Decision-theoretic sensitivity analysis for reservoir development under uncertainty using multilevel quasi-Monte Carlo methods

At various stages of petroleum reservoir development, we encounter a large degree of geological uncertainty under which a rational decision has to be made. In order to identify which parameter or group of parameters significantly affects the output of a decision model, we investigate decision-theoretic sensitivity analysis and its computational issues in this paper. In particular, we employ the so-called expected value of partial perfect information (EVPPI) as a sensitivity index and apply multilevel Monte Carlo (MLMC) methods to efficient estimation of EVPPI. In a recent paper by Giles and Goda, an antithetic MLMC estimator for EVPPI is proposed and its variance analysis is conducted under some assumptions on a decision model. In this paper, for an improvement on the performance of the MLMC estimator, we incorporate randomized quasi-Monte Carlo methods within the inner sampling, which results in an multilevel quasi-Monte Carlo (MLQMC) estimator. We apply both the antithetic MLMC and MLQMC estimators to a simple waterflooding decision problem under uncertainty on absolute permeability and relative permeability curves. Through numerical experiments, we compare the performances of the MLMC and MLQMC estimators and confirm a significant advantage of the MLQMC estimator.     

Volcanism in the earliest stage of back-arc rifting in the Izu-Bonin arc revealed by laser-heating Ar/Ar dating

The back-arc region of the Izu-Bonin arc has complex bathymetric and structural features, which, due to repeated back-arc rifting and resumption of arc volcanism, have prevented us from understanding the volcano-tectonic history of the arc after 15 Ma. The laser-heating ⁴⁰Ar/³⁹Ar dating technique combined with high density sampling of volcanic rocks from the back-arc region of this arc successfully revealed the detailed temporal variation of volcanism related to the back-arc rifting. Based on the new ⁴⁰Ar/³⁹Ar dating results: (1) Back-arc rifting initiated at around 2.8 Ma in the middle part of the Izu-Bonin arc (30°30′N–32°30′N). Volcanism at the earliest stage of rifting is characterized by the basaltic volcanism from north–south-trending fissures and/or lines of vents. (2) Following this earliest stage of volcanism, at ca. 2.5 Ma, compositionally bimodal volcanism occurred and formed small cones in the wide area. This volcanism and rifting continued until about 1 Ma in the region west of the currently active rift zone. (3) After 1 Ma, active volcanism ceased in the area west of the currently active rift zone, and volcanism and rifting were confined to the currently active rift zone. The volcano-tectonic history of the back-arc region of the Izu-Bonin arc is an example of the earliest stage of back-arc rifting in the oceanic island arc. Age data on volcanics clearly indicate that volcanism changed its mode of activity, composition and locus along with a progress of rifting.     

Splitting of the subtropical gyre in the western North Pacific

Examined here is a hypothetical idea of the splitting of the subtropical gyre in the western North Pacific on the basis of two independent sources of data,i.e., the long-term mean geopotential-anomaly data compiled by the Japanese Oceanographic Data Center and the synoptic hydrographic (STD) data taken by the Hakuho Maru in the source region of the Kuroshio and the Subtropical Countercurrent in the period February and March 1974. Both of the synoptic and the long-term mean dynamic-topographic maps reveal three major ridges, which indicate that the western subtropical gyre is split into three subgyres. Each subgyre is made up of the pair of currents, the Kuroshio and the Kuroshio Countercurrent, the Subtropical Countercurrent and a westward flow lying just south of the Countercurrent (18°N–21°N), and the northern part of the North Fquatorial Current and an eastward flow at around 18°N. The subgyres are more or less composed of a train of anticyclonic eddies with meridional scales of between 300 and 600 km, so that the volume transport of the subgyres varies by a factor of two or more from section to section. The upper-water characteristics also support the splitting of the subtropical gyre; the water characteristics are fairly uniform within each subgyre, but markedly different between them. The northern rim of each subgyre appears as a sharp density front accompanied by an eastward flow. The bifurcations of the sharp density fronts across the western boundary current indicate that the major part of the surface waters in the North Equatorial Countercurrent is not brought into the Kuroshio. The western boundary current appears as a continuous feature of high speed, but the waters transported change discontinuously at some places.     

Some thoughts on the Cold Eddy south of Enshunada

On the basis of the results confirmed in the new volume Kuroshio, a figure is presented on subsurface temperature arranged chronologically for the selected one-degree square to clearly document the bimodal state of the Kuroshio in this area. To extend this analysis of the state further into the non-documented past, a preliminary survey is attempted with the data on air and sea-temperatures at Hachijojima of these 45 years. As may be anticipated, those data are found to bear little in-phase correlation with the Cold Eddy, though they might prove useful after further analysis. Some ideas of analyzing tree-rings on Hachijojima and shallow sea sediments are also discussed in this connection.     

Cenozoic lithospheric extension induced magmatism in Southwest Japan

Island chains off western Kyushu are the surface exposure in the northern margin of the Taiwan–Sinzi Folded Zone that spreads along the arc–trench system in the back-arc side from SW Japan to Taiwan. Intermittent igneous activity between the Middle Miocene and Holocene occurred on these islands and widely covered or intruded sedimentary rocks of Early–Middle Miocene. Geochemistry of the volcanic rocks from the Hirado, Ikitsuki and Takushima islands believed to relate to the back-arc opening along the East China and Japan Seas shows a temporal change in source material. Submarine to sub-aerial volcanism occurred on Hirado Island at 15 Ma during the final opening stage of the East China Sea producing tholeiitic basalt and associated andesite–dacite. These eruptives show low incompatible element contents and high FeO*/MgO ratios and reflect a tholeiitic differentiation trend. High Sr and Pb and low Nd isotopic ratios suggest the involvement of EM2-like lithospheric mantle and crustal material in the formation of these syn-opening volcanic rocks. Post-opening alkali basalt volcanism occurred at 9–6 Ma on the islands is characterized by OIB-like higher large ionic lithophile elements (LILE) and high field strength elements (HFSE) compared to 15 Ma basalts in this region and Quaternary basalts along the volcanic front. They have variable range of incompatible element concentrations and ratios along with variable Sr, Pb and Nd isotopic ratios suggesting the involvement of both lithospheric and asthenospheric sources at variable melting degrees (from 4% to less than 15%). The observation that the isotopic compositions of Quaternary alkali basalts south of the studied area are even more depleted suggests an increase in the involvement of asthenospheric source with time.     

In-situ dissolution experiment of radiolaria in the central North Pacific ocean

Monospecific phaeodarian radiolarian assemblages of Castanidium longispinum were suspended in plastic cages built with 225 μm nylon mesh at different water depths from 378 to 5582 m in the central North Pacific. Weight losses of these samples after a suspension period of 61 days were used to determine dissolution rates. The highest weight losses were observed at 378 m where samples lost ～90% of their initial weight. Through the main thermocline weight losses decreased from 90 to 60% and reached a constant value of 40% below it. These weight losses are roughly an order of magnitude higher than those reported by earlier workers. The higher weight losses can be attributed in part to the more soluble nature of the phaeodarian radiolarian skeletons and in part to the improved experimental technique. Kinetic considerations show that temperature is the major factor that controls silica dissolution rates in the ocean. Using an Arrehnius plot for the apparent rate constants, it can be shown that in surface water dissolution rats should be two orders of magnitude higher than in deep water below the main thermocline.     

The coastal undercurrent— A role of longshore scales in coastal upwelling dynamics

A simple three-dimensional model of a time-dependent coastal upwelling is discussed for time scales of several days to a week, with the linear, two-layer, flat-bottom and $\text{?-}\text{plane}$ approximation. Emphasis is placed on the effects of longshore scales determined by the longshore variabilities in the wind stress distributions. The responses of the inshore motions are shown to depend critically on the longshore scales. For a certain wide range of the scales, the system reveals dominantly baroclinic responses and a full development of the poleward coastal undercurrent without β effect. Somewhat detailed discussions are given on the coastal upwelling, the coastal jet and the poleward undercurrent, which are interpreted simply as the orbital velocities of the forced Kelvin-type waves.     

Relationship between time-series diatom fluxes in the central and western equatorial Pacific and ENSO-associated migrations of the Western Pacific Warm Pool

The water masses of the central and western equatorial Pacific can be divided into two parts: the Western Pacific Warm Pool (WPWP) and the Equatorial Upwelling Region (EUR). The behavior of the WPWP plays a significant role in global climate changes such as the El Niño-Southern Oscillation (ENSO), and it drastically modifies the oceanographic conditions in the area every few years. It is important to evaluate changes in time-series diatom fluxes during both the El Niño and the La Niña events. As a part of the Global Carbon Cycle and Related Mapping based on Satellite Imagery (GCMAPS) Program, time-series sediment trap moorings were deployed and recovered along the Equator at seven stations (Sites MT1–MT7) during five R/V Mirai cruises in the central and western Pacific during January 1999–January 2003. The entire length of this study is divided into two phases depending on the oceanographic conditions: the La Niña event (1999 and 2000); and the El Niño event (2002). Site MT3 was located in the WPWP and Sites MT5–MT7 were in the EUR. Annual means of total diatom fluxes increased towards the east in each year. The fluxes observed at Sites MT4–MT6 decreased from the La Niña event to the El Niño event. However, the fluxes observed at Site MT3 in 2001 and 2002 were higher than those in 2000. Total diatom fluxes showed different seasonal patterns at all sites. The diatom assemblages in the WPWP differed from those of the EUR. Pennate diatoms (e.g., Nitzschia bicapitata, Thalassionema nitzschioides) dominated in the WPWP, while the relative abundances of centric diatoms (e.g., Rhizosolenia bergonii, Azpeitia spp., Thalassiosira spp.) were higher than those of pennate diatoms in the EUR. The diatom fluxes during the La Niña event reflected seasonal oscillation of the WPWP in spatial extent. At Site MT3 during El Niño, terrestrial materials appeared to have been transported by subsurface currents, which might be a secondary influence on total diatom fluxes. The spatial extent of the WPWP reached Site MT7 in 2002, when total diatom fluxes decreased in the sediment traps located in the eastern region including Site MT7. Therefore, we conclude that the relationships between the ENSO and diatoms fluxes in the western and central equatorial Pacific can be explained by the geographic (west–east) expansion or contraction of the WPWP.