A hidden Markov model segmentation procedure for hydrological and environmental time series

In this paper we present a procedure for the segmentation of hydrological and enviromental time series. We consider the segmentation problem from a purely computational point of view which involves the minimization of Huberts segmentation cost; in addition this least squares segmentation is equivalent to Maximum Likelihood segmentation. Our segmentation procedure maximizes Likelihood and minimizes Huberts least squares criterion using a hidden Markov model (HMM) segmentation algorithm. This algorithm is guaranteed to achieve a local maximum of the Likelihood. We evaluate the segmentation procedure with numerical experiments which involve artificial, temperature and river discharge time series. In all experiments, the procedure actually achieves the global minimum of the Likelihood; furthermore execution time is only a few seconds, even for time series with over a thousand terms.     

Dynamic programming approach for segmentation of multivariate time series

In this paper, dynamic programming (DP) algorithm is applied to automatically segment multivariate time series. The definition and recursive formulation of segment errors of univariate time series are extended to multivariate time series, so that DP algorithm is computationally viable for multivariate time series. The order of autoregression and segmentation are simultaneously determined by Schwarz’s Bayesian information criterion. The segmentation procedure is evaluated with artificially synthesized and hydrometeorological multivariate time series. Synthetic multivariate time series are generated by threshold autoregressive model, and in real-world multivariate time series experiment we propose that besides the regression by constant, autoregression should be taken into account. The experimental studies show that the proposed algorithm performs well.     

Modified dynamic programming approach for offline segmentation of long hydrometeorological time series

For the offline segmentation of long hydrometeological time series, a new algorithm which combines the dynamic programming with the recently introduced remaining cost concept of branch-and-bound approach is developed. The algorithm is called modified dynamic programming (mDP) and segments the time series based on the first-order statistical moment. Experiments are performed to test the algorithm on both real world and artificial time series comprising of hundreds or even thousands of terms. The experiments show that the mDP algorithm produces accurate segmentations in much shorter time than previously proposed segmentation algorithms.     

Dynamic programming-based optimization for segmentation and clustering of hydrometeorological time series

In this study, we propose a new segmentation algorithm to partition univariate and multivariate time series, where fuzzy clustering is realized for the segments formed in this way. The clustering algorithm involves a new objective function, which incorporates an extra variable related to segmentation, while dynamic time warping (DTW) is applied to determine distances between non-equal-length series. As optimizing the introduced objective function is a challenging task, we put forward an effective approach using dynamic programming (DP) algorithm. When calculating the DTW distance, a DP-based method is developed to reduce the computational complexity. In a series of experiments, both synthetic and real-world time series are used to evaluate the performance of the proposed algorithm. The results demonstrate higher effectiveness and advantages of the constructed algorithm when compared with the existing segmentation approaches.     

Hydraulic Conductivity Calibration of Logging NMR in a Granite Aquifer,Laramie Range,Wyoming

In granite aquifers, fractures can provide both storage volume and conduits for groundwater. Characterization of fracture hydraulic conductivity (K) in such aquifers is important for predicting flow rate and calibrating models. Nuclear magnetic resonance (NMR) well logging is a method to quickly obtain near-borehole hydraulic conductivity (i.e., K_NMR) at high-vertical resolution. On the other hand, FLUTe flexible liner technology can produce a K profile at comparable resolution but requires a fluid driving force between borehole and formation. For three boreholes completed in a fractured granite, we jointly interpreted logging NMR data and FLUTe K estimates to calibrate an empirical equation for translating borehole NMR data to K estimates. For over 90% of the depth intervals investigated from these boreholes, the estimated K_NMR are within one order of magnitude of K_FLUTe. The empirical parameters obtained from calibrating the NMR data suggest that “intermediate diffusion” and/or “slow diffusion” during the NMR relaxation time may occur in the flowing fractures when hydraulic aperture are sufficiently large. For each borehole, “intermediate diffusion” dominates the relaxation time, therefore assuming “fast diffusion” in the interpretation of NMR data from fractured rock may lead to inaccurate K_NMR estimates. We also compare calibrations using inexpensive slug tests that suggest reliable K_NMR estimates for fractured rock may be achieved using limited calibration against borehole hydraulic measurements.     

Driving the high-latitude ionosphere with variable time resolution “K-like” geomagnetic indices

The 3-h K_p index is widely used as a measure of geomagnetic activity for ionospheric studies. Specifically, it is the planetary index used to determine the geomagnetic dependence of statistical auroral patterns and the convection electric field for certain models. Its quasi anti-logarithm, the A_p index, is similarly used in statistical models of the neutral atmosphere and neutral wind. Physics-based ionospheric models, such as the Utah State University (USU) Time-Dependent Ionospheric Model (TDIM), use these statistical models as magnetospheric and thermospheric inputs. However, the 3-h time interval between index computations is now considered a shortfall with regard to specifying and forecasting phenomena known to have faster time constants, e.g., auroral electrojet variations during a substorm. Therefore, these indices have been targeted for high-time resolution development; we have developed such indices in Della-Rose et al. (1999). We now use our 15-minute station “K-like” index to determine the effect of introducing high-time resolution magnetic fluctuations into the TDIM inputs. This study represented the high-latitude ionosphere by a grid of 1484 locations, and was carried out for a geomagnetic storm period during solar maximum and “simulated” winter solstice conditions. We found that, for fixed Interplanetary Magnetic Field (IMF) B_y/B_z ratio, driving the TDIM with our 15-minute “K-like” index altered the average high-latitude N_mF₂ value by as much as 8% (vs. the average N_mF₂ obtained using a 3-h index to drive the TDIM). More significantly, the standard deviation of the N_mF₂ variations was up to 35%. Under some conditions, the average N_mF₂ was changed by up to 30% with a standard deviation of over 60%. However, the effect of selecting different convection patterns that represented three southward IMF B_z orientations led to larger effects. The high-latitude average N_mF₂ changed by 10% or less, but the spread in the distribution always ranged from standard deviations of 29 to 68%. These results indicate that there is a substantial need to consider both short-term magnetic fluctuations and inclusion of real-time IMF data in the inputs to ionospheric models.     

Resolving geomagnetic disturbances using “K-like” geomagnetic indices with variable time intervals

One of the efforts of the space weather community is to find better near real-time indices of geomagnetic activity. Many models developed for, and used by, space weather forecasters rely on the Kp/ap indices. However, the 3-h time interval between index computations is now considered a shortfall with regard to specifying and forecasting phenomena known to have faster time constants, e.g., auroral electrojet variations during a substorm. Therefore these indices have been targeted for high-time resolution development. Our study addresses this question by attempting to develop a “K-like” station index with a variable time interval. By comparing the distributions of these different time interval indices with the traditional 3-h K index an immediate difficulty is uncovered. Namely, the new distribution has a markedly different average index value. Hence no straightforward use of these indices in lieu of the traditional K index is possible. However, we demonstrate that, through a simple re-normalization process, the frequency distribution of our variable-time indices can be made to approximate the 3-h K index distribution. Further, when the temporal variability of the 3-h K index is compared against both a “sliding” 3-h index and a 15-min index, it is found that the 15-min index is significantly better at reproducing the station geomagnetic variability. The question not addressed here, but one that needs to be raised, concerns the possible difference in physical processes reflected by the 3-h index vs the shorter time interval indices. If there is no difference, then after a suitable range-to-index conversion these higher time resolution indices could potentially be used in place of the traditional 3-h station K index.     

Vertically Integrated Hydraulic Conductivity: A New Parameter for Groundwater-Surface Water Analysis

Numerical modeling of groundwater-surface water interactions provides vital information necessary for determining the extent of nutrient transport, quantifying water budgets, and delineating zones of ecological support. The hydrologic data that drive these models are often collected at disparate scales and subsequently incorporated into numerical models through upscaling techniques such as piecewise constancy or geostatistical methods. However, these techniques either use basic interpolation methods, which often simplifies the system of interest, or utilize complex statistical methods that are computationally expensive, time consuming, and generate complex subsurface configurations. We propose a bulk parameter termed “vertically integrated hydraulic conductivity” (K_V), and defined as the depth-integrated resistance to fluid flow sensed at the groundwater-surface water interface, as an alternative to hydraulic conductivity when investigating vertical fluxes across the groundwater-surface water interface. This bulk parameter replaces complex subsurface configurations in situations dominated by vertical fluxes and where heterogeneity is not of primary importance. To demonstrate the utility of K_V, we extracted synthetic temperature time series data from a forward numerical model under a variety of scenarios and used those data to quantify vertical fluxes using the amplitude ratio method. These quantified vertical fluxes and the applied hydraulic head gradient were subsequently input into Darcy's Law and used to quantify K_V. This K_V was then directly compared to the equivalent hydraulic conductivity (K_T) assuming an infinitely extending layer. Vertically integrated hydraulic conductivity allows for more accurate and robust flow modeling across the groundwater-surface water interface in instances where complex heterogeneities are not of primary concern.     

Stress-strain state of the lithosphere in the southern Baikal region and northern Mongolia from data on seismic moments of earthquakes

Investigation and understanding of the present-day geodynamic situation are of key importance for the elucidation of the laws and evolution of the seismic process in a seismically active region. In this work, seismic moments of nearly 26000 earthquakes with K _p ≥ 7 (M _LH ≥ 2) that occurred in the southern Baikal region and northern Mongolia (SBNM) (48°–54°N, 96°–108°E) from 1968 through 1994 are determined from amplitudes and periods of maximum displacements in transverse body waves. The resulting set of seismic moments is used for spatial-temporal analysis of the stress-strain state of the SBNM lithosphere. The stress fields of the Baikal rift and the India-Asia collision zone are supposed to interact in the region studied. Since the seismic moment of a tectonic earthquake depends on the type of motion in the source, seismic moments and focal mechanisms of earthquakes belonging to four long-term aftershock and swarm clusters of shocks in the Baikal region were used to “calibrate” average seismic moments in accordance with the source faulting type. The study showed that the stress-strain state of the SBNM lithosphere is spatially inhomogeneous and nonstationary. A space-time discrepancy is observed in the formation of faulting types in sources of weak (K _p = 7 and 8) and stronger (K _p ≥ 9) earthquakes. This discrepancy is interpreted in terms of rock fracture at various hierarchical levels of ruptures on differently oriented general, regional, and local faults. A gradual increase and an abrupt, nearly pulsed, decrease in the vertical component of the stress field S _v is a characteristic feature of time variations. The zones where the stress S _v prevails are localized at “singular points” of the lithosphere. Shocks of various energy classes in these zones are dominated by the normal-fault slip mechanism. For earthquakes with K _p = 9, the source faulting changes with depth from the strike-slip type to the normal-strike-slip and normal types, suggesting an increase in S _v . On the whole, the results of this study are well consistent with the synergism of open unstable dissipative systems and are usable for interpreting the main observable variations in the stress-strain state of the lithosphere in terms of spatiotemporal variations in the vertical component of the stress field S _v . This suggests the influence of rifting on the present-day geodynamic processes in the SBNM lithosphere.     

Rocking response of SDOF systems on shallow improved sand: An experimental study

Recent studies have highlighted the potential advantages of allowing inelastic foundation response during strong seismic shaking. Such an alternative seismic design philosophy, in which soil failure is used as a “fuse” for the superstructure has recently been proposed, in the form of “rocking isolation”. Within this context, foundation rocking may be desirable as a means of bounding the inertia forces transmitted onto the superstructure, but incorporates the peril of unacceptable settlements in case of a low static factor of safety FS_v. Hence, to ensure that rocking is materialized through uplifting rather than sinking, an adequately large FS_v is required. Although this is feasible in theory, soil properties are not always well-known in engineering practice. However, since rocking-induced soil yielding is only mobilized within a shallow layer underneath the footing, “shallow soil improvement” is considered as an alternative approach to release the design from the jeopardy of unforeseen inadequate FS_v. For this purpose, this paper studies the rocking response of relatively slender SDOF structures (h/B ratio equals 3 and rocking dominates over sliding), with emphasis on the effectiveness of shallow soil improvement stretching to various depths below the foundation. A series of reduced-scale monotonic and slow-cyclic pushover tests are conducted on SDOF systems lying on a square surface foundation. It is shown that shallow soil improvement may, indeed, be quite effective provided that its depth is equal to the width of the foundation. For lightly-loaded systems, an even shallower soil improvement may also be considered effective, depending on design requirements. The effectiveness of shallow soil improvement is ameliorated with the increase of cyclic rotation amplitude, and with repeating cycles of loading.     

Improved Gath–Geva clustering for fuzzy segmentation of hydrometeorological time series

In this paper, an improved Gath–Geva clustering algorithm is proposed for automatic fuzzy segmentation of univariate and multivariate hydrometeorological time series. The algorithm considers time series segmentation problem as Gath–Geva clustering with the minimum message length criterion as segmentation order selection criterion. One characteristic of the improved Gath–Geva clustering algorithm is its unsupervised nature which can automatically determine the optimal segmentation order. Another characteristic is the application of the modified component-wise expectation maximization algorithm in Gath–Geva clustering which can avoid the drawbacks of the classical expectation maximization algorithm: the sensitivity to initialization and the need to avoid the boundary of the parameter space. The other characteristic is the improvement of numerical stability by integrating segmentation order selection into model parameter estimation procedure. The proposed algorithm has been experimentally tested on artificial and hydrometeorological time series. The obtained experimental results show the effectiveness of our proposed algorithm.     

Impacts of Urbanization and Station-relocation on Surface Air Temperature Series in Anhui Province, China

Since the 1990s, many meteorological stations in China have passively “entered” cities, which has led to frequent relocation and discontinuity in observational records at many stations. To study the impacts of urbanization on surface air temperature series, 52 meteorological stations in Anhui Province were chosen based firstly on a homogeneity test of the time series, and then their surrounding underlying surfaces during different decades were identified utilizing Landsat Multispectral Scanner images from the 1970s, Landsat Thematic Mapper images from 1980s and 1990s, and Enhanced Thematic Mapper images after 2000, to determine whether or not the station “entered” city, and then these stations were categorized into three groups: urban, suburban, and rural using Landsat-measured land use/land cover (LULC) around the station. Finally, variations in annual mean air temperature (T _mean), maximum air temperature (T _max), and minimum air temperature (T _min) were analyzed in urban-type stations and compared to their surrounding rural-type stations. The results showed that, in Anhui Province over the past two decades, many rural stations experienced urbanization and changed into urban or suburban locations. This process is referred as the “city-entering” phenomena of stations. Consequently, many of the latest stations were relocated and moved to currently rural and suburban areas, which significantly influenced the continuity of observational records and the homogeneity of long-term trends. Based on homogeneous data series, the averaged annual T _mean, T _max, and T _min over Anhui Province increased at a rate of 0.407, 0.383 and 0.432 °C decade^?1 from 1970 to 2008. The strongest effect of urbanization on annual T _mean, T _max, and T _min trends occurred at urban stations, with corresponding contributions of 35.824, 14.286, and 45.161 % to total warming, respectively. This work provides convincing evidences that (1) urban expansion has important impacts on the evaluation of regional climate change, (2) high spatial resolution images of Landsat are very useful for selecting reference climate stations for evaluating the potential urban bias in the surface air temperature data in certain regions of the continents, and (3) meteorological observation adjustments of station-relocation-induced inhomogeneities are essential for the study of regional or global climate change.     

Rocking-isolated frame structures: Margins of safety against toppling collapse and simplified design approach

This paper aims to explore the limitations associated with the design of “rocking-isolated” frame structures. According to this emerging seismic design concept, instead of over-designing the isolated footings of a frame (as entrenched in current capacity–design principles), the latter are under-designed with the intention to limit the seismic loads transmitted to the superstructure. An idealized 2-storey frame is utilized as an illustrative example, to investigate the key factors affecting foundation design. Nonlinear FE analysis is employed to study the seismic performance of the rocking-isolated frame. After investigating the margins of safety against toppling collapse, a simplified procedure is developed to estimate the minimum acceptable footing width B_min, without recourse to sophisticated (and time consuming) numerical analyses. It is shown that adequate margins of safety against toppling collapse may be achieved, if the toppling displacement capacity of the frame δ_topl (i.e. the maximum horizontal displacement that does not provoke toppling) is sufficiently larger than the seismic demand δ_dem. With respect to the capacity, the use of an appropriate “equivalent” rigid-body is suggested, and shown to yield a conservative estimate of δ_topl. The demand is estimated on the basis of the displacement spectrum, and the peak spectral displacement SD_max is proposed as a conservative measure of δ_dem. The validity and limitations of such approximation are investigated for a rigid-block on rigid-base, utilizing rigorous analytical solutions from the bibliography; and for the frame structure on nonlinear soil, by conducting comprehensive nonlinear dynamic time history analyses. In all cases examined, the simplified SD_max approach is shown to yield reasonably conservative estimates.     

Heat flow studies: Constraints on the distribution of uranium,thorium and potassium in the continental crust

To study the amount of heat generated by radioactive decay in the continental crust, the usual practice in the literature is to fit to the heat flow and radioactivity data a relationship of the form: Q = Q_r + D · A where Q and A are the observed heat flow and radiogenic heat production. Q_r is the “reduced” heat flow and D is a depth scale. This procedure implicitly assumes that uranium, thorium and potassium have identical distributions in the crust. We suggest that significant information may be lost as the three radioelements may in fact be affected by processes operating over different depths.Data published for four heat flow provinces throughout the world are used to estimate the distributions of uranium, thorium and potassium in the continental crust. These distributions are characterized by a depth scales defined as follows: D_i =∫0h C_i(z)C_i(0)dz where h is the thickness of the layer containing the bulk of radioactivity and C_i(z) the concentration of element i at depth z. Three depth scales are computed from a least-squares fit to the following relationship: Q = Q_r + D_U · A_U + D_T · A_T + D_K · A_T where Q is the observed heat flow and Q_r some constant (a reduced heat flow). A_i is the heat generation rate due to the radioactive decay of element i, and D_i is the corresponding depth scale.The analysis suggests that the three distributions are different and that they have the same basic features in the four provinces considered. The depth scale for potassium is large in granitic areas, that for thorium is small and that for uranium lies between the other two.We propose a simple model according to which each radioelement essentially provides a record for one process. Potassium gives a depth scale for the primary differentiation of the crust. Thorium gives the depth scale of magmatic or metamorphic fluid circulation. Finally, the uranium distribution reflects the late effects of alteration due to meteoric water. We show that the heat flow and radioactivity data are compatible with this model.Our analysis and numerical results are supported by data from deep boreholes and by geochemical evidence, such as detailed investigations of plutonic series and studies of U-Th-Pb systematics.     

Assessment of the Relative Largest Earthquake Hazard Level in the NW Himalaya and its Adjacent Region

In the present study, the level of the largest earthquake hazard is assessed in 28 seismic zones of the NW Himalaya and its vicinity, which is a highly seismically active region of the world. Gumbel’s third asymptotic distribution (hereafter as GIII) is adopted for the evaluation of the largest earthquake magnitudes in these seismic zones. Instead of taking in account any type of M_max, in the present study we consider the ω value which is the largest earthquake magnitude that a region can experience according to the GIII statistics. A function of the form Θ(ω, RP_6.0) is providing in this way a relatively largest earthquake hazard scale defined by the letter K (K index). The return periods for the ω values (earthquake magnitudes) 6 or larger (RP_6.0) are also calculated. According to this index, the investigated seismic zones are classified into five groups and it is shown that seismic zones 3 (Quetta of Pakistan), 11 (Hindukush), 15 (northern Pamirs), and 23 (Kangra, Himachal Pradesh of India) correspond to a “very high” K index which is 6.     

SEISMIC REFRACTION METHOD TO STUDY THE FOUNDATION ROCK OF A DAM*

Dynamic elastic moduli like E, μ, K and μ of the foundation rock of a dam have been determined by finding V_p- and V_s-velocities by seismic refraction with a hammer as source. Some parameters such as “fracture frequency” and “rock quality designation” (RQD) of the foundation rock have been derived using “average regression curves” and V_p-velocities. By comparing K/μ with V_p/V_s, a few locations showing weathered conditions have been demarcated. This compares well with RQD values of those locations.     

Population dynamics of earthquakes and mathematical modeling

We present a mathematical model that describes temporal variations of earthquakes. This model is represented as $$dn(t)/dt = n(t)\left[ {\alpha - \beta n(t) - \int_{ - \infty }^t {n(s)h(t - s)ds} } \right].$$ Heren(t) shows the numberof earthquakes per unit time in a certain region. α and β are constants. The functionh(t) denotes the hysteresis effect of the earthquake occurrences and can take the following forms depending on the physical conditions of the crusts; (A)h(t)=0: the equation represents a logistic type increase or decrease and approaches a stationary state asymptotically. This describes aftershock series of large earthquakes and earthquake swarms of large scale such as the Wakayama and Matsushiro swarms in Japan; (B)h(t)=constant (β=0): frequencyn(t) increases initially and then decreases gradually and shows some kind of volcanic swarms; (C)h(t) = κ · {exp(?γ₁ t) ? exp(γ₂ t)}, (γ₂ > γ₁): this denotes time delay effects and the model shows periodic patterns of bursts or “rhythms” of earthquakes, which are observed in earthquake swarms. When external effects are taken into consideration, the model is further generalized and can describe various seismic patterns. These effects represent various influences of the circumstances like the earth tide and fluctuations of plate motions, etc. Whenh(t) takes type (A) and the external effect is random, the equation displays repetitive random patterns with bursts. Particularly interesting cases may be those whenh(t) is type (C) and the external force is periodic like the earth tide. Various nonperiodic as well as periodic patterns of earthquakes appear. These are the phenomena of “chaos” and “entrainment”, etc. and can be commonly observed. Varieties of actual earthquake patterns seem to be, at least partly, explained by the nonlinear coupling between the tidal forces and autonomous rhythms of earthquakes.     

Estimation of internal nutrient release in large shallow Lake Taihu,China

Based on field investigation of wave, sediment suspension and the changes in nutrient concentration of the water column in Lake Taihu, China, we proposed two release models to quantify nutrient release under static and dynamic conditions, respectively. Under static conditions, nutrient release from sediments to the overlying water mainly depends on chemical diffusion induced by concentration gradient, in which the nutrient release is controlled by the temperature, dissolved oxygen concentration in the sediment-water interface, oxidation-reduction potential and the concentration difference between porewater and overlying water. Under dynamic condition (or disturbed condition), both dissolved and particulate nutrients in sediments are released into the water column because of wind-induced sediment suspension. The amount of nutrient release under dynamic conditions is larger than that under the static condition. The release of dissolved nutrients, however, does not increase because the wind induced turbulence made oxidation of metallic elements such as Fe (ferric iron), Mn which are capable of precipitating soluble reactive phosphate (SRP). Under dynamic conditions, therefore, the release of total phosphorus (TP) increases dramatically but the release of SRP is close to those under static conditions. In sediments of Lake Taihu, high Fe content leads to a high ratio of Fe to P contents in sediments (Fe:P ratio). Under dynamic conditions, therefore, nutrient release is controlled by the intensity of disturbance, sediment consolidation and nutrient content in sediments. As for dissolved nutrients, especially SRP, the release is also controlled by the intensity of dynamic re-oxidation, Fe content in sediments and nutrient concentration gradient between porewater and overlying water. Based on these two release modes, the release flux in Lake Taihu has been estimated. In the static condition (i.e. laboratory experimental condition), total release of NH₄ ⁺-N for whole lake is ca. 10,000 ton/a, and PO₄ ^3?-P is ca. 900 ton/a. In the dynamic condition, nutrient release following sediment suspension was estimated according to three different intensities of wind forcing which were defined as “calm” (wind speed is less than 2 m/s), “gentle” (wind speed is greater than 2 m/s and less than 6 m/s) and “gust” (wind speed is greater than 6 m/s). The release rate in the condition of “calm” was estimated in terms of the nutrient release in the laboratory experimental static condition; whereas the release rate in conditions of “gentle” and “gust” was estimated in terms of measurement during sediment resuspension conducted in flume experiments. With the observation of wind velocity and frequency in 2001, each type of wind forcing took the frequency of 12%, 82% and 6% for “calm”, “gentle” and “gust”, respectively. The yearly release of nitrogen was 81,000 ton and phosphorus was 21,000 ton, which is about 2–6 folds of annual external loading, respectively.     

Galactic cosmic rays—clouds effect and bifurcation model of the Earth global climate. Part 2. Comparison of theory with experiment

The solution of energy-balance model of the Earth global climate and the EPICA Dome C and Vostok experimental data of the Earth surface palaeotemperature evolution over past 420 and 740 kyr are compared.In the framework of proposed bifurcation model (i) the possible sharp warmings of the Dansgaard-Oeschger type during the last glacial period due to stochastic resonance is theoretically argued; (ii) the concept of climatic sensitivity of water in the atmosphere, whose temperature instability has the form of so-called hysteresis loop, is proposed, and based on this concept the time series of global ice volume over the past 1000 kyr, which is in good agreement with the time series of δ¹⁸O concentration in the sea sediments, is obtained; (iii) the so-called “CO₂ doubling” problem is discussed.     

The TiO2–K2O–P2O5 diagram: A method of discriminating between oceanic and non-oceanic basalts

The TiO₂–K₂O–P₂O₅ ternary diagram is proposed as a method of discriminating between oceanic and non-oceanic (continental) basalts. This diagram is effective for non-alkaline “primitive” basalts: fractionated rocks cannot be adequately discriminated. Suitable analyses are those which have total alkalies ≤ 20% in an (Fe₂O₃ + FeO)–MgO–(Na₂O + K₂O) diagram. The proposed dividing line separates 93% of 222 ocean-floor and ocean-ridge basalts into the oceanic field and > 80% of continental basalt analyses into the non-oceanic field. Two exceptions are the Tertiary basalts of Greenland and the Deccan Traps which have oceanic affinities. “Continental” suites displaying an oceanic affinity in the TiO₂–K₂O–P₂O₅ diagram may be a result of abortive attempts to generate new sea floor. Preliminary results for dike swarms and Archean basalts suggest preponderant oceanic affinities. Alteration and metamorphism of oceanic basalts generally occasion enrichment of K₂O relative to TiO₂ and P₂O₅.