Fractal interrelationships in field and seismic data. Quarterly report, September 21 - December 31, 1995

Under task 1 contour irregularities traced over both study areas in the previous quarter were scanned into the computer and digitized at a 30 meter interval. Patters mapped in both the Granny Creek and Middle Mountain field areas are presented in Figures 1 and 2 respectively. One of the hypotheses of this research project is that contour irregularities must be controlled by a combination of sedimentation features, lithologic variation, and local structure and fracture distribution. The most promising result obtained thus far in this study are those reported under Tasks 4 and 5, seismic analysis. If further tests continue to support the observation that increased fractal dimension reflects the presence of detached structure, the analytical techniques employed here may be of use in the routine evaluation of seismic data to locate subtle traps. The observations may allow one to predict the variation of fractal dimension within a subsurface fracture network based on seismic observation of resolvable structural parameters. Such predictions would provide a working hypothesis, which could be modified within the context of available subsurface data

Dendritic flux avalanches in superconducting Nb3Sn films

The penetration of magnetic flux into a thin superconducting film of Nb3Sn with critical temperature 17.8K and critical current density 6MA/cm^2 was visualized using magneto-optical imaging. Below 8 K an avalanche-like flux penetration in form of big and branching dendritic structures was observed in response to increasing perpendicular applied field. When a growing dendritic branch meets a linear defect in the film, several scenarios were observed: the branch can turn and propagate along the defect, continue propagation right through it, or "tunnel" along a flux-filled defect and continue growth from its other end. The avalanches manifest themselves in numerous small and random jumps found in the magnetization curve.Comment: 3 pages, 4 figures, submitted to Cryogenics. Revision: M(H) data adde

Wilson function transforms related to Racah coefficients

The irreducible $*$-representations of the Lie algebra $su(1,1)$ consist of discrete series representations, principal unitary series and complementary series. We calculate Racah coefficients for tensor product representations that consist of at least two discrete series representations. We use the explicit expressions for the Clebsch-Gordan coefficients as hypergeometric functions to find explicit expressions for the Racah coefficients. The Racah coefficients are Wilson polynomials and Wilson functions. This leads to natural interpretations of the Wilson function transforms. As an application several sum and integral identities are obtained involving Wilson polynomials and Wilson functions. We also compute Racah coefficients for U_q(\su(1,1)), which turn out to be Askey-Wilson functions and Askey-Wilson polynomials.Comment: 48 page

Askey-Wilson Type Functions, With Bound States

The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it transparent that these functions satisfy a beautiful symmetry property. It essentially means that the geometric and the spectral parameters are interchangeable in these functions. We call the resulting functions the Askey-Wilson functions. Then, we show that by adding bound states (with arbitrary weights) at specific points outside of the continuous spectrum of some instances of the Askey-Wilson difference operator, we can generate functions that satisfy a doubly infinite three-term recursion relation and are also eigenfunctions of $q$-difference operators of arbitrary orders. Our result provides a discrete analogue of the solutions of the purely differential version of the bispectral problem that were discovered in the pioneering work [8] of Duistermaat and Gr\"unbaum.Comment: 42 pages, Section 3 moved to the end, minor correction

Site 1220

Site 1220 (10°10.600´N, 142°45.503´W; 5218 meters below sea level (mbsl); Fig. F1) forms a southerly component of the 56-Ma transect drilled during Leg 199. It is situated about midway between the Clipperton and Clarion Fracture Zones in typical abyssal hill topography. On the basis of regional magnetic anomalies, we anticipated basement age at Site 1220 to be equivalent to Chron C25n (~56 Ma; Cande et al., 1989), slightly older than at Site 1219. At the outset of drilling at Site 1220, our estimate for total sediment depth was ~225 meters below seafloor (mbsf) (Fig. F2). Based upon a fixed hotspot model (Gripp and Gordon, 1990, for 0- to 5-Ma Pacific hotspot rotation pole; Engebretson et al., 1985, for older poles), Site 1220 should have been located ~3° south of the equator at 56 Ma and in an equatorial position at 40 Ma. Thus, Site 1220 should have been situated underneath the South Equatorial Current in the early Eocene. A nearby piston core (EW9709-13PC) taken during the site survey cruise recovered >16 m of red clay, with the base of the core dated as middle-early Miocene on the basis of radiolarian biostratigraphy (Lyle, 2000). Site 1220 will be used to study equatorial ocean circulation from the late Paleocene through the late Eocene during the early Cenozoic thermal maximum. Sediment records from this site will help to define the calcite compensation depth (CCD) and lysocline during the Paleocene-Eocene and Eocene-Oligocene transitions. In this and other respects, Site 1220 will act as an interesting analog to Site 1218. Both sites are thought to have been located on the equator at ~40 Ma, but the older crustal age anticipated at Site 1220 dictates a greater paleowater depth than for contemporaneous sediments accumulating at Site 1218

Site 1216

Site 1216 (21°27.16´N, 139°28.79´W; 5152 meters below sea level [mbsl]; Fig. F1) is situated in abyssal hill topography south of the Molokai Fracture Zone and two small associated unnamed parasitic fracture zones (Fig. F2). Based on magnetic lineations, Site 1216 appears to be situated on normal ocean crust formed during the C25r magnetic anomaly (~57 Ma; Atwater and Severinghaus, 1989). Site 1216 was chosen for drilling because it is near the thickest section of lower Eocene sediments along the 56-Ma transect, which was based upon the seismic stratigraphy of seismic reflection data acquired on site survey cruise EW9709 during transits between the proposed drill sites (Lyle et al., this volume; Moore et al., 2002). The Cenozoic history of sedimentation in this region was poorly constrained prior to Leg 199, being largely based on two Deep Sea Drilling Project (DSDP) drill sites (40 and 41) and piston core data (EW9709-3PC) from ~1.5° in latitude to the south. Based on data from these drill sites, we expected the sedimentary sequence at Site 1216 to comprise red clays (a mixture of wind-blown dust and authigenic precipitates) overlying a biogenic sediment section composed of an upper middle Eocene radiolarian ooze and lower carbonate ooze deposited when the site was near the ridge crest in the late Paleocene and early Eocene. The broad paleoceanographic objectives of drilling the sedimentary sequence anticipated at Site 1216 are as follows: (1) to help define the shift in the Intertropical Convergence Zone through the Paleogene by following the change in eolian-dust composition and flux through time (red clays) and (2) to help define the latitudinal extent, composition, and mass accumulation of plankton communities in the north equatorial Pacific region thereby constraining ocean circulation patterns and the extent of the equatorial high-productivity belt in the Eocene ocean. Results from Site 1216 will also provide important information to test whether there was significant motion of the Hawaiian hotspot with respect to the Earth's spin axis during the early Cenozoic. At 56 Ma, the backtracked location of Site 1216 based upon a hotspot reference frame (Gripp and Gordon, 1990, for 0- to 5-Ma Pacific hotspot rotation pole; Engebretson et al., 1985, for older poles) is about 9°N, 108°W. If significant hotspot motion or true polar wander occurred since 57 Ma (Petronotis et al., 1994), this drill site could have been much nearer to the equator

Site 1222

Site 1222 (13°48.98´N, 143°53.35´W; 4989 meters below sea level [mbsl]; Fig. F1) forms a south-central component of the 56-Ma transect drilled during Leg 199 and is situated ~2° south of the Clarion Fracture Zone in typical abyssal hill topography. On the basis of regional magnetic anomalies, we anticipated basement age at Site 1222 to be equivalent to Chron C25r or Chron C25n (~56-57 Ma) (Cande et al., 1989), which is slightly older than at Site 1219. At the outset of drilling at Site 1222, our estimate for total sediment thickness was ~115 m (Fig. F2). Based upon a fixed hotspot model (Gripp and Gordon, 1990, for 0- to 5-Ma Pacific hotspot rotation pole; Engebretson et al., 1985, for older poles) Site 1222 should have been located ~1° north of the equator at 56 Ma and ~4°N at 40 Ma. A nearby gravity core (EW9709-17GC), taken during the site survey cruise, recovered >5 m of red clay with a late-middle Miocene age on the basis of radiolarian biostratigraphy (Lyle, 2000). Deep Sea Drilling Project (DSDP) Site 42 located ~4° east of Site 1222, was not drilled to basement but contains a thin sedimentary section (~100 m thick) of upper Oligocene nannofossil ooze through middle Eocene radiolarian nannofossil ooze. In turn, DSDP Site 162 lies ~1° north of DSDP Site 42 and is situated on young crust (49 Ma) that contains ~150 m of clayey radiolarian and nannofossil oozes of early Oligocene-middle Eocene age. Site 1222 will be used to study the position of the Intertropical Convergence Zone in the late Eocene and Oligocene, to sample late Paleocene and early Eocene sediments in the central tropical Pacific Ocean, and to help determine whether or not there has been significant southward movement of the hotspots with respect to the spin axis prior to 40 Ma

Site 1217

Site 1217 (16°52.02´N, 138°06.00´W; 5342 meters below sea level [mbsl]; Fig. F1) is one of seven sites drilled to target upper Paleocene crust along a latitudinal transect during Leg 199 and will be used to investigate paleoceanographic processes in the northern tropical early Eocene Pacific Ocean. Site 1217 is situated ~1° north of the Clarion Fracture Zone on abyssal hill topography typical of the central Pacific. Based on magnetic lineations, basement age at Site 1217 should be in magnetic Anomaly C25r or ~57 Ma (Cande et al., 1989; timescale of Cande and Kent, 1995). The Cenozoic history of sedimentation in this region was poorly constrained prior to Leg 199 drilling because the nearest drill site (Deep Sea Drilling Project [DSDP] Site 162) is situated ~300 km south and west on 48-Ma crust. Based on data from this early rotary-cored hole, magnetic anomaly maps, a shallow-penetration piston core near Site 1217 (EW9709-4PC), and seismic profiling (Fig. F2), we expected the sedimentary sequence at Site 1217 to comprise a relatively thick (25 to 35 m thick) section of red clays overlying a radiolarian ooze and a basal carbonate section with possible chert near basement (estimated total depth ~125-150 meters below seafloor [mbsf]) deposited when the site was near the ridge crest in the late Paleocene and early Eocene. Site 1217 was chosen because it is anticipated to have been located just outside of the equatorial region at 56 Ma, ~5°N, 106°W based upon a fixed hotspot model (Gripp and Gordon, 1990, for 0- to 5-Ma Pacific hotspot rotation pole; Engebretson et al., 1985, for older poles). On the same basis at 40 Ma, the site was located at ~8°N, 111°W. Thus, Site 1217 should help define the paleoceanography of the northern tropical Pacific, in particular locating the ancient North Equatorial Countercurrent (NECC) region. General circulation-model experiments for the early Eocene (see Huber, this volume) suggest that the NECC was a well-developed current during this time period. Other paleoceanographic and paleoclimatic objectives of drilling the sedimentary sequence anticipated at Site 1217 are as follows: (1) to help define the shift in the Intertropical Convergence Zone through the Paleogene by following the change in eolian dust composition and flux through time (red clays); (2) to help constrain the middle-late Eocene calcite compensation depth (CCD); and (3) to sample the Paleocene/Eocene (P/E) boundary, one of the most climatologically critical intervals of Cenozoic time. Recovery of deep-sea sediments from this time interval during Leg 199 is a high priority because the P/E boundary has never before been sampled in the central tropical Pacific Ocean. Results from Site 1217 will also provide important information to test whether there was significant motion of the Hawaiian hotspot, with respect to the Earth's spin axis during the early Cenozoic. At 56 Ma, the backtracked location based upon a hotspot reference frame is ~5°N, 106°W, and at 40 Ma is ~8°N, 106°W. If significant hotspot motion or true polar wander occurred since 57 Ma (Petronotis et al., 1994), this drill site could have been much nearer to the equator