The Backus–Gilbert approach to the 3-D structure in the upper mantle – II. SH and SV velocity

Summary. Phase velocity variations obtained in the previous paper are inverted by the Backus–Gilbert method for the velocity structure of the upper mantle. Spheroidal modes and toroidal modes in the period range of 125–260 s are used in the inversion. The data cannot constrain all six parameters in a transversely isotropic medium and we chose to perturb only two parameters, SH and SV velocities. SV velocities are resolved between the depths of about 200 and 400 km and SH velocities between 0 and 200 km. Resolution kernels have half-peak widths of about 200–300 km in depth, becoming broader for deeper target depths. SV velocity kernels show secondary peaks near the surface of the Earth, with widths varying from 50 to 100 km. The deeper the target depths, the wider the secondary peaks near the surface. SH velocity kernels do not possess such secondary peaks. The trade-off between SV and SH velocities is small. SV velocity is essentially determined by spheroidal modes and SH velocity by toroidal modes. Because of the broad width of the resolution kernels, the structure in the resolved region is difficult to detect from our data set; for example the differences in SV velocity structure between 250 and 350 km or the differences in SH velocity between 100 and 200 km are difficult to distinguish. Considering the horizontal resolution of about 2000 km, obtained in the previous paper, averaging kernels for 3-D structure are quite elongated in the horizontal dimension.     

Linear programming approach to moment tensor inversion of earthquake sources and some tests on the three-dimensional structure of the upper mantle

Summary. A new method of moment tensor inversion is developed, which combines surface wave data and P -wave first motion data in a linear programming approach. Once surface wave spectra and first motion data are given, the method automatically obtains the solution that satisfies first motion data and minimizes the L1 norm of the surface wave spectra. We show the results of eight events in which the method works and is stable even for shallow events. We also show one event in which surface wave data and P -wave first motion data seem to be incompatible. In such cases, our method does not converge or converges to a solution which has a large minor (second) double couple component. It is an advantage that the method can determine the compatibility of two data sets without trial and error.
Laterally heterogeneous phase velocity corrections are used to obtain spectra at the source. The method is also applied to invert moment tensors of eight events in two recent three-dimensional (3-D) upper mantle structures. In both 3-D models, variances of spectra are smaller than those in a laterally homogeneous model at 256 s. Statistical tests show that those reductions are significant at a high confidence level for five events out of eight examined. For three events, we examined those reductions at shorter periods, 197 and 151 s. The reduction of variances is comparable to the results at 256 s and is again statistically significant at a high confidence level. Orientation of fault planes does not change very much by incorporation of lateral variations of phase velocity or by doing inversions at different periods. This is mainly because of the constraints from P -wave first motion data. Scatter of phase spectra at shorter periods, especially at 151 s, is great and suggests that surface wave ray paths deviate from great circle paths substantially and these effects cannot be ignored.     

Determination of plastic regions around underground openings by a coupled boundary-element-characteristics method

A two-dimensional hybrid method for solving elastoplastic problems in engineering is presented by coupling two existing methods, namely, the boundary element method and the characteristics method. The formulation of this method is presented, as well as an excellent procedure for the determination of the boundary between elastic and plastic regions. It is shown not only that this method is a powerful and accurate method for evaluating the shape and extent of the plastic region around rock caverns, which is of prime importance for the construction of rock caverns, but also applicable to a given range of the initial stress field ratio where only compressive failure occurs. Then, some typical examples are solved in order to check the accuracy of the solution by this method. Furthermore, its successful applications are presented and discussed to determine the shape and the extent of the plastic regions around parallel, circular and rectangular openings.     

Ocean anoxic events in the mid-Cretaceous simulated by a 3-D biogeochemical general circulation model

The mid-Cretaceous is well known for its ocean anoxic events. The causal mechanisms are controversial: stagnant deepwater, high biological productivity in the surface waters, and other possibilities have been suggested. Our study simulated the mid-Cretaceous ocean, using general circulation models combined with a marine biogeochemical cycle model to explore the relationship between thermohaline circulation and biogeochemical cycles and investigate the causes of ocean anoxic events. The simulated thermohaline circulation shows an unsteady inactive state. Oxygen concentrations in the deepwater decrease under the inactive state, but a horizontal gradient develops, with higher oxygen concentrations in the Tethys and lower concentrations in eastern Panthalassa. This is not due to the different ages of the deepwater but rather to the differences in biological productivity in the surface water, meaning that the relationship between thermohaline circulation and biogeochemical cycles under the inactive state is different from that in the present ocean. In the standard simulation, assuming the present level of the total amount of phosphate in the ocean, 29% of the bottom water is anoxic. The experiments increasing the amount of phosphate show its high sensitivity for extending the anoxic region with global-scale anoxia simulated under the doubled amount of phosphate. The high amount of phosphate would be reasonable because the inactive state would induce an imbalance of phosphate between riverine input and sediment output. Therefore, both the inactive thermohaline circulation and the increase in the total amount of phosphate in the ocean induce the global-scale anoxic condition in the deepwater.     

Roles of Physical Processes in the Carbon Cycle Using a Simplified Physical Model

A simplified physical model is proposed in this article to describe differences among basins in substance distributions which were not well described by previous simplified models. In the proposed model, the global ocean is divided into the Pacific/Indian Ocean (PI), the Atlantic Ocean (AT), the Southern Ocean and the Greenland/Iceland/Norwegian Sea. The model is consisted of five physical parameters, namely the air-sea gas exchange, the thermohaline circulation, the horizontal and vertical diffusions, and the deep convection in the high-latitude regions. Individual values of these parameters are chosen by optimizing model distribution of natural ¹⁴C as a physical tracer. The optimal value for a coefficient of vertical diffusion in the low-latitude region is 7.5 × 10^–5 [m²s^–1]. Vertical transports by the Antarctic Bottom Water and the North Atlantic Deep Water are estimated at 1.0 Sv and 9.0 Sv. Global-mean air-sea gas exchange time is calculated at 9.0 years. Using these optimal values, vertical profiles of dissolved inorganic carbon without biological production in PI and AT are estimated. Oceanic responses to anthropogenic fluctuations in substance concentrations in the atmosphere induced by the industrialization and nuclear bomb are also discribed, i.e., the effects appear significantly in AT while a signal is extremely weak in PI. A time-delay term is effective to make the PI water older near the bottom boundary.     

Surface currents around Hokkaido in the late fall of 1981 obtained from analysis of satellite images

This paper describes the characteristics of currents around Hokkaido using a current vector map compiled by chasing the displacement of sea marks on a pair of successive thermal infrared images taken from a satellite, NOAA-6. The points of some sea surface patterns showing distinctive features which can be commonly identified in both images are called Sea Marks≓. This sea mark chase method≓ has a great advantage over velocity measurements by boats or buoys, in that it gives a synoptic view of the velocity distribution over a broad sea area extending for some hundreds of miles on a short time scale of half a day.In order to investigate the current in the late fall of 1981, we used the data taken at 19:05 JST on 30 October and at 7:20 JST on 31 October. With these data taken with a 12 hr difference, the measurement accuracy of the speed of sea marks reached ±0.1 knot through geometrical correction. The velocity vectors of sea marks agreed with results of GEK measurements performed on those days, and also with the mean current pattern obtained in the past based on sea surface data.The most distinct features recognized were some cyclonic and anticyclonic eddies of the order of 100 km in diameter which dominated in the Kuril Basin of the Okhotsk Sea. They appeared clearly in the original NOAA images and their physical parameters were determined quantitatively from the vector map. These eddies were located in the region of decay of the Soya Warm Current and were rotating at a speed nearly as large as that of the current. The problems of what feeds energy to these eddies and how long they live remain to be solved in future studies.     

Graphitization of carbonaceous matter during metamorphism with references to carbonate and pelitic rocks of contact and regional metamorphisms,Japan

This study is an attempt to correlate the graphitization process of carbonaceous matter during metamorphism with metamorphic grade. Graphitization can be parameterized using crystal structure and chemical and isotopic compositions. The extent of graphitization could be characterized mainly by temperature, duration of metamorphism and rock composition. We compared the graphitization trends for two metamorphic terrains, a contact aureole of the Kasuga area and a regional metamorphic terrain of high-temperature/low pressure type of the Ryoke metamorphic terrain in Northern Kiso area, Central Japan, and for two different lithologies (carbonate and pelite), using X-ray diffractogram, DTA-TG analysis, and chemical and stable isotope analyses. During contact metamorphism, graphitization and carbon isotopic exchange reactions proceeded simultaneously in pelitic and carbonate rocks. The decreases in basal spacing d(002) of the carbonaceous matter in carbonate rocks is greatly accelerated at temperatures higher than about 400° C. Furthermore, carbon isotopic ratios of graphite in carbonate rocks also change to ¹³C-enriched values implying exchange with carbonates. The beginning of this enrichment of ¹³C in the carbonaceous matter coincides with an abrupt increase of the graphitization processes. Carbon isotopic shifting up to 5 in pelites could be observed as metamorphic temperature increased probably by about 400° C. Carbonaceous matter in pelitic rocks is sometimes a mixture of poorly crystallized organic matter and well-crystallized graphite detritus. DTA-TG analysis is an effective tool for the distinction of detrital graphitic material. Two sources for the original carbon isotopic composition of carbonaceous matter in pelites in the Kasuga contact aureole can be distinguished, about-28 and-24 regardless of the presence of detrital graphite, and were mainly controlled by depositional environment of the sediments. Graphitization in limestones and pelitic rocks in regional metamorphism proceeds further than in a contact aureole. In the low-temperature range, the differences in extent of graphitization between the two metamorphic regions is large. However, at temperatures higher than 600° C, the extent of graphitization in both regions is indistinguishable. The degree of graphitization is different in limestones and pelitic rocks from the Ryoke metamorphic terrain. We demonstrate that the graphitization involves a progressive re-construction process of the crystal structure. The sequence of the first appearance of crystal inter planar spacing correlates with the metamorphic grade and indicates the crystal growth of three-dimensional structured graphite.