PRINCIPLES AND APPLICATION OF MAXIMUM KURTOSIS PHASE ESTIMATION1

Methods of minimum entropy deconvolution (MED) try to take advantage of the non-Gaussian distribution of primary reflectivities in the design of deconvolution operators. Of these, Wiggins’(1978) original method performs as well as any in practice. However, we present examples to show that it does not provide a reliable means of deconvolving seismic data: its operators are not stable and, instead of whitening the data, they often band-pass filter it severely. The method could be more appropriately called maximum kurtosis deconvolution since the varimax norm it employs is really an estimate of kurtosis. Its poor performance is explained in terms of the relation between the kurtosis of a noisy band-limited seismic trace and the kurtosis of the underlying reflectivity sequence, and between the estimation errors in a maximum kurtosis operator and the data and design parameters. The scheme put forward by Fourmann in 1984, whereby the data are corrected by the phase rotation that maximizes their kurtosis, is a more practical method. This preserves the main attraction of MED, its potential for phase control, and leaves trace whitening and noise control to proven conventional methods. The correction can be determined without actually applying a whole series of phase shifts to the data. The application of the method is illustrated by means of practical and synthetic examples, and summarized by rules derived from theory. In particular, the signal-dominated bandwidth must exceed a threshold for the method to work at all and estimation of the phase correction requires a considerable amount of data. Kurtosis can estimate phase better than other norms that are misleadingly declared to be more efficient by theory based on full-band, noise-free data.     

Coalification in Carboniferous sediments from the Lötschberg base tunnel

Vitrinite reflectance (Rr), proximate analysis and carbon isotope composition (δ¹³C) have been used to characterise coal samples from two zones of Late Carboniferous sediments (Gastern and Ferden) in the Aar massif where they are penetrated by the Lötschberg base tunnel (constructed between 1999 and 2005). Samples are characterised by variable ash yields (21.7–93.9%; dry basis); those with ash yields of less than ~50% and with volatile matter content (V;dry ash-free basis) within the limits 2 < V% ≤ 8 are anthracite. Values of Rr range from 3.89% to 5.17% and indicate coalification to the rank of anthracite and meta-anthracite in both Gastern and Ferden Carboniferous zones. Samples of anthracite and shale from the Gastern Carboniferous exhibit a relatively small range in δ¹³C values (–24.52‰ to –23.38‰; mean: –23.86‰) and are lighter than anthracite samples from the Ferden Carboniferous (mean: –22.20‰). The degree of coalification in the Gastern and Ferden Carboniferous zones primarily depends on the maximum rock temperature (T) attained as a result of burial heating. Vitrinite reflectance based estimates of T range from ~290° –360 °C. For a proposed palaeogeothemal gradient of 25 ° C/km at the time of maximum coalification the required overburden is attributable to relatively thin autochtonous Mesozoic/Cenozoic sedimentary cover of the Aar massif and Gastern granite and deep tectonic burial beneath advancing Helvetic, Ultrahelvetic and Prealpine (Penninic) nappes in Early Oligocene to Miocene.     

Consolidation properties and structural alteration of Old Alluvium

Acta Geotechnica - We present experimental observations and a conceptual model for understanding the compression and swelling characteristics of Old Alluvium (OA) from San Juan, Puerto Rico. Prior...     

Geology and regional significance of the Sarnoo Hills,eastern rift margin of the Barmer Basin,NW India

The Barmer Basin is a poorly understood rift basin in Rajasthan, northwest India. Exposures in the Sarnoo Hills, situated along the central eastern rift margin of the Barmer Basin, reveal a sedimentary succession that accumulated prior to the main Barmer Basin rift event, and a rift‐oblique fault network that displays unusual geometries and characteristics. Here, we present a comprehensive study of Lower Cretaceous sedimentology on the basin margin, along with a detailed investigation of rift‐oblique faults that are exposed nowhere else in the region and provide critical insights into Barmer Basin evolution. Lower Cretaceous sediments were deposited within a rapidly subsiding alluvial plain fluvial system. Subsequent to deposition, the evolving Sarnoo Hills fault network was affected by structural inheritance during an early, previously unrecognised, rift‐oblique extensional event attributed to transtension between India and Madagascar, and formed a juvenile fault network within the immediate rift‐margin footwall. Ghaggar‐Hakra Formation deposition may have been triggered by early rifting which tectonically destabilised the Marwar Craton prior to the main northeast–southwest Barmer Basin rift event. The identification of early rifting in the Barmer Basin demonstrates that regional extension and the associated rift systems were established throughout northwest India prior to the main phase of Deccan eruptions. Inheritance of early oblique fault systems within the evolving Barmer Basin provides a robust explanation for poorly understood structural complications interpreted in the subsurface throughout the rift. Critically, the presence of syn‐rift sedimentary successions within older oblique rift systems obscured beneath the present‐day Barmer Basin has significant implications for hydrocarbon exploration.     

The impact of the Laacher See Volcano (11 000 yr B.P.) on terrestrial vegetation and diatoms

Late-glacial lake sediments containing the Laacher See Tephra (LST, 11 000 yr B.P.) have been analyzed for their pollen and diatom content at three sites at varying distances from the volcano and on different bedrock geologies. The aim was to test the null hypothesis that this major volcanic eruption had no effect on terrestrial pollen or aquatic diatom assemblages. The pollen spectra at all sites show a short-lived increase in grass pollen following the LST. Partial redundancy analysis and associated Monte Carlo permutation tests suggest, however, that the LST had no statistically significant effect at two sites but it had a statistically significant impact on the pollen assemblages at the site nearest (60 km) to the volcano.The diatom assemblages at the three sites changed individualistically after the LST deposition, with increases inAchnanthes minutissima at one site, an expansion ofAulacoseira species at another, and an increase ofAsterionella formosa andFragilaria brevistriata at the third site. Partial redundancy analysis and associated permutation tests suggest a statistically significant change in diatoms in relation to the LST and associated changes in sediment lithology at the one site situated on acidic bedrock. No significant impacts were found at the sites on volcanic or calcareous rocks. Due to the interaction between tephra and sediment lithology, it is not possible to conclude if the statistically significant diatom changes were a direct result of the LST deposition or an indirect result of lithological changes following LST deposition.This is the first paper in a series of papers published in this issue on high-resolution paleolimnology. These papers were presented at the Sixth International Paeolimnology Symposium held 19–21 April, 1993 at the Australian National University, Canberra, Australia. Dr A. F. Lotter and Dr. M. Sturm served as guest editors for these papers.     

Structure of the αFexAl1:xOOH solid solution

The three-dimensional local organisation around Fe atoms in a natural diaspore (Al_0.9955Fe_0.0045OOH) has been investigated by angular measurements of X-ray absorption spectra. It is demonstrated that in a single crystal of diaspore, the absorption cross-section exhibits the special case of trichroism where three independent measurements are needed to determine the absorption cross-section for any direction of polarization. Extended X-ray absorption fine structure (EXAFS) spectra were thus recorded at the following orientations of the polarization vector: , , and . The incoming white beam was monochromatized using two Si(331) crystals, which deliver at the Fe K-edge a completely linearly polarized X-ray beam. The reliability of our measurements was checked by comparing the isotropic EXAFS spectrum calculated from the three orthogonal measurements to the one of the diaspore powder recorded at the magic angle. It is shown that Fe³⁺ ions are not randomly distributed within the diaspore framework. Furthermore, only part of the Fe³⁺ ions substitutes Al, the others being located in the channels of the structure. The 3D local structure of the Fe domains has been modeled assuming hematite-like clusters of three Fe octahedra topotactically grafted to aluminous chains. These Fe clusters are thought to represent ancient multinuclear Fe surface complexes having formed at the time of the diaspore growth, and being sealed in its bulk structure. The whole crystal of diaspore is then thought to have kept the memory of the heterogeneous nucleation mechanism of these hematite nuclei. In addition to the well-known examples of atom segregations, ion vacancies, and intergrowths of discrete phases, this new type of crystal defect represents another evidence of non-equilibrium crystallization process under the thermodynamic and kinetic conditions that prevail at the earth's surface.     

Element sets for high-order Poincaré mapping of perturbed Keplerian motion

The propagation and Poincaré mapping of perturbed Keplerian motion is a key topic in Celestial Mechanics and Astrodynamics, e.g., to study the stability of orbits or design bounded relative trajectories. The high-order transfer map (HOTM) method enables efficient mapping of perturbed Keplerian orbits using the high-order Taylor expansion of a Poincaré or stroboscopic map. The HOTM is only accurate close to the expansion point and therefore the number of revolutions for which the map is accurate tends to be limited. The proper selection of coordinates is of key importance for improving the performance of the HOTM method. In this paper, we investigate the use of different element sets for expressing the high-order map in order to find the coordinates that perform best in terms of accuracy. A new set of elements is introduced that enables extremely accurate mapping of the state, even for high eccentricities and higher-order zonal perturbations. Finally, the high-order map is shown to be very useful for the determination and study of fixed points and center manifolds of Poincaré maps.     

Composition and heterogeneity of the microbial community in a coastal microbial mat as revealed by the analysis of pigments and phospholipid-derived fatty acids

The beaches of the North Sea barrier island Schiermonnikoog (The Netherlands) are covered by microbial mats. Five types of microbial mats were distinguished based on a variety of characteristics, located along a transect perpendicular to the coast. Biomass abundance and composition of the microbial community were analyzed in these mats using pigments and phospholipid-derived fatty acids (PLFA) as biomarkers. Biomass per gram sediment increased more than six-fold from the mats at the low water mark to mats found at the edge of the dunes. Microscopic analysis revealed that the increase in biomass was accompanied by a change in species composition. Pigment- and PLFA composition reflected the changes in species composition. The PLFA data could be used to estimate the relative group abundance using the matrix factorization program CHEMTAX., whereas the pigment data were found not to be suitable for this purpose.     

Fractal properties of crater ejecta outlines on Venus

Fractal property or self-similarity exists abundantly in many aspects in our universe. Fractals are rich in geology and have certain relations to various geological processes. This article presents analyses of fractal properties of 18 impact crater ejecta margins on the surface of Venus. The structured walk method was used to measure the length of perimeter of the ejecta margin and the resulting Richardson plots were investigated. EveryR-plot has a first linear part, a second part and a main scattering part. The variations seen in the second part include information on the formation and geology of the crater ejectas. The fractal dimension of the second part is related to the perimeter of the ejecta and thus to the impact energy. The ratio of the square of the perimeter to the area describes the lobateness of the ejecta and has a positive correlation to the perimeter in a way similar to that between the fractal dimension of the second part and the perimeter. Two linear subparts in the second part indicate different fractal properties due to various processes dominating on different scales. Scattering in the middle of the second part indicates the scale and type of the ejecta lobes. The smooth scattering over the entire second part is related to impact angle and energy. A threshold value beyond which the structured walk method cannot be used was observed at a ruler length of about 1/10 of the perimeter.