few narrow-band traces that cumulatively retain the full source bandwidth. From prior knowledge of the source waveform, we have defined suitable bandwidths to describe broadband (3.0 octaves) data using just six frequency bands. Kirchhoff migration of these narrow-band traces using coefficients determined at their central frequencies significantly improves the preservation of higher frequencies and cancellation of steeply dipping aliased energy over traditional time-domain antialiasing methods. If, however, two bands per octave cease to be a robust approach, our frequency-approximated approach provides the processor with ultimate control over the frequency decimation, balancing increased resolution afforded by more bands against computing cost, whereas the number of frequency bands is few enough to permit detailed control over frequency-dependent antialias filtering parameters.

scholarly journals An explicit marching-on-in-time scheme for solving the time domain Kirchhoff integral equation

2019 ◽  
Vol 146 (3) ◽  
pp. 2068-2079 ◽  
Author(s):  
Rui Chen ◽  
Sadeed Bin Sayed ◽  
Noha Alharthi ◽  
David Keyes ◽  
Hakan Bagci
Keyword(s):  
Integral Equation ◽  
Time Domain ◽  
The Time Domain ◽  
Kirchhoff Integral

scholarly journals Classification of Motor Imagery Using a Combination of User-Specific Band and Subject-Specific Band for Brain-Computer Interface

2019 ◽  
Vol 9 (23) ◽  
pp. 4990 ◽  
Author(s):  
Jusas ◽  
Samuvel
Keyword(s):  
Feature Extraction ◽  
Time Domain ◽  
Extraction Process ◽  
Computer Interface ◽  
Eeg Signals ◽  
Frequency Bands ◽  
Fisher Ratio ◽  
Frequency Domains ◽  
Subject Specific ◽  
The Time Domain

The essential task of a Brain-Computer Interface (BCI) is to extract the motor imagery features from Electro-Encephalogram (EEG) signals for classifying the thought process. It is necessary to analyse these obtained signals in both the time domain and frequency domains. It is observed that the combination of multiple algorithms increases the performance of the feature extraction process. This paper identifies combinations that have not been attempted previously and improves the accuracy of the overall process, although other authors implemented different combinations of the techniques. The focus is given more on the feature extraction process and frequency bands, which are user-specific and subject-specific frequency bands. In both time and frequency domains, after analysing EEG signals with the time domain parameter, we select the frequency band and the timing while using the Fisher ratio of the time domain parameter (TDP). We used Fisher discriminant analysis (FDA)-type F-score to simultaneously select the frequency band and time segment for multi-class classification. We extracted subject-specific TDP features from the training trials to train the classifier when optimal time-frequency areas were selected for each subject. In this paper, various methods are explored for obtaining the features, which are Time Domain Parameters (TDP), Fast Fourier Transform (FFT), Principal Component Analysis (PCA), R2, Fast Correlation Based Filter (FCBF), Empirical Mode Decomposition (EMD), and Intrinsic time-scale decomposition (ITD). After the extraction process, PCA is used for dimensionality reduction. An efficient result was obtained with the combination of TDP, FFT, and PCA. We used the multi-class Fisher′s linear discriminant analysis (LDA) as the classifier, which was in line with the FDA-type F-score. It is observed that the combination of feature extraction techniques to the frequency bands that were selected by the Fisher ratio and FDA type F-score along with Fisher′s LDA classifier had higher accuracy than the results obtained other researches. A kappa coefficient accuracy of 0.64 is obtained for the proposed technique. Our method leads to better classification performance when compared to state-of-the-art methods. The novelty of the approach is based on the combination of frequency bands and two feature extraction methods.

Clutter removal for measuring low-frequency narrow-band antenna using spectral estimation

2018 ◽  
Vol 11 (3) ◽  
pp. 215-219
Author(s):  
C. F. Hu ◽  
N. J. Li
Keyword(s):  
Time Domain ◽  
Measurement Accuracy ◽  
Narrow Band ◽  
Spectral Estimation ◽  
Low Frequency ◽  
Ar Model ◽  
Signal Processing Technique ◽  
Antenna Measurement ◽  
The Time Domain ◽  
Time Gating

AbstractThe measurement accuracy of low-frequency narrow-band antenna is heavily influenced by its environment, which is also difficult to remove the clutter with a time gating. This paper proposes a method to improve the measurement accuracy of low-frequency narrow-band antenna using signal processing technique. The method is to predict the unknown value out of received original signal with an auto-regressive model (AR model) based on modern spectral estimation theory, and the parameters in AR model are calculated by maximum entropy spectral estimation algorithm. Thus, a wideband signal compared with the original band is obtained, and then the time-domain resolution is enhanced. The time gating is more exactly to separate the antenna radiation signal from multipath signals. The simulation and experimental results show that about 50% extended data for each ends of original band can be obtained after spectral extrapolation, and the time-domain resolution after extrapolation is twice than the original narrow-band signal, and the influence of measurement environment can be eliminated effectively. The method can be used to improve accuracy in actual antenna measurement.

Depth-domain seismic reflectivity inversion with compressed sensing technique

2017 ◽  
Vol 5 (1) ◽  
pp. T1-T9 ◽  
Author(s):  
Rui Zhang ◽  
Kui Zhang ◽  
Jude E. Alekhue
Keyword(s):  
Compressed Sensing ◽  
Time Domain ◽  
Seismic Data ◽  
Reservoir Characterization ◽  
Synthetic Data ◽  
Seismic Inversion ◽  
Inversion Method ◽  
Depth Migration ◽  
Band Limited ◽  
The Time Domain

More and more seismic surveys produce 3D seismic images in the depth domain by using prestack depth migration methods, which can present a direct subsurface structure in the depth domain rather than in the time domain. This leads to the increasing need for applications of seismic inversion on the depth-imaged seismic data for reservoir characterization. To address this issue, we have developed a depth-domain seismic inversion method by using the compressed sensing technique with output of reflectivity and band-limited impedance without conversion to the time domain. The formulations of the seismic inversion in the depth domain are similar to time-domain methods, but they implement all the elements in depth domain, for example, a depth-domain seismic well tie. The developed method was first tested on synthetic data, showing great improvement of the resolution on inverted reflectivity. We later applied the method on a depth-migrated field data with well-log data validated, showing a great fit between them and also improved resolution on the inversion results, which demonstrates the feasibility and reliability of the proposed method on depth-domain seismic data.

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.

SEISMIC DATA COMPRESSION METHODS

Geophysics ◽  
1974 ◽  
Vol 39 (4) ◽  
pp. 499-525 ◽  
Author(s):  
Lawrence C. Wood
Keyword(s):  
Time Domain ◽  
Seismic Data ◽  
Walsh Transform ◽  
Data Sets ◽  
Convergence Properties ◽  
Long Distance ◽  
Visual Degradation ◽  
Band Pass ◽  
The Time Domain ◽  
Seismic Data Compression

This paper discusses two ways of compressing seismic data prior to long‐distance transmission for display. A Walsh transform technique and an analogous time‐domain method eliminate redundant seismic information allowing data sets to be compressed with little visual degradation. The basic approach consists of using an average 3-bit code to describe data in such a way as to minimize information loss; the method also uses the Walsh transform to achieve further compaction through sequency bandlimiting. A second technique is entirely a time‐domain operation and does not use transforms. The Walsh method, however, produces larger compression ratios than the time technique before serious image degradation occurs. Both schemes have six basic parts: bandlimiting, quantization, encoding, decoding, interpolation, and band‐pass filtering; they differ only in band limiting and interpolation. Band limiting sequencies in the Walsh domain is very similar to, but not the same as, alias filtering and resampling in time. Reducing Walsh bandwidths by some power of two has a time‐domain implementation consisting of an averaging procedure with subsequent resampling, while the inverse Walsh transform step can be viewed as a means of interpolating in the time domain. The convergence properties of three Rademacher derived transforms—Hadamard, Paley, and Walsh—are studied with regard to exploration seismic data. Hadamard energy has been found to be uniformly distributed over its entire spectrum, whereas Walsh and Paley transforms concentrate about 80 percent of the total energy into a major lobe occupying about 15 percent of the total bandwidth (2 msec sampling). Smaller minor lobes containing the remaining 20 percent are discarded while bandlimiting. The major lobe energy suffices for many seismic applications such as VA/VD plot displays. Optimum quantization and encoding of major lobe energy results in an overall 28:1 compression factor for 12 bit data sampled every 2 msec. Analogous time domain compression, on the other hand, only achieves a 16:1 reduction because of the power of two restriction imposed by the resampling and averaging process.

Intermittent Intensity Clutter Removal of Wind Profiling Radar Based on FrFT

2011 ◽  
Vol 130-134 ◽  
pp. 2094-2097
Author(s):  
Jia Qiang Li ◽  
Xian He Qin ◽  
Yin Sheng Zhang
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Fractional Fourier Transform ◽  
Narrow Band ◽  
Energy Concentration ◽  
Spectrum Estimation ◽  
Fourier Frequency ◽  
Band Stop Filter ◽  
Clutter Removal ◽  
The Time Domain

Intermittent intensity clutter in wind profiling radar severely interferes with the identification and spectrum estimation of atmospheric echo signals. In order to remove such clutter, a method based on Fractional Fourier transform (FrFT) is presented. The proposed method makes use of energy concentration property of intermittent clutter in fractional Fourier frequency domain. Not only the intermittent intensity clutter can be removed in the fractional Fourier frequency domain by using a narrow band-stop filter, but also the atmospheric signal in the time domain can be reconstructed after removing the clutter. Computer simulations have verified the effectiveness of the method.

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