A sparse spectrum technique for gridding and separating potential field anomalies

Geophysics ◽  
2000 ◽  
Vol 65 (4) ◽  
pp. 1154-1161 ◽  
Author(s):  
Fernando Guspí ◽  
Beatriz Introcaso
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Potential Field ◽  
Low Frequency ◽  
Seismic Signal ◽  
Separation Procedure ◽  
Virtual Absence ◽  
Large Matrix ◽  
Frequency Components ◽  
The Difference

The separation of regional and residual potential field anomalies, regarded as a spectral problem, can be greatly facilitated when a spectrum estimate shows a clear break between low‐ and high‐frequency components, a feature that normal fast‐Fourier‐transform (FFT) methods fail to present. In this work, we model the discrete Fourier transform of a potential field, measured at stations irregularly distributed on a surface, by means of a high‐resolution sparse estimate derived originally for seismic signal processing. The coefficients of this estimate, which are distributed according to the Cauchy probability law, produce a model with only few components having a significant value. A steepest‐descent algorithm gives a computing alternative to large matrix multiplications and inversions. Advantages of taking this approach are twofold. First, the high‐resolution transform can be used as a gridding tool to evaluate the potential field either on a horizontal plane or on the topographic surface. The enhancement of the spectral peaks and the virtual absence of sidelobes prevents oscillations and edge effects in the result. Secondly, the sparse distribution of the spectral elements allows the interpreter to locate clearly the low‐frequency components related to the regional field. After a second and faster pass, the values of those coefficients can be redefined in order to obtain a more robust separation, ajusting the residuals by the Cauchy criterion. A theoretical noise‐free example to separate the magnetic anomaly of a prism from a polynomial background illustrates well the difference between sparse and FFT spectra. An example with real Bouguer anomalies in the Interserrana basin, Argentina, shows that gridding results, in this case reduced to sea level, compare well with those obtained by other gridding methods, and that the separation procedure is able to outline well defined areas of positive and negative residual anomalies.

A time-lapse seismic repeatability test using the P-Cable high-resolution 3D marine acquisition system

2020 ◽  
Vol 39 (7) ◽  
pp. 480-487
Author(s):  
Patrick Smith ◽  
Brandon Mattox
Keyword(s):  
High Resolution ◽  
Seismic Data ◽  
Low Cost ◽  
Low Frequency ◽  
Time Lapse ◽  
Seismic Signal ◽  
Residual Energy ◽  
Acquisition System ◽  
Positioning Errors ◽  
Seismic Surveying

The P-Cable high-resolution 3D marine acquisition system tows many short, closely separated streamers behind a small source. It can provide 3D seismic data of very high temporal and spatial resolution. Since the system is containerized and has small dimensions, it can be deployed at short notice and relatively low cost, making it attractive for time-lapse seismic reservoir monitoring. During acquisition of a 3D high-resolution survey in the Gulf of Mexico in 2014, a pair of sail lines were repeated to form a time-lapse seismic test. We processed these in 2019 to evaluate their geometric and seismic repeatability. Geometric repetition accuracy was excellent, with source repositioning errors below 10 m and bin-based receiver positioning errors below 6.25 m. Seismic data comparisons showed normalized root-mean-square difference values below 10% between 40 and 150 Hz. Refinements to the acquisition system since 2014 are expected to further improve repeatability of the low-frequency components. Residual energy on 4D difference seismic data was low, and timing stability was good. We conclude that the acquisition system is well suited to time-lapse seismic surveying in areas where the reservoir and time-lapse seismic signal can be adequately imaged by small-source, short-offset, low-fold data.

Hydrocarbon identification using the AVO response correction method based on high-resolution complex spectral decomposition

2020 ◽  
Vol 8 (1) ◽  
pp. SA49-SA61
Author(s):  
Huihuang Tan ◽  
Donghong Zhou ◽  
Shengqiang Zhang ◽  
Zhijun Zhang ◽  
Xinyi Duan ◽  
...  
Keyword(s):  
High Resolution ◽  
Seismic Data ◽  
Spectral Decomposition ◽  
Oil And Gas ◽  
Low Frequency ◽  
Seismic Signal ◽  
Correction Method ◽  
Bohai Bay ◽  
Oil And Gas Exploration ◽  
Response Correction

Amplitude-variation-with-offset (AVO) technique is one of the primary quantitative hydrocarbon discrimination methods with prestack seismic data. However, the prestack seismic data are usually have low data quality, such as nonflat gathers and nonpreserved amplitude due to absorption, attenuation, and/or many other reasons, which usually lead to a wrong AVO response. The Neogene formations in the Huanghekou area of the Bohai Bay Basin are unconsolidated clastics with a high average porosity, and we find that the attenuation on seismic signal is very strong, which causes an inconsistency of AVO responses between seismic gathers and its corresponding synthetics. Our research results indicate that the synthetic AVO response can match the field seismic gathers in the low-frequency end, but not in the high-frequency components. Thus, we have developed an AVO response correction method based on high-resolution complex spectral decomposition and low-frequency constraint. This method can help to achieve a correct high-resolution AVO response. Its application in Bohai oil fields reveals that it is an efficient way to identify hydrocarbons in rocks, which provides an important technique for support in oil and gas exploration and production in this area.

scholarly journals Multi-timescale data assimilation for atmosphere–ocean state estimates

2016 ◽  
Vol 12 (6) ◽  
pp. 1375-1388 ◽  
Author(s):  
Nathan Steiger ◽  
Gregory Hakim
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Spectral Characteristics ◽  
Low Frequency ◽  
Meridional Overturning Circulation ◽  
Climate System ◽  
Time Averaging ◽  
Proxy Data ◽  
Multiple Timescales ◽  
Frequency Components

Abstract. Paleoclimate proxy data span seasonal to millennial timescales, and Earth's climate system has both high- and low-frequency components. Yet it is currently unclear how best to incorporate multiple timescales of proxy data into a single reconstruction framework and to also capture both high- and low-frequency components of reconstructed variables. Here we present a data assimilation approach that can explicitly incorporate proxy data at arbitrary timescales. The principal advantage of using such an approach is that it allows much more proxy data to inform a climate reconstruction, though there can be additional benefits. Through a series of offline data-assimilation-based pseudoproxy experiments, we find that atmosphere–ocean states are most skillfully reconstructed by incorporating proxies across multiple timescales compared to using proxies at short (annual) or long (∼ decadal) timescales alone. Additionally, reconstructions that incorporate long-timescale pseudoproxies improve the low-frequency components of the reconstructions relative to using only high-resolution pseudoproxies. We argue that this is because time averaging high-resolution observations improves their covariance relationship with the slowly varying components of the coupled-climate system, which the data assimilation algorithm can exploit. These results are consistent across the climate models considered, despite the model variables having very different spectral characteristics. Our results also suggest that it may be possible to reconstruct features of the oceanic meridional overturning circulation based on atmospheric surface temperature proxies, though here we find such reconstructions lack spectral power over a broad range of frequencies.

Forecast of Power Quality Index Based on the Discrete Fourier Decomposition and AR Model

2013 ◽  
Vol 732-733 ◽  
pp. 1420-1426 ◽  
Author(s):  
Cong Xi Wen ◽  
Shan Gao ◽  
Xiang Ning Xiao ◽  
Yong Hai Xu ◽  
Shun Tao
Keyword(s):  
Fourier Transform ◽  
Fourier Analysis ◽  
Discrete Fourier Transform ◽  
Harmonic Distortion ◽  
Low Frequency ◽  
Total Harmonic Distortion ◽  
Ar Model ◽  
Frequency Noise ◽  
Discrete Fourier Analysis ◽  
Frequency Components

A method of autoregressive (AR) based on discrete Fourier analysis is proposed to forecast the indexes of unbalance factor and total harmonic distortion. The discrete Fourier transform of the index sequence is analyzed and the low frequency components are extracted. Autoregressive method is applied to forecast each low frequency component. Through inverse discrete Fourier transform, the forecasting low frequency components are inverted to forecasting sequence of the index in time domain. Actual data is used to test this method and the results show that discrete Fourier analysis is possible to reduce the influence of high frequency noise and that the AR method based on Fourier transform can effectively forecast the indexes of unbalance factor and total harmonic distortion.

scholarly journals Simultaneous ground-based observations of O<sub>3</sub>, HCl, N<sub>2</sub>O, and CH<sub>4</sub> over Toronto, Canada by three Fourier transform spectrometers with different resolutions

2007 ◽  
Vol 7 (5) ◽  
pp. 1275-1292 ◽  
Author(s):  
D. Wunch ◽  
J. R. Taylor ◽  
D. Fu ◽  
P. Bernath ◽  
J. R. Drummond ◽  
...  
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Optical Path Difference ◽  
Path Difference ◽  
Optical Path ◽  
Lower Sensitivity ◽  
Critical Importance ◽  
The Difference ◽  
Total Column ◽  
Better Than

Abstract. An intercomparison of three Fourier transform spectrometers (FTSs) with significantly different resolutions is presented. The highest-resolution instrument has a maximum optical path difference of 250 cm, and the two lower-resolution instruments have maximum optical path differences of 50 cm and 25 cm. The results indicate that the two lower-resolution instruments can retrieve total column amounts of O3, HCl, N2O and CH4 using the SFIT2 retrieval code with percent differences from the high-resolution instrument generally better than 4%. Total column amounts of the stratospheric species (O3 and HCl) have larger differences than those of the tropospheric species (N2O and CH4). Instrument line shape (ILS) information is found to be of critical importance when retrieving total columns of stratospheric gases from the lower-resolution instruments. Including the ILS information in the retrievals significantly reduces the difference in total column amounts between the three instruments. The remaining errors for stratospheric species total column amounts can be attributed to the lower sensitivity of the lower-resolution FTSs to the stratosphere.

Error Analyzing Method for Rotation Inertial Navigation System Based on Fourier Transform

2013 ◽  
Vol 336-338 ◽  
pp. 982-987 ◽  
Author(s):  
Jian Hua Cheng ◽  
Bing Yu Wang ◽  
Dai Dai Chen
Keyword(s):  
Fourier Transform ◽  
Navigation System ◽  
Inertial Navigation System ◽  
Inertial Navigation ◽  
Low Frequency ◽  
Pass Filter ◽  
Low Pass Filter ◽  
Low Pass ◽  
Frequency Components ◽  
Navigation Errors

According with the problem that the error propagative characteristics of rotation inertial navigation system can not be quantitatively analyzed, a new error analyzing method is proposed. As the inertial navigation system can be equivalent to a low pass filter, the method converted the complex gyro drifts into signal which can be quantitatively analyzed after modulating through Fourier transform, thus the low frequency components of the error can be extracted. The relationship between navigation errors and gyro drifts is built by using the conventional error equations of strapdown inertial navigation system. The comparative analyses and computer simulation of conventional, uniaxial unidirectional and uniaxial reciprocating system prove the correctness and feasibility of this method. This method provides an effective reference for other same types of control system error analyses.

Precise GPS Positioning with Low-Cost Single-Frequency System in Multipath Environment

2010 ◽  
Vol 63 (2) ◽  
pp. 301-312 ◽  
Author(s):  
Abdulla Alnaqbi ◽  
Ahmed El-Rabbany
Keyword(s):  
High Resolution ◽  
Low Cost ◽  
Low Frequency ◽  
Ionospheric Delay ◽  
Single Frequency ◽  
Static Mode ◽  
Phase Measurements ◽  
System Noise ◽  
Differential Positioning ◽  
The Difference

Low-cost, single-frequency GPS systems provide economical positioning solutions to many geomatics applications, including GIS and low-accuracy surveying applications. Unfortunately however, the positioning accuracy obtained with those systems is not sufficient for many surveying applications. This is mainly due to the presence of ionospheric delay and multipath. In this research ionospheric delay is accounted for using regional high-resolution ionospheric maps produced by the US National Oceanic and Atmospheric Administration (NOAA). The major remaining constraint and challenging problem is multipath. This is because multipath is environmentally-dependent, difficult to model mathematically and cannot be reduced through differential positioning. This research proposes a new approach to identify multipath-contaminated L1 measurements through wavelet analysis. First, the difference between the code and carrier-phase measurements is estimated, leaving essentially twice the ionospheric delay, multipath and system noise. The ionospheric delay is largely removed by using high-resolution ionospheric delay maps produced by NOAA. The remaining residuals contain mainly low-frequency multipath, if it exists, and high-frequency system noise, which are decomposed using Daubechies family wavelets (db8). A satellite signal is identified as contaminated by multipath based on the standard deviation of the low-frequency part of the residual component. The L1 measurements obtained from the satellites with the lowest multipath are used to compute the final positions using two software packages, namely Trimble Total Control (TTC) and Bernese scientific processing software. The Magellan AC12 low-cost single-frequency GPS receiver was extensively tested in static mode. It is shown that accuracies within 5 cm are routinely obtained for baselines up to 65 km under various multipath environments.

Seismic spectral decomposition using deconvolutive short-time Fourier transform spectrogram

Geophysics ◽  
2013 ◽  
Vol 78 (2) ◽  
pp. V43-V51 ◽  
Author(s):  
Wenkai Lu ◽  
Fangyu Li
Keyword(s):  
Fourier Transform ◽  
Spectral Decomposition ◽  
Reservoir Characterization ◽  
Low Frequency ◽  
Seismic Signal ◽  
Frequency Resolution ◽  
Short Time Fourier Transform ◽  
Distribution Method ◽  
Time Frequency ◽  
Short Time

The spectral decomposition technique plays an important role in reservoir characterization, for which the time-frequency distribution method is essential. The deconvolutive short-time Fourier transform (DSTFT) method achieves a superior time-frequency resolution by applying a 2D deconvolution operation on the short-time Fourier transform (STFT) spectrogram. For seismic spectral decomposition, to reduce the computation burden caused by the 2D deconvolution operation in the DSTFT, the 2D STFT spectrogram is cropped into a smaller area, which includes the positive frequencies fallen in the seismic signal bandwidth only. In general, because the low-frequency components of a seismic signal are dominant, the removal of the negative frequencies may introduce a sharp edge at the zero frequency, which would produce artifacts in the DSTFT spectrogram. To avoid this problem, we used the analytic signal, which is obtained by applying the Hilbert transform on the original real seismic signal, to calculate the STFT spectrogram in our method. Synthetic and real seismic data examples were evaluated to demonstrate the performance of the proposed method.

scholarly journals Multi-time scale data assimilation for atmosphere–ocean state estimates

2015 ◽  
Vol 11 (4) ◽  
pp. 3729-3757 ◽  
Author(s):  
N. Steiger ◽  
G. Hakim
Keyword(s):  
High Resolution ◽  
Data Assimilation ◽  
Time Scales ◽  
Time Scale ◽  
Low Frequency ◽  
Climate System ◽  
Multiple Time Scales ◽  
Multiple Time ◽  
Proxy Data ◽  
Frequency Components

Abstract. Paleoclimate proxy data span seasonal to millennial time scales, and Earth's climate system has both high- and low-frequency components. Yet it is currently unclear how best to incorporate multiple time scales of proxy data into a single reconstruction framework and to also capture both high- and low-frequency components of reconstructed variables. Here we present a data assimilation algorithm that can explicitly incorporate proxy data at arbitrary time scales. Through a series of pseudoproxy experiments, we find that atmosphere–ocean states are most skilfully reconstructed by incorporating proxies across multiple time scales compared to using proxies at short (annual) or long (~ decadal) time scales alone. Additionally, reconstructions that incorporate long time-scale pseudoproxies improve the low-frequency components of the reconstructions relative to using only high-resolution pseudoproxies. We argue that this is because time averaging high-resolution observations improves their covariance relationship with the slowly-varying components of the coupled-climate system, which the data assimilation algorithm can exploit. These results are insensitive to the choice of climate model, despite the model variables having very different spectral characteristics. Our results also suggest that it may be possible to reconstruct features of the oceanic meridional overturning circulation based solely on atmospheric surface temperature proxies.

scholarly journals Simultaneous ground-based observations of O<sub>3</sub>, HCl, N<sub>2</sub>O, and CH<sub>4</sub> over Toronto, Canada by three Fourier transform spectrometers with different resolutions

2006 ◽  
Vol 6 (5) ◽  
pp. 10883-10928
Author(s):  
D. Wunch ◽  
J. R. Taylor ◽  
D. Fu ◽  
P. Bernath ◽  
J. R. Drummond ◽  
...  
Keyword(s):  
Fourier Transform ◽  
High Resolution ◽  
Optical Path Difference ◽  
Path Difference ◽  
Optical Path ◽  
Lower Sensitivity ◽  
Critical Importance ◽  
The Difference ◽  
Total Column ◽  
Better Than

Abstract. An intercomparison of three Fourier transform spectrometers (FTSs) with significantly different resolutions is presented. The highest-resolution instrument has a maximum optical path difference of 250 cm, and the two lower-resolution instruments have maximum optical path differences of 50 cm and 25 cm. The results indicate that the two lower-resolution instruments can retrieve total column amounts of O3, HCl, N2O and CH4 using the SFIT2 retrieval code with percent differences from the high-resolution instrument generally better than 3%, with respect to the high-resolution FTS. Total column amounts of the stratospheric species (O3 and HCl) have larger differences than those of the tropospheric species (N2O and CH4). Instrument line shape (ILS) information is found to be of critical importance when retrieving total columns of stratospheric gases from the lower-resolution instruments. Including the ILS information in the retrievals significantly reduces the difference in total column amounts between the three instruments. The remaining errors for stratospheric species total column amounts can be attributed to the lower sensitivity of the lower-resolution FTSs to the stratosphere.

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