From time series analysis to a modified ordinary differential equation

In understanding Big Data, people are interested to obtain the trend and dynamics of a given set of temporal data, which in turn can be used to predict possible futures. This paper examines a time series analysis method and an ordinary differential equation approach in modeling the price movements of petroleum price and of three different bank stock prices over a time frame of three years. Computational tests consist of a range of data fitting models in order to understand the advantages and disadvantages of these two approaches. A modified ordinary differential equation model, with different forms of polynomials and periodic functions, is proposed. Numerical tests demonstrated the advantage of the modified ordinary differential equation approach. Computational properties of the modified ordinary differential equation are studied

A joint inversion of receiver function and Rayleigh wave phase velocity dispersion data to estimate crustal structure in West Antarctica

We determine crustal shear-wave velocity structure and crustal thickness at recently deployed seismic stations across West Antarctica, using a joint inversion of receiver functions and fundamental mode Rayleigh wave phase velocity dispersion. The stations are from both the UK Antarctic Network (UKANET) and Polar Earth Observing Network/Antarctic Network (POLENET/ANET). The former include, for the first time, 4 stations along the spine of the Antarctic Peninsula, 3 in the Ellsworth Land and 5 stations in the vicinity of the Pine Island Rift. Within the West Antarctic Rift System (WARS) we model a crustal thickness range of 18-28 km, and show that the thinnest crust (∼18 km) is in the vicinity of the Byrd Subglacial Basin and Bentley Subglacial Trench. In these regions we also find the highest ratio of fast (Vs = 4.0-4.3 km/s) (likely mafic) lower crust to felsic/intermediate upper crust. The thickest mafic lower crust we model is in Ellsworth Land, a critical area for constraining the eastern limits of the WARS. Although we find thinner crust in this region (∼30 km) than in the neighbouring Antarctic Peninsula and Haag-Ellsworth Whitmore block (HEW), the Ellsworth Land crust has not undergone as much extension as the central WARS. This suggests that the WARS does not link with the Weddell Sea Rift System through Ellsworth Land, and instead has progressed during its formation towards the Bellingshausen and Amundsen Sea Embayments. We also find that the thin WARS crust extends towards the Pine Island Rift, suggesting that the boundary between the WARS and the Thurston Island block lies in this region, ∼200 km north of its previously accepted position. The thickest crust (38-40 km) we model in this study is in the Ellsworth Mountain section of the HEW block. We find thinner crust (30-33 km) in the Whitmore Mountains and Haag Nunatak sectors of the HEW, consistent with the composite nature of the block. In the Antarctic Peninsula we find a crustal thickness range of 30-38 km and a likely dominantly felsic/intermediate crustal composition. By forward modelling high frequency receiver functions we also assess if any thick, low velocity subglacial sediment accumulations are present, and find a 0.1-0.8 km thick layer at 10 stations within the WARS, Thurston Island and Ellsworth Land. We suggest that these units of subglacial sediment could provide a source region for the soft basal till layers found beneath numerous outlet glaciers, and may act to accelerate ice flow

Inversion of provenance data and sediment load into spatially varying erosion rates

Sediment fingerprinting methods aim to determine the relative contribution of different source areas in detrital sediments based on natural properties – fingerprints – of the source areas. Here, we use U/Th–Pb age signatures as fingerprints, assuming that the age signal is not altered during erosion–transportation–deposition events, and given that recent technological advances enable precise dating of large amounts of grains. We introduce a formal inversion method that allows to disentangle the amalgamation of source contributions in detrital zircon data and enables to convert this information into an erosion rate map starting from the spatial distribution of zircon age signatures. Relying on the least‐squares method and using prior and covariance information to deal with non‐uniqueness, we show, using synthetic and natural examples, that we are able to retrieve erosion rate patterns of a catchment when the age distribution and zircon fertility for each source area are well known. Moreover, we show that not only zircon age fingerprints but also other tracers such as mineral content can be used. Furthermore, we found that adding data from samples taken at the outlet of tributaries improves the estimation of erosion rate patterns. We conclude that the least squares inverse model applied to detrital data has great potential for investigating erosion rates

The global seismographic network reveals atmospherically coupled normal modes excited by the 2022 Hunga Tonga Eruption

Summary The eruption of the submarine Hunga Tonga-Hunga Haʻapai (Hunga Tonga) volcano on January 15, 2022, was one of the largest volcanic explosions recorded by modern geophysical instrumentation. The eruption was notable for the broad range of atmospheric wave phenomena it generated and for their unusual coupling with the oceans and solid Earth. The event was recorded worldwide across the Global Seismographic Network (GSN) by seismometers, microbarographs, and infrasound sensors. The broadband instrumentation in the GSN allows us to make high fidelity observations of spheroidal solid Earth normal modes from this event at frequencies near 3.7 and 4.4 mHz. Similar normal modes reported following the 1991 Pinatubo (Volcanic Explosivity Index of 6) eruption and were predicted, by theory, to arise from the excitation of mesosphere-scale acoustic modes of the atmosphere coupling with the solid Earth. Here, we compare observations for the Hunga Tonga and Pinatubo eruptions and find that both strongly excited the Earth normal mode 0S29 (3.72 mHz) and that the modal amplitude was roughly 11 times larger for the 2022 Hunga Tonga eruption. Estimates of attenuation (Q) for 0S29 across the GSN from temporal modal decay give Q = 332 ± 101, which is higher than estimates of Q for this mode using earthquake data (Q = 186.9 ± 5; Dziewonski &amp; Anderson 1981). Two microbarographs located at regional distances (&amp;lt; 1000 km) to the volcano provide direct observations of the fundamental acoustic mode of the atmosphere. These pressure oscillations, first observed approximately 40 minutes after the onset of the eruption, are in phase with the seismic Rayleigh wave excitation and are recorded only by microbarographs in proximity (&amp;lt; 1500 km) to the eruption. We infer that excitation of fundamental atmospheric modes occurs within a limited area close to the site of the eruption, where they excite select solid Earth fundamental spheroidal modes of similar frequencies that are globally recorded and have a higher apparent Q due to the extended duration of atmospheric oscillations.</jats:p

Slepian functions and their use in signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and on the surface of a sphere.Comment: Submitted to the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verla

Scalar and vector Slepian functions, spherical signal estimation and spectral analysis

It is a well-known fact that mathematical functions that are timelimited (or spacelimited) cannot be simultaneously bandlimited (in frequency). Yet the finite precision of measurement and computation unavoidably bandlimits our observation and modeling scientific data, and we often only have access to, or are only interested in, a study area that is temporally or spatially bounded. In the geosciences we may be interested in spectrally modeling a time series defined only on a certain interval, or we may want to characterize a specific geographical area observed using an effectively bandlimited measurement device. It is clear that analyzing and representing scientific data of this kind will be facilitated if a basis of functions can be found that are "spatiospectrally" concentrated, i.e. "localized" in both domains at the same time. Here, we give a theoretical overview of one particular approach to this "concentration" problem, as originally proposed for time series by Slepian and coworkers, in the 1960s. We show how this framework leads to practical algorithms and statistically performant methods for the analysis of signals and their power spectra in one and two dimensions, and, particularly for applications in the geosciences, for scalar and vectorial signals defined on the surface of a unit sphere.Comment: Submitted to the 2nd Edition of the Handbook of Geomathematics, edited by Willi Freeden, Zuhair M. Nashed and Thomas Sonar, and to be published by Springer Verlag. This is a slightly modified but expanded version of the paper arxiv:0909.5368 that appeared in the 1st Edition of the Handbook, when it was called: Slepian functions and their use in signal estimation and spectral analysi

Flanker performance in female college students with ADHD: a diffusion model analysis

Attention-deficit hyperactivity disorder (ADHD) is characterized by poor adaptation to environmental demands, which leads to various everyday life problems. The present study had four aims: (1) to compare performance in a flanker task in female college students with and without ADHD (N = 39) in a classical analyses of reaction time and error rate and studying the underlying processes using a diffusion model, (2) to compare the amount of focused attention, (3) to explore the adaptation of focused attention, and (4) to relate adaptation to psychological functioning. The study followed a 2-between (group: ADHD vs. control) × 2-within (flanker conflict: incongruent vs. congruent) × 2-within (conflict frequency: 20 vs. 80 %) design. Compared to a control group, the ADHD group displayed prolonged response times accompanied by fewer errors in a flanker task. Results from the diffusion model analyses revealed that the members of the ADHD group showed deficits in non-decisional processes (i.e., higher non-decision time) and leaned more toward accuracy than participants without ADHD (i.e., setting higher boundaries). The ADHD group showed a more focused attention and less adaptation to the task conditions which is related to psychological functioning. Deficient non-decisional processes and poor adaptation are in line with theories of ADHD and presumably typical for the ADHD population, although this has not been shown using a diffusion model. However, we assume that the cautious strategy of trading speed of for accuracy is specific to the subgroup of female college students with ADHD and might be interpreted as a compensation mechanism

Developmental dyscalculia: a dysconnection syndrome?

Numerical understanding is important for everyday life. For children with developmental dyscalculia (DD), numbers and magnitudes present profound problems which are thought to be based upon neuronal impairments of key regions for numerical understanding. The aim of the present study was to investigate possible differences in white matter fibre integrity between children with DD and controls using diffusion tensor imaging. White matter integrity and behavioural measures were evaluated in 15 children with developmental dyscalculia aged around 10 years and 15 matched controls. The main finding, obtained by a whole brain group comparison, revealed reduced fractional anisotropy in the superior longitudinal fasciculus in children with developmental dyscalculia. In addition, a region of interest analysis exhibited prominent deficits in fibres of the superior longitudinal fasciculus adjacent to the intraparietal sulcus, which is thought to be the core region for number processing. To conclude, our results outline deficient fibre projection between parietal, temporal and frontal regions in children with developmental dyscalculia, and therefore raise the question of whether dyscalculia can be seen as a dysconnection syndrome. Since the superior longitudinal fasciculus is involved in the integration and control of distributed brain processes, the present results highlight the importance of considering broader domain-general mechanisms in the diagnosis and therapy of dyscalculia