Terrain methods on spectral analysis for paleoclimate interpretations: A novel visualization technique using python

[EN] In this thesis it is introduced a method to filter GNSS height time series from vertical displacements derived from load variations in the Earth's surface, obtained from the monthly geopotential coefficients from the GRACE mission. These load variations are originated mainly by the seasonal hydrological variations as it can be confirmed from the hydrological GLDAS model. This filtering method is based on spectral analysis techniques that allow the manipulation of time series in both time and frequency domains.\n\nTo test this method data from 66 IGS Core Network reference stations have been used. The origin of the GNSS data are the weekly solutions provided by the First Data Reprocessing Campaign carried out by IGS. Monthly level-2 data from GRACE Mission provided by GFZ, with a time-span of more than 11 years, have been used to generate hydrological load and equivalent water thickness monthly time series at every reference station from which GNSS data are available. In addition, soil water content time series have also been created from monthly GLDAS data.\n\nWith the periodograms of the four time series datasets a signal with frequency close to 1 cycle per year is detected in the GNSS height, load, equivalent water thickness and GLDAS time series. As this signal has the same frequency in the equivalent water thickness and GLDAS time series it is confirmed that its origin is the hydrological cycle. Therefore the variations observed in the GNSS height and load time series can be explained, at least part of it, by these hydrological variations.\n\nThe spectral filtering technique introduced in this thesis is based on the detection and isolation of the annual signal in the load time series from GRACE data. This process is done in the frequency domain by using the Discrete Fourier Transform (DFT) with the Fast Fourier Transform (FFT) algorithm. Using the linearity property of the DFT, the isolated annual signal from the load time series is subtracted from the DFT of the GNSS height time series in the frequency domain. The new time series in the frequency domain is the GNSS height without the annual signal generated by the hydrological variations in the GNSS reference station area.\n\nAfter testing the spectral filter with times series dataset from 66 reference stations, it is demonstrated that for stations in areas with important hydrological activity the GNSS height time series reduce their WRMS by 18 % on average, with some special cases where WRMS reduction is higher than 25 %. Other parameters like GNSS height vs. GRACE load correlation before and after the filtering process show a reduction of the correlation from 53.9 % to 15.0 % In areas where the hydrological variations are not clearly detected by GNSS and GRACE, like islands, coasts or deserts, there is no WRMS reduction, and other parameters do not show any improvement in the GNSS height time series after the filtering process.

Spectral and cross-spectral analysis of uneven time series with the smoothed Lomb–Scargle periodogram and Monte Carlo evaluation of statistical significance

The spectral analysis techniques has been widely used to extract information about certain signals and the process in which those are generated. Ultrasonic (US) signal acquired from biological tissues are a particular case of that. Spectral analysis has been used to extract information from US signal related to biological tissue condition, mainly related with the internal scattering structure distribution and regularity. High-resolution spectral analysis techniques are applied to determine pathological characteristics that could indicate the presence of disease in the tissue. Some small changes in harmonics location could be drastically affected by the presence of noise in the analyzed signal. In this work, an evaluation of two parametric HR spectral analysis techniques is performed, first applied to signals acquired from a biological tissue phantom in a temperature range from 21°C to 45°C. A second evaluation was performed, considering simulated US signals, which were added with three different levels of SNR, and then they were analyzed with two parametric methods, which present variations in the error estimated for different noise level conditions. But the general behavior is a smaller error when noise decreases.

The stratigraphic and tectonic setting in the northwest part of Himalayan belt is complex and thrusted due to the collision of Indian plate and the Eurasian plate. During the past, the Himalaya is divided into four parts; these are Outer Himalaya, Lesser Himalaya, Greater or Higher Himalaya and Tethys Himalaya. The appearance of basement rocks played a significant role in the Himalayan periphery for stratigraphic, structural and tectonic movement. The deformation pattern of the crustal rocks causing the rise of basement rocks which constitutes an integral part of crustal configuration during the evolutionary stages of the Himalaya. In this study, an attempt has been made to estimate the basement depth configuration using spectral analysis and Euler deconvolution technique of gravity data in the northwest Himalaya region. The elevation increases continuously from 500 m to 5100 m in SW to NE direction, however, Bouguer gravity anomaly decreases continuously from -130 mGal to -390 mGal in SW to NE direction due to the isostaic adjustment. Gravity anomaly is very low near Harsil, Badrinath and Joshimath area and observed higher elevation due to the deep rooted basement. However, there are extrusion of crystalline basement in and around the Badrinath area due to the resettlement of geologic process which are overlaid to the top surface of the sedimentary layers. Euler deconvolution technique has been applied to detect the direct basement depth and results show a good correlation with the average depth of the spectral analysis and other works carried by different authors. Three gravity profiles are selected in appropriate places orienting SW-NE direction with a profile length of 160 km, 150 km and 140 km respectively in the study area for calculating the average depth of the basement rock. The average basement depth calculated is around 11.27 km using the spectral analysis technique and results are well correlated with the results of various workers. Euler deconvolution studies along the three selected profiles have been interpreted. It has been observed that there are more number of cluster points falling between depth ranges of 10 to 15 km, dipping in SW to NE direction. Euler’s study shows deep rooted connection near Main Frontal Thrust (MFT), Main Boundary Thrust (MBT), Main Central Thrust (MCT), Bearing Thrust (BT) and Vaikrita Thrust (VT) locations as per profile study. Based on these studies three geological models have been prepared along the profiles showing different tectonic resettlement and depth of crystalline basement. Crystalline rocks exposed at the surface may be due to uplift along the shear in the MCT zone by kinetic flow basically, Munsiayari Thrust (MT) and VT in the of NW-Himalaya region.

Application of the spectral analysis technique Ensemble Empirical Mode Decomposition (EEMD) to hydroclimatic time series produces an orthogonal set of decreasing frequency Intrinsic Mode Functions (IMFs) and a residual (or trend). As the EEMD algorithm is locally adaptive it is suitable for decomposing time series that appear non-stationary in terms of mean and variance: characteristics that are not uncommon in hydroclimatic series. EEMD utilises ensemble averaging to overcome the mode mixing problem observed in traditional Empirical Mode Decomposition (EMD). Here EEMD is briefly outlined and issues relating to the calculation of the Hilbert spectrum from EEMD output are discussed. EEMD is then applied to three climatic indices relevant to Australian hydroclimatic variability, namely the Southern Oscillation Index, Indian Ocean Dipole mode index and the Tasman Sea Index. Analysis of these indices reveals EEMD is capable of identifying physical process signals. For example, the known spectral structure of the SOI is identified by the EEMD algorithm. It was observed during analysis of the Indian Ocean Dipole mode index that EMD post processing may introduce end effects previously minimised by the EEMD ensemble average. These effects may inflate existing features, or potentially introduce low frequency artefacts, though this danger can be mitigated through careful examination of the complete Hilbert spectrum. EEMD and Hilbert spectrum analysis of hydroclimatic data provides insight into long-term trends, dominant frequencies and changes in energy with time for time series that are usually problematic to analyse with traditional spectral analysis techniques. The spectral fingerprints of the climatic indices assessed here are used in a companion paper that looks for those fingerprints within Australian precipitation and temperature data (Srikanthan et al., 2011).

Understanding the structural framework controlling the sedimentary basins from the integration of gravity and magnetic data: A case study from the east of the Qattara Depression area, Egypt

To the Editor: In a recent issue of Circulation , Stambler et al1 provide an intriguing but possibly misleading set of results regarding the variability of atrial flutter cycle length (AFCL) and the role of the autonomic nervous system in AFCL modulation. Previous studies2 3 4 5 identified in the AFCL variability the existence of 2 rhythmic oscillations, 1 controlled by the ventricular rate and 1 by respiratory activity, suggesting a modulatory effect of atrial stretch. Using spectral analysis, Stambler et al claimed the existence of an additional low-frequency oscillation (band 1) mediated by sympathetic tone. Their conclusions are not supported by their study design and results. In fact, the newly proposed low-frequency oscillation band was concentrated in the extremely low-frequency region of the spectrum and on average was centered around 0.006±0.002 Hz (Table 2 of the article by Stambler et al). This should correspond to an AFCL oscillation with a period of 166 seconds, clearly longer than the 2 minutes of analyzed recording time. This means that we are dealing with a baseline trend rather than a rhythmic oscillation. In other words, band 1 is simply a DC component of the spectrum reflecting the nonstationary nature of the analyzed time series and thus should be avoided in the interpretation of the power spectra.6 In their study, Stambler et al also examined the role of the autonomic nervous system in the modulation of AFCL by studying the effect of pharmacological interventions on the power-band distribution of AFCL spectra. Stimulation and inhibition of sympathetic tone obtained by intravenous infusion of isoproterenol and long-term therapy with …

This article summarizes the main findings on problems related to the measurement and identification of business cycles. The aim of this study is to define and identify the determinants of business cycles. This paper provides an overview of the methodology and its future course. Our investigation suggests that some methodological frameworks are available in the literature, but none is perfect. A new development in the field lies in spectral analysis methods for measuring business cycles, which may have advantages over existing methodologies (nonlinearity, stationarity issues). We feel that fractional integration is important in the proper monitoring and explanation of business cycles. Spectral analysis techniques have also proved to be useful for addressing the problems of stationarity and structural breaks in time series when analyzing business cycles. Another important issue that is excluded when studying business cycles is that the link between cycles and economic growth is presumed to be non-existent, implying money neutrality.

Geographical AnalysisVolume 13, Issue 2 p. 95-116 Free Access Maximum Entropy Spectra and the Spatial and Temporal Dimensions of Economic Fluctuations in an Urban System Claude Marchand, Claude Marchand The cartographic work of Jennifer Wilcox, University of Toronto, is gratefully acknowledged. Claude Marchand is assistant professor of geography, University of Montreal.Search for more papers by this author Claude Marchand, Claude Marchand The cartographic work of Jennifer Wilcox, University of Toronto, is gratefully acknowledged. Claude Marchand is assistant professor of geography, University of Montreal.Search for more papers by this author First published: April 1981 https://doi.org/10.1111/j.1538-4632.1981.tb00719.xCitations: 17 Claude Marchand is assistant professor of geography, University of Montreal. The cartographic work of Jennifer Wilcox, University of Toronto, is gratefully acknowledged. AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat LITERATURE CITED Bartels, C. P. A. (1977). “The structure of Regional Unemployment in the Netherlands. Regional Science and Urban Economics, 7, 103– 5. Bartels, C. P. A., M. Booleman, and W. H. Peters (1978). “A Statistical Analysis of Regional-Unemployment Series. Environment and Planning A, 10, 937– 54. Bennett, R. J. (1979). Spatial Time Series: Analysis—Forecasting—Control. London: Pion. Brechling, F. (1967). “Trends and Cycles in British Regional Unemployment. Oxford Economic Papers, 19, 1– 21. Burg, J. P. (1968). A New Analysis Technique for Time Series Data. Netherlands: Advanced Study Institute in Signal Processing. Bums, F., and W. Mitchell (1947). Measuring Business Cycles. New York: National Bureau of Economic Research. Cho, D. W., and D. S. McDougall (1978). “Regional Cyclical Patterns and Structure, 1954-1975. Economic Geography, 54, 66– 74. Fishman, G. S. (1969). Spectral Methods in Econometrics. Cambridge, Mass.: Harvard University Press. Granger, C. W. J. (1966). “The Typical Spectral Shape of an Economic Variable. Econometrica, 24, 150– 61. Granger, C. W. J., and M. Hatanaka (1964). Spectral Analysis of Economic Time Series, Princeton, N. J.: Princeton University Press. Haggett, P. (1975). “ Time Series Comparison: Unemployment. In Elements of Spatial Structure, edited by A. D. Cliff et al, Cambridge: Cambridge University Press. Hanna, F. A. (1954). “Cyclical and Secular changes in State per Capita Incomes, 1920-1950. Review of Economics and Statistics, 36, 320– 30. Hansen, A. H. (1951). Business Cycles and the National Income, New York: W. W. Norton. Harris, C. P., and A. P. Thirlwall (1968). “Interregional Variations in Cyclical Sensitivity to Unemployment in the U.K. 1949-1964. Bulletin of the Oxford University Institute of Economics and Statistics, 55– 66. Hepple, L. (1975). “ Spectral Techniques and the Study of Interregional Economic Cycles.” In Processes in Physical and Human Geography, edited by R. Peel, M. Chisholm, and P. Haggett, pp. 392– 408. London: Heinmann. Jeffrey, D. (1974). “Regional Fluctuations in Unemployment Within the Australian Urban Economic System: A Study of the Spatial Impact of Short Term Economic Change. Economic Geography, 50. Jeffrey, D. and D. J. Webb (1972). “Economic Fluctuations in the Australian Regional System 1955-70. Australian Geographical Studies, 10, 141– 60. Jenkins, G. M., and D. G. Watts (1968). Spectral Analysis and its Applications, San Francisco: Holden-Day. Kanasewich, E. R. (1973). Time Sequence Analysis in Geophysics. Edmonton: The University of Alberta Press. King, L., E. Casetti, and D. Jeffrey (1969). “Economic Impulses in a Regional System of Cities: A Study of Spatial Interaction. Regional Studies, 3, 213– 18. King, L., E. Casetti, and D. Jeffrey (1974). “Cyclical Fluctuations in Unemployment Levels in the U.S. Metropolitan Areas. Tidjdschrift Voor Economische en Social Geographie, 50, 345– 52. King, L. J., and G. R. Clark (1978). “Regional Unemployment Patterns and the Spatial Dimensions of Macro-Economic Policy: The Canadian Experience 1966-1975. Regional Studies, 12, 283– 96. Lacoss, R. T. (1971). “Data Adaptative Spectral Analysis Methods. Geophysics, 36, 661– 75. Schumpeter, J. (1935). “The Analysis of Economic Change. Review of Economic Statistics, 17, 1– 10. Thompson, W. R. (1965). A Preface to Urban Economics. Baltimore: Johns Hopkins University Press. Thompson, W. R. (1975). “ Internal and External Factors in the Development of Urban Economies.” In Regional Policy: Readings in Theory and Applications, edited by J. Friedman and W. Alonso, pp. 210– 20. Cambridge, Mass.: M. I. T. Press. Tiebout, T. M. (1975). “ Exports and Regional Economic Growth.” In Regional Policy: Readings in Theory and Applications, edited by J. Friedman and W. Alonso, pp. 348– 52. Cambridge, Mass.: M. I. T. Press. Citing Literature Volume13, Issue2April 1981Pages 95-116 ReferencesRelatedInformation

When deriving a directional ocean wave spectrum from a synthetic-aperture radar (SAR) image of the ocean surface, spectral analysis of the image data is a key step. In this paper, a quantitative comparison of spectral analysis techniques for analysis of multilook SAR image data of ocean waves is presented. Performance is rated using a spectral SNR, defined as the ratio of the desired spectral signature to the speckle noise as it appears in the SAR image spectrum. Spectral techniques considered cover all of those now in use (including SAR processor focus adjustment) as well as new experimental methods. It is shown that the spectral-phase-shift technique, introduced in this paper, is the best approach: it maximizes the spectral SNR, it allows resolution of the 180 degrees directional ambiguity, and it applies simultaneously to all wave components present in the scene.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Fatigue damage to marine pipelines subjected to wave forces is evaluated using time-domain and frequency-domain methods. Spectral techniques are applied to North Sea, Gulf of Mexico and offshore Atlantic Canada wave conditions. Time-domain analysis is applied to wave conditions in the Canadian North Atlantic Ocean. The frequency-domain analysis is performed using spectral and probabilistic techniques suggested by L. Borgman {?.). The pipeline dynamic characteristics are described by classical analytical descriptions. The time-domain analysis computes time histories of wave force loading on the submerged pipeline from actual wave records. The traditional Morison wave force equation is used to obtain the time history of the loading on the pipeline. Empirically determined wave spectra are shown not to produce as good a correlation with the deterministic results as the actual wave spectra. Free spanning submarine pipelines subjected to cyclic surface wave loading accumulate strength reductions leading to failure from material fatigue. The Palmgren-Miner rule for the linear accumulation of fatigue damage is applied to evaluate the time to failure. The American Welding Society X-X stress accumulation curve is applied. The results of the deterministic analysis were compared with those of the more efficient spectral analysis. It is shown that comparable results can be obtained from the spectral analysis provided the actual spectra of the water surface elevation is employed in the spectral analysis.

: The goal of this project is to develop spectral analysis techniques for ocean color analysis that are explicitly designed for use with hyperspectral data. The CoBOP program offers a rare opportunity to test any spectral analysis techniques with a wealth of remote sensing and in situ spectral data. Our objective is to develop a set of spectral analysis methods that are appropriate for remote sensing and to adapt them to remote sensing of ocean color. Our eventual objective is to expand the capability to accurately classify water types and bottom types and to extract accurate bathymetry using hyperspectral image data. The procedures will be tested and evaluated using data collected during the CoBOP field programs. We have defined a three-pronged approach: (1) adapt laboratory spectroscopy techniques to remote sensing, (2) expand multispectral approaches where applicable, and (3) develop novel approaches where necessary.

Four spectral analysis techniques were applied to pulsed Doppler ultrasonic quadrature signals to compare the relative merits of each technique for estimation of flow velocity and Doppler spectra. The four techniques were 1) the fast Fourier transform method, 2) the maximum likelihood method, 3) the Burg autoregressive algorithm, and 4) the modified covariance approach to autoregressive modeling. Both simulated signals and signals obtained from an in vitro flow system were studied. Optimal parameter values (e.g., model orders) were determined for each method, and the effects of signal-to-noise ratio and signal bandwidth were investigated. The modern spectral analysis techniques were shown to be superior to Fourier techniques in most circumstances, provided the model order was chosen appropriately. Robustness considerations tended to recommend the maximum likelihood method for both velocity and spectral estimation. Despite the restrictions of steady laminar flow, the results provide important basic information concerning the applicability of modern spectral analysis techniques to Doppler ultrasonic evaluation of arterial disease.

Fluctuations in fetal breathing rates (FBRs) have been investigated using spectral analysis techniques. Fetal breathing movements were recorded with chronically implanted diaphragmatic EMG electrodes in fetal lambs. Burst-burst intervals were determined using a template recognition method. The distribution of FBR over a long time series can be approximated by log-normal distribution. The power spectral density was found to be inversely proportional to Fourier frequency below 0.06 Hz, suggesting long-range density modulation. Analysis in the time domain revealed that self-similarity is preserved over different time scales, and that bursts tend to be bunched in clusters within which intervals between bursts are roughly uniform. Sequential distribution histograms over short time series revealed multiple peaks that vary over time. >

Abstract. Paleoclimate time series are often irregularly sampled and age uncertain, which is an important technical challenge to overcome for successful reconstruction of past climate variability and dynamics. Visual comparison and interpolation-based linear correlation approaches have been used to infer dependencies from such proxy time series. While the first is subjective, not measurable and not suitable for the comparison of many data sets at a time, the latter introduces interpolation bias, and both face difficulties if the underlying dependencies are nonlinear. In this paper we investigate similarity estimators that could be suitable for the quantitative investigation of dependencies in irregular and age-uncertain time series. We compare the Gaussian-kernel-based cross-correlation (gXCF, Rehfeld et al., 2011) and mutual information (gMI, Rehfeld et al., 2013) against their interpolation-based counterparts and the new event synchronization function (ESF). We test the efficiency of the methods in estimating coupling strength and coupling lag numerically, using ensembles of synthetic stalagmites with short, autocorrelated, linear and nonlinearly coupled proxy time series, and in the application to real stalagmite time series. In the linear test case, coupling strength increases are identified consistently for all estimators, while in the nonlinear test case the correlation-based approaches fail. The lag at which the time series are coupled is identified correctly as the maximum of the similarity functions in around 60–55% (in the linear case) to 53–42% (for the nonlinear processes) of the cases when the dating of the synthetic stalagmite is perfectly precise. If the age uncertainty increases beyond 5% of the time series length, however, the true coupling lag is not identified more often than the others for which the similarity function was estimated. Age uncertainty contributes up to half of the uncertainty in the similarity estimation process. Time series irregularity contributes less, particularly for the adapted Gaussian-kernel-based estimators and the event synchronization function. The introduced link strength concept summarizes the hypothesis test results and balances the individual strengths of the estimators: while gXCF is particularly suitable for short and irregular time series, gMI and the ESF can identify nonlinear dependencies. ESF could, in particular, be suitable to study extreme event dynamics in paleoclimate records. Programs to analyze paleoclimatic time series for significant dependencies are included in a freely available software toolbox.