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Operations planning in smart grids is likely to become a more complex and demanding task in the next decades. In this paper we show how to formulate the problem of planning short-term load curtailment in a dense urban area, in the presence of uncertainty in electricity demand and in the state of the distribution grid, as a stochastic mixed-integer optimization problem. We propose three rolling-horizon look-ahead policies to approximately solve the optimization problem: a deterministic one and two based on approximate dynamic programming (ADP) techniques. We demonstrate through numerical experiments that the ADP-based policies yield curtailment plans that are more robust on average than the deterministic policy, but at the expense of the additional computational burden needed to calibrate the ADP-based policies. We also show how the worst case performance of the three approximation policies compares with a baseline policy where all curtailable loads are curtailed to the maximum amount possible.

A one-dimensional model of fluid pressure and porosity evolution is used to investigate the physical processes that control the development and maintenance of overpressure in a compacting sedimentary basin. We show that for shale-dominated sequences the variation of the hydraulic diffusivity in both space and time is such that it produces a minimum between 2 and 4 km depth, consistent with observations from the Gulf Coast basin. This minimum inhibits the upward flow of fluid by acting as a “bottleneck” and thus determines the shallowest position of the depth to the top of overpressure. Above this region of bottleneck, overpressure does not develop because the porosity is sufficiently large to maintain high values of hydraulic diffusivity that are conducive to the rapid dissipation of excess fluid pressure. Within the overpressured shales, compaction propagates downward through the section, releasing fluids from the upper part of the section while continuing to restrain the upward flow of fluids from deeper within the section. As such, overpressures are predicted to be maintained within the deeper regions of a basin for tens to hundreds of millions of years. Further, fluid viscosity plays an important role in defining the depth behavior of hydraulic diffusivity as a function of time. Assuming a temperature-dependent fluid viscosity guarantees that the hydraulic diffusivity minimum will always exist during the development of the basin. On the basis of our results, we find that the depth at which the porosity equals 14±4% correlates with the depth to the local hydraulic diffusivity minimum and thus the depth to the top of overpressure. Moreover, we interpret that the 14±4% represents the threshold porosity for which a shale actually begins to act as a seal. Within the Gulf Coast basin, the gross sediment facies consists of lower massive shales across which deltaic systems have prograded allowing the deposition of an alternating series of sandstones and shales that grade vertically into massive sandstones. The massive sandstones are highly permeable and are connected hydrologically to the surface. We conclude that these sandstones play little role in the development of overpressure because of their high permeability except to the extent that the base of the massive sandstones marks the minimum depth possible for the top of overpressure. In contrast, overpressuring is observed to develop within either the shale-dominated sequence or the region of interspersed/interfingering sands and clays. The clay-encompassed sands play only a passive role in the development and maintenance of overpressure because it is the low-permeability clays that control the movement of fluids into and out of the sands.

Heat Flow values, determined from temperature logs and estimates of thermal conductivity from geophysical logs range from 23 to 37 mW/m2 from 800 to 2500 m depth in the Toa Baja scientific drillhole on the north, central coast of Puerto Rico. Near the target seismic reflector at the base of the well, an active hydrothermal system was encountered in which heat flow of up to 90 mW/m2 was found in a mineralized zone beneath a volcanic sill or flow. The heat flow then dropped to 50 mW/m2 beneath this subhorizontal flow zone. The mining of heat from downdip is proposed to account for this thermal anomaly, as well as the scatter in the heat flow determined from the few other wells drilled into Puerto Rico. The time-temperature history of the well indicates that Eocene volcaniclastics of the lower 2 km were deposited into a geothermal gradient of 60°C/km north of an active arc (heat flow estimated to have been 120–180 mW/m2). Uplift, erosion and cooling occurred between 40 and 30 Ma. Reburial and deposition of Oligocene-Miocene Limestones produced the present-day geothermal gradient of 15 °C/km (heat flow of 30–50 mW/m2). Based upon comparisons with slab cooling models, the crustal thickness beneath Puerto Rico is estimated to be closer to continental than oceanic.

Milankovitch cycles in the upper part of the Toa Baja drillhole, detected by geophysical logs, are used to estimate sedimentation rates, and to localize the depths at which sedimentation rate changes occur. The log-derived age information is then combined with reference dates from palaeontological data and the “Vail” global sea-level curve to build a detailed record of the chronology of the upper stratigraphic sequence in the well.

Geophysical logs from the Toa Baja drillhole on the north central coast of Puerto Rico are used to distinguish the variation in physical properties with depth in this non-volcanic island arc massif. A marked unconformity separates shallow Oligocene to Miocene limestones with considerable permeability contrast from a deeper sequence of volcaniclastic rocks with decreasing shaliness. A volcanic sill or flow overlying a strongly mineralized zone is found to cause the impedance contrast responsible for the strong seismic reflection anomaly (bright spot) that was the exploration target.

Reflectors imaged in a multichannel seismic line at Toa Baja, Puerto Rico, were studied by comparing the positions of reflection events with changes in rock properties determined through analysis of logs and cuttings. Reflectors appear to be associated primarily with changes in rock properties across facies or formation boundaries, and more rarely unconformities and faults. Faults that seal versus faults that leak can be recognized on the basis of gas Chromatograph data. Several laterally discontinuous reflectors characterized by modest amplitude anomalies seem to correlate in depth with minor shows of methane gas, measured by onsite gas chromatography. Gas was not recognizeable using geophysical logs indicating small quantities. The gas is apparently associated with rock types and rock properties which affect reflector amplitude rather than directly enhancing reflector amplitude.

Closely spaced heat flow surveys at four sites on the flanks of the Central Indian Ridge and the Southeast Indian Ridge delineate a pattern of oscillatory heat flow which can only result from cellular convection of oceanic bottom water through the oceanic crust and overlying sediment. These cells have a wavelength of 5 to 10 kilometers and are presently active in sea floor 18 x 10(6), 25 x 10(6), and 45 x 10(6) years old of the Crozet Basin and in sea floor 55 x 10(6) years old of the Madagascar Basin. The precise measurement of nonlinear temperature profiles makes it possible to calculate the conductive and convective heat transfer components through the sea floor. Even in the oldest sites, geothermal convection is still a major component of heat transfer through both the crust and sedimentary layers. These observations coupled with the results of earlier oceanwide geothermal studies indicate that more than one-third of the entire surface area of the world's ocean floor contains presently active geothermal convection that is cellular in plan form.

Sixteen new heat flow stations plus a seismic reflection, bathymetric, and magnetic survey of the north flank of the Galapagos Spreading Center have provided additional data to further delineate a low heat flow zone approximately 50 km wide running from 85.5°W to 88°W. This anomalous, low heat flow zone appears to be related to a graben which is found as a continuous, fault-bounded trough, offset by fracture zones and trending parallel to the present spreading center. Thin sediment, symmetric magnetic anomalies, shoaling topography, and a topographic step between the graben and the present spreading center suggest that it is the central rift valley of a fossil spreading center which jumped to the south ∼4 m.y. B.P. The low heat flow measurements appear to be a manifestation of our inability to measure convective heat transfer in this area of thin sediment cover. The thin sediment cover appears to be caused by (1) the youth of the fossil ridge crest relative to the surrounding sea floor and (2) burial by extrusive activity which might have continued after the major components of sea floor spreading jumped to the presently active ridge crest.

An analysis of downhole geophysical logs, and their relation to surface geological data constrain the structure in the first 700 m of the Cajon Pass scientific drillhole. Several angular folds, mapped in a small canyon 150 m to the southeast of the drillsite, are associated with a steep northeast dipping reverse fault at depth. This fault is inferred to cut the scientific drillhole in basement at 700 m, and to intercept a nearby oil-exploration well, Arkoma Federal 1-26, within the sediments at 350 m. The folds mapped at the surface are thought to have developed in Late Miocene to Early Pliocene time, during the Squaw Peak thrusting event. The inferred reverse fault offsets the sediment-basement contact 180 m between the two holes.

The frequency-magnitude distribution (b value) in the upper plane of the deep seismic zone beneath Tohoku, Japan, shows significant variation with depth which we attribute to dewatering of the oceanic crust during the subduction process. High b value from the surface to 40 km in the upper seismic plane and overlying mantle wedge is thought to be caused by the advection of free water from the oceanic crust. The fact that the b value drops to 1.0 is attributed to the passing of the hydrous oceanic crust through a dehydration front. The resulting increase in pore pressure lowers the effective stress and increases the b value in the upper plane. Beneath the volcanic line, b drops back to

Heat flow measurements in the eastern Pacific now total over 800, a sufficient number to permit the analysis of their distribution within a wide range of age zones. Major results are that (1) the mid-ocean ridge crestal regions have lower heat flow than that expected from conductive cooling models of the lithospheric plate, (2) an increase in heat flow is observed some distance away from the crest in a zone which appears to delineate a transition from dominantly convective to conductive heat transfer, and (3) the heat flow in crust older than this transition zone closely approximates that predicted by conductive cooling models for oceanic lithospheric plates. The transition from low to high heat flow occurs when 150-200 m of sediment is deposited over basement, apparently preventing convective transfer of heat from the oceanic crust to seawater. Thus the general shape of the empirical heat flow versus age curve for the East Pacific Rise (EPR) agrees with that from the Galapagos Spreading Center, but the age of the transition zone occurs in 5- to 6-m.y.-old crust on the Galapagos Spreading Center, whereas it occurs in 10- to 15-m.y.-old sea floor on the EPR. Proximity to the equatorial high sedimentation regionmore » causes the deposition of a thick layer of sediment much more quickly on the Galapagos Spreading Center than on the East Pacific Rise. Quantitatively, the degree of heat transfer by convection appears to correlate inversely with the ratio of sediment thickness to topographic relief.« less

Geochemical well logs recorded in the Cajon Pass Scientific drillhole provide an estimate of the elemental concentrations of Si, Al, Fe, Ca, K, Th, Ti, S, and the HREE Gd. The continuous geochemical profiles were used to define a lithostratigraphy in the cystalline basement from 501 to 1,829 m. The interval between the faulted top of basement and a thrust fault at 689 m consists of six alternating slivers of granite and granodiorite. Interlayered granitic and granodioritic units were then encountered to another fault at 1290 m, whereas gneisses of granitic to tonalitic composition were logged in the basal portion of the hole. Linear discriminant analysis of major element chemistry, as well as variations in Gd, Th, Ti, and S, were used to demonstrate that each of the major lithostratigraphic units is chemically distinct. Different trace element signatures and variable degrees of metamorphism indicate a complex thermal and hydrological history for the basement rocks encountered in the Cajon Pass well.

Wireline logs from the Cajon Pass drillhole provide observations of crustal properties and processes near the San Andreas fault. Mineralogical profiles developed from geochemical logs are combined with a technique for calculating thermal conductivity from the volume fractions of component minerals. Variations in the equilibrium temperature gradient correlate with conductivity contrasts, and thus with lithology, rather than with fluid circulation. K, U, and Th contents calculated from gamma spectroscopy logs yield heat production values which range from 1.3 to 2.4 µW/m³, averaging 1.8 µW/m³ in the section from 500 to 1800 m. Evidence for depletion of U relative to Th raises the possibility of extensive fluid circulation in the past. However, discontinuity of depletion across faults suggests that the fluid regime responsible for U depletion predated San Andreas faulting.

The well logging activity of the Ocean Drilling Programme, which deploys the most technically advanced suite of downhole measurements available for routine use, is providing new opportunities for advancement in marine geoscience. Particular examples are cited of the application of wireline data to problems associated with global environmental changes, crust/ mantle interactions, crustal fluid circulation in the context of a global geochemical budget, lithospheric stress and deformation, and evolutionary processes in oceanic communities. Further technological developments will expand the scientific role of downhole measurements still further, especially in terms of the integration of geophysical data at different scales of measurement, and the interpretation of these data in accordance with; global scientific themes.

In-situ deep and shallow measurements of electrical resistivity recorded with the Dual Laterolog in the basement of the Cajon Pass scientific drillhole are compared with laboratory measurements of resistivity and porosity on fracture-free core samples. This comparison is the basis of a simple electrical model of the pore space of the rock from which both matrix and fracture porosity are derived. In parallel, the analysis of borehole electrical images obtained with the Formation Microscanner provides a means to identify the fractures that intersect the borehole wall, to evaluate their frequency, and to determine their orientation. Further processing of these images enables us to distinguish mineralized from fluid-filled fractures. The comparison of laterolog-derived fracture porosity, computed over a large volume of rock, with a pair of fracture intensity profiles obtained from the analysis of the two images of the borehole wall is the key of a new technique by which drillhole-related fractures (either due to hydraulic fracturing or to stress-induced borehole breakouts) and natural fractures (either open or mineralized) are discriminated. The fractures in the upper part of Cajon Pass basement are inferred from the analysis of in-situ resistivity measurements as mostly steep and mineralized.

Twenty-one new heat flow measurements in the Mariana Trough delineate a central zone of high heat flow corresponding to an axial topographic high and a flank zone of low heat flow. The high heat flow is an indication that the axial high is a narrow zone of magmatlc intrusion and that sea floor spreading is occurring in the Mariana Trough in a manner similar to its occurrence on midocean ridges. The low heat flow values appear to be the result of the occurrence of hydrothermal circulation in the oceanic crust of the Mariana Marginal Basin.

We present 206 new heat flow measurements in the Indian Ocean. These and approximately 300 previously published heat flow values are individually evaluated for sedimentary environment and instrumental performance. The relationship between average heat flow and age is found to be little affected by selection of the most reliable experiments, although the scatter about the mean is significantly lowered. The variation of mean heat flow with age is found to be very similar to that in the eastern Pacific and Atlantic oceans: There is a crestal low heat flow zone with large variability, a transition zone within which the heat flow increases from values considerably below to values in agreement with predictions from thermal models of the oceanic lithosphere, and a region where heat flow values are in accord with theoretical predictions. However, the transition zone occurs over different crustal ages from ocean to ocean: 40–60 m.y. in the Indian Ocean, 4–6 m.y. in the Galapagos spreading center, 10–15 m.y. on the East Pacific Rise, and 50–70 m.y. on the Mid-Atlantic Ridge. The transition zone generally corresponds to a sea floor age where (1) sedimentary thickness increases to ≥300 m, (2) sea floor roughness is significantly smoothed by sediment blanketing, and (3) the carbonate content of surface sediments decreases to ≤40%. The transition zone occurs where water circulation in the oceanic crust stops affecting the surface heat flow strongly. There are two possible explanations for the transition. First, a change in composition from carbonate to siliceous sediments results in a decrease in bulk permeability. This combined with general thickening of the sedimentary blanket with aging results in the deposition of an impermeable layer which prevents the convective exchange of heat from the oceanic crust to the ocean. Second, hydrothermal flow within the oceanic crust is plugged by filling of circulation cracks in the oceanic crust. The fact that in several basins of the Indian Ocean the heat flow transition corresponds with the carbonatesiliceous boundary is support for the former mechanism. However, the fact that locations of increases in velocity of seismic layer 2A generally correspond to the transition regions in the Atlantic and Pacific oceans provides support for the latter mechanism. Heat flow measurements in the world's oceans allow us to calculate the variations of bulk permeability and basal temperature in the oceanic crust as a function of age and to evaluate the geochemical implications of the variation in these parameters between oceans. The combination of conductive heat flow and elevation versus age observations in old lithosphere demonstrates the deviation from t1/2 cooling in the Indian Ocean and indicates that the Mozambique and western Somali basins are considerably older than preliminary deep-sea drilling results suggest. 1 Supplementary table is available with entire article on microfiche. Order from American Geophysical Union, Suite 1000, 1909 K Street, N.W., Washington, D.C. 20006. Document J77-003; $1.00. Payment must accompany order.

Measurements of temperature gradient and excess pore pressure in the surficial sediment of a fault block basin in the Guatemala Basin correlate with sediment thickness. The temperature gradient is smaller and the excess pore pressure gradient is more negative in areas of thinner sediment. This correlation is explained by postulating downward pore water advection within the sediments, with flow velocities on the order of 10−9 to 10−8 m/s in the thinnest sediments and much less flow in the thickest sediments. Sediment physical properties and pore water chemistry also support this interpretation. Since the conductive heat flow of the basin as a whole is less than one third that predicted by sea floor spreading models, the oceanic basement may be the site of a vigorous hydrothermal circulation system. The pore water advection in the sediments may be driven by this larger scale circulation.

One of the major problems in the use of heat flow data in a quantitative manner has been the variability of closely spaced measurements. It is suggested that this variability is directly related to hydrothermal circulation in an ''effectively permeable'' oceanic crust. As a consequence, only where this crust is sealed from the seawater by an extensive and thick layer of impermeable sediment can reliable estimates be made of the flux at depth. Heat flow data from such areas are analyzed. It is shown that the scatter in the data is low and that in most areas the mean heat flow through a province of known age is close to that predicted by plate models which account for the increase in depth with increasing age of the ocean floor. From this analysis it is argued that these heat flow means are a reliable estimate of the flux at depth. In order to be able to use heat flow measurements to investigate the age of the crust, the thickness of the lithospheric plate, upper mantle convection, and local anomalies, it is necessary to substantiate this analysis and to find an adequate explanation of the low mean heat flow observed at themore » center of the sediment bulge in the equatorial Pacific.« less

Estimates of elemental and mineralogical abundances from geochemical logs are compared to preliminary chemical and modal analyses from cores in the Cajon Pass Scientific Drillhole. Accuracies of log-computed weight percent oxide and mineralogy determinations range from 10 to 30%.

An empirical relationship between ridge elevation and age of the oceanic crust is presented for the Pacific, Atlantic, and Indian oceans. This relationship is accounted for by the thermal contraction of a cooling lithosphere as it moves away from a center of spreading, and thus is compatible with plate theory. Hence, it is possible to use topographic profiles to predict the age of the ocean floor. Detailed examination of profiles in different areas indicates that slow-spreading ridges (half-rate 3 cm/yr). However, all ridges appear to show a uniform subsidence rate near the ridge crest. This uniform rate makes it possible to use topographic profiles in regions of smooth topography to predict the age of oceanic crust, less than 40 m.y. old, to better than ±2 m.y. Topographic profiles will be particularly useful for predicting age where magnetic anomaly patterns are absent or difficult to interpret. Magnetic, topographic, seismic reflection, twenty-nine new, and all other heat-flow observations across the east Pacific rise and Mathematician and Clipperton seamount chains in the central eastern Pacific are examined. The magnetic and heat-flow observations are too inconclusive to enable a tectonic reconstruction of the area. However, topographic profiles at right angles to the rise between 20°N and the equator show that the Mathematician and Clipperton seamount chains are the old crest of the east Pacific rise. These parts of the rise crest terminated approximately 5 m.y. B.P. by the spreading center jumping 4° to the east. Seismic reflection profiles at right angles to the crest support this conclusion. The topography west of these two chains is used as the basis for a proposed evolution of the central eastern Pacific during the past 20 m.y.

The procedure of lowering geophysical instruments down boreholes on a wire has, over the past 60 years, been a useful aid in defining the physical nature of the rock formations through which the borehole passes. Current developments, however, herald the advent of the use of such techniques for the measurement of geochemical concentrations in a quantitative way. This opens the door to a whole new series of applications in a wide range of geological disciplines.

Hole 504B is by far the deepest hole yet drilled into the oceanic crust in situ, and it therefore provides the most complete “ground truth” now available to test our models of the structure and evolution of the upper oceanic crust. Cored in the eastern equatorial Pacific Ocean in 5.9-m.y.-old crust that formed at the Costa Rica Rift, hole 504B now extends to a total depth of 1562.3 m below seafloor, penetrating 274.5 m of sediments and 1287.8 m of basalts. The site was located where the rapidly accumulating sediments impede active hydrothermal circulation in the crust. As a result, the conductive heat flow approaches the value of about 200 mW/m² predicted by plate tectonic theory, and the in situ temperature at the total depth of the hole is about 165°C. The igneous section was continuously cored, but recovery was poor, averaging about 20%. The recovered core indicates that this section includes about 575 m of extrusive lavas, underlain by about 200 m of transition into over 500 m of intrusive sheeted dikes; the latter have been sampled in situ only in hole 504B. The igneous section is composed predominantly of magnesium-rich olivine tholeiites with marked depletions in incompatible trace elements. Nearly all of the basalts have been altered to some degree, but the geochemistry of the freshest basalts is remarkably uniform throughout the hole. Successive stages of on-axis and off-axis alteration have produced three depth zones characterized by different assemblages of secondary minerals: (1) the upper 310 m of extrusives, characterized by oxidative “seafloor weathering“; (2) the lower extrusive section, characterized by smectite and pyrite; and (3) the combined transition zone and sheeted dikes, characterized by greenschist-facies minerals. A comprehensive suite of logs and downhole measurements generally indicate that the basalt section can be divided on the basis of lithology, alteration, and porosity into three zones that are analogous to layers 2A, 2B, and 2C described by marine seismologists on the basis of characteristic seismic velocities. Many of the logs and experiments suggest the presence of a 100- to 200-m-thick layer 2A comprising the uppermost, rubbly pillow lavas, which is the only significantly permeable interval in the entire cored section. Layer 2B apparently corresponds to the lower section of extrusive lavas, in which original porosity is partially sealed as a result of alteration. Nearly all of the logs and experiments showed significant changes in in situ physical properties at about 900–1000 m below seafloor, within the transition between extrusives and sheeted dikes, indicating that this lithostratigraphic transition corresponds closely to that between seismic layers 2B and 2C and confirming that layer 2C consists of intrusive sheeted dikes. A vertical seismic profile conducted during leg 111 indicates that the next major transition deeper than the hole now extends—that between the sheeted dikes of seismic layer 2C and the gabbros of seismic layer 3, which has never been sampled in situ—may be within reach of the next drilling expedition to hole 504B. Therefore despite recent drilling problems deep in the hole, current plans now include revisiting hole 504B for further drilling and experiments when the Ocean Drilling Program returns to the eastern Pacific in 1991.

A four‐channel sonic log of a 1‐km section of oceanic crust at site 504B, Eastern Equatorial Pacific Ocean has been spectrally analyzed. The cross‐spectrum of seismic waveform pairs was converted into integrated energy and peak‐frequency at each shot point for both compressional and shear coda. These plus an ultrasonic borehole televiewer fracture count were combined into a “fracture spectrum log” over the bottom 500 m of the borehole. Cross correlation of P and S frequency and energy variations downhole revealed a natural resonance at wavelengths of 30–40 cm in the oceanic crust. This resonance appears as a low‐pass filter of P energy and a high‐pass filter of S energy. Because the energy attenuation is phase coherent with the fracture density, we interpret this natural resonance to be caused by venting of acoustic energy through intersecting fractures of an aspect ratio appropriate to the resonance wavelength. This is the first time such uniform fracturing has ever been observed in the oceanic crust. [Work supported by ONR.]

Cenozoic marine sediments were drilled and cored by the Deep Sea Drilling Project at Site 613 in the Baltimore Canyon Trough, and four‐channel sonic waveforms were recorded from 115 to 585 m below sea floor. Compressional wave velocities and spectra were calculated from the sonic waveforms. In situ porosity was estimated and compared to core measurements. As expected, velocity increased with depth as porosity decreased. However, the energy loss between near and far receivers increased and the peak crosspower frequency decreased with depth, suggesting that attenuation increases over the same interval. The large changes in energy and frequency cannot be explained solely by changes in the elastic propeties of the sediments. We model the observed compressional wave spectra using measured values of velocity and density. Reasonable fits to the observed spectra are obtained using either a constant Q (CO) or nonconstant Q model. For the CO model, O decreases from 100 to 20 over this depth interval. Diagenesis obs...