Equilibrium Depth Research Articles

Generation mechanism of overpressures caused by disequilibrium compaction in the northwestern Bozhong subbasin, China

In sedimentary basins, deep-seated overpressure conditions are frequently encountered. However, the precise origins of these overpressure conditions and the assessment of their formation times have long presented challenges. Previous studies have primarily relied on qualitative approaches to investigate overpressure origins, leading to substantial uncertainties in their findings. Based on theories such as the effective stress law, disequilibrium compaction, equilibrium depth, and nested fluid trapping containers in this paper, a new quantitative methodology is introduced for identifying the disequilibrium-compaction-induced origins of overpressure conditions. Additionally, the formation times of overpressure can be also estimated by nested fluid trapping container theory. This methodology is successfully applied to the northwestern Bozhong subbasin in the Bohai Bay Basin, China. The results indicate that the overpressure within the Dongying Formation of the northwestern Bozhong subbasin is primarily attributed to the disequilibrium compaction of mudstone, because the disequilibrium compaction of mudstone accounts for over 90% of the pressure in sandstone. Furthermore, the overpressure system in this area is not singular but comprises multiple nested relative fluid trapping containers. The application of nested fluid trapping container theory allows for an estimation of the overpressure’s formation time, although further validation of these estimates is required. It should be noted that the method proposed in this paper is particularly suited for sedimentary basins with relatively weak tectonic activity.

Wear at an incipient ploughing–cutting transition

Ductile wear is highly desirable in manufacturing and machining operations to achieve a high quality of finish. In a ductile regime of operation, a characteristic transition from ploughing to cutting is often observed in materials with different mechanical properties. We unveil the origin of this transition through a plastic, debris-free model of a tip causing wearing of a flat surface. The abraded volume depends on the equilibrium depth which is reached once the normal force is balanced by the lifting force during scratching. We show that the dependence of the equilibrium depth on the lifting force is highly non-linear and diverges above a threshold force that depends on the hardness, friction force and geometry of the tip. The threshold corresponds to a characteristic depth marking the ploughing–cutting transition. When this characteristic depth is below the ductile–brittle depth of cut, ploughing, cutting and brittle modes of operation are all possible. These abrasive wear modes are summarised in a unified mechanism map. The findings of this model, derived from theoretical considerations, are validated by DEM simulations and literature data from experiments.

Low temperature and high pressure dramatically thicken the gas hydrate stability zone in rapidly formed sedimentary basins

Rapid sedimentation reduces the temperature and raises the pore pressure in sedimentary basins. During rapid sedimentation (>0.5 mm yr−1), cold sediment is buried fast and there is insufficient heat flow to keep the sediment at its steady state conductive equilibrium temperature. In addition, rapid deposition of low permeability mud results in overpressure due to the inability of the pore fluid to drain. It dramatically expands the thickness of the zone where hydrates are stable (the gas hydrate stability zone or GHSZ). We explore this effect with one-dimensional models. We then simulate the two-dimensional evolution of temperature and pressure of the Terrebonne Basin in the Gulf of Mexico. We use seismic, well data, and salt restoration to provide the initial and boundary conditions. We show that rapid burial reduces the geothermal gradient from ∼30 °C/km, which would be expected under equilibrium pressure and temperature, to as low as ∼10 °C/km; we also show that 25 MPa of overpressure is developed. This deepens the thickness of the GHSZ from ∼600 mbsf (its equilibrium depth) at the basin margin, to as much as 2000 mbsf basin-ward, in response to the increasing sedimentation rates. The model successfully simulates the deepening of the base of GHSZ that is interpreted from a bottom simulating reflection in the seismic data. The model and the observations suggest that the thickness of the GHSZ may be much thicker than commonly presumed and as a result the volume of carbon stored may be underestimated. Furthermore, the thickness of the hydrate stability will change significantly with time as sedimentation rate waxes and wanes implying that the hydrate stability zone is a dynamic component of the carbon cycle.

Equilibrium depth and time scale of local scour around a forced vibrating pipeline

Equilibrium depth and time scale of local scour around a forced vibrating pipeline

Intruder trajectory tracking in a three-dimensional vibration-driven granular system: Unveiling the mechanism of the Brazil nut effect

We employ a Hall-effect magnetic sensor array to accurately track the trajectory of a single magnetic sphere, referred to as the “intruder,” within a three-dimensional vibro-fluidized granular bed to unravel the underlying physical mechanism governing the motion of the intruder. Within the acceleration range of 3.5 g ≥ Γ ≥ 1.5 g, we find that, regardless of the intruder’s initial position, it consistently reaches the same equilibrium depth when the vibration acceleration (Γ) and frequency (ω) are fixed. For Γ ≤ 2.5 g, the equilibrium position lies on the surface of the granular bed, while for Γ > 2.5 g, it shifts below the surface. Additionally, intruders with different densities exhibit varying equilibrium depths, with higher density resulting in a deeper equilibrium position. To understand the mechanism behind the intruder’s upward or downward motion, we measure its rising or sinking velocities under different vibration parameters. Our findings demonstrate that the rising velocity of the intruder, under varying vibration accelerations (Γ) and frequencies (ω), can be collapsed using the ratio Γ/ω, while the sinking velocity remains unaffected by the vibration strength. This confirms that the upward motion of the larger sphere, associated with the Brazil nut effect, primarily arises from the void-filling mechanism of the bed particles. Furthermore, our experiments reveal that the presence of convection within the bed particles has minimal impact on the motion of the intruder.

Magmatic evolution during proto-oceanic rifting at Alu, Dalafilla and Borale Volcanoes (Afar) determined by trace element and Sr-Nd-Pb isotope geochemistry

Continental rifting and associated magmatism can eventually result in the formation of new ocean basins. However, the characteristics of magmatism in the latest stages of rifting are poorly understood. The Erta-Ale volcanic segment (EAVS) in the Danakil Depression of Afar, Ethiopia, provides a unique natural laboratory in which to investigate how magma generation evolves during the shift from continental rifting to oceanic spreading. Here we present new trace element data combined with Sr-Nd-Pb isotope ratios for three volcanoes, Alu, Dalafilla and Borale, in the north of the EAVS. These data shed light on the changes in melt production and storage that occur at this late stage in the rifting cycle. Elevated Ce/Pb and ΔNb (33–48, 0.25–0.47 respectively) of the basalts, alongside Sr-Nd-Pb isotope geochemistry indicate the presence of a HIMU component, supplied by the Afar plume, together with contamination by the crust. Melting conditions, estimated using the trace element ratios, Smn/Ybn, Dyn/Ybn and Cen/Smn, indicate that magmas were primarily derived from spinel lherzolite (85–90%) with minor garnet lherzolite (10–15%) with a melt fraction of ~4%. Melt-mantle equilibrium depths are estimated to be on the order of 64 to 83 km, shallower than that previously inferred within Afar. We suggest that this is likely a result of the increased plate thinning beneath the EAVS compared to other parts of Afar. Basaltic volcanics are found to exhibit heterogeneous Sr-Nd-Pb isotope compositions whilst more evolved rocks (i.e., SiO2 ≥52 wt%) exhibit consistent radiogenic compositions. This indicates that homogenisation of all melt compositions occurs prior to or during melt differentiation, with the latter process occurring rapidly in the upper crust with minimal crustal contamination. Overall whilst the Afar plume appears to be the dominant mantle component in the volcanic rocks, the melt characteristics and magmatic storage conditions beneath the EAVS shows variability that is likely controlled by a dynamic interplay between rifting and mantle processes.

Geographic and transport controls of temperature response in karst springs

Thermal responses of groundwater are useful signatures to reveal the recharge-discharge process and characterize aquifer structure in karst groundwater. Four karst springs with varying circulation depths ranging from ∼ 60 to 820 m in South China, were used to decipher the mechanism of heat exchange between recharge water and surrounding rock formations. An analytical solution of heat transfer in karst conduit was proposed to simulate the peak or trough temperatures of pulse flow. Hydraulic diameter, flow velocity, input temperature and circulation depth in karst aquifer, mainly depending on the recharge water volume after rainfall events, are important transport factors to control the thermal equilibrium depth and the efficiency of heat exchange that directly controls the behavior of warm peaks or cold troughs in groundwater temperature. In shallow karst aquifers wherein the circulation depth is less than its theoretical thermal equilibrium depth, the recharge water does not sufficiently exchange heat with the surrounding rocks, resulting in clear event-scale warm peaks in summer and cold troughs in winter. Otherwise, the recharge water will firstly reach a thermal equilibrium state and then mix with the warmer base flow at deeper location, which is verified in a karst spring with anomalous event-scale temperature drops after rainfall events all year around. The thermal response simulations obtained from this work provide new ways and insights to characterize geographic structure of karst aquifer and elucidate heat transfer mechanism in karst aquifer systems.

Magma system and equilibrium depth of the Cenozoic basalts in the central North China craton

Magma system and equilibrium depth of the Cenozoic basalts in the central North China craton

Mechanical response of dropping a Hall anchor and its penetration depth in riverbed silt

To ensure the safety of an underwater pipeline embedded within riverbeds, it is essential to evaluate its burial depth and penetration depth during the emergency anchoring of a ship. In this research, the mechanical behaviour of the entire anchoring process with considering the penetration depth of the Hall anchor in the riverbed silt, was holistically examined using experimental measurements, theoretical calculations and computational analysis. Mock-up Hall anchors (5 and 7.5 kg) were dropped at five different heights beforehand, and their transient velocities during the underwater motion were measured using a 2D image sonar. When the water is deep enough, the velocity of Hall anchor when it touches the ground is predominantly determined by its weight with regardless of the height of the drop. Moreover, a theoretical analysis was employed to investigate the behaviours of uniform motion at the state of equilibrium and infinite depths of water, and the exact coefficient of fluid resistance of the Hall anchor was presented. Computational analysis based on the formulation of the arbitrary Lagrangian–Eulerian method was proposed to examine the anchor in the riverbed silt and predict its penetration depth with considering the influence of boundary restrictions. In addition, the riverbed silt with a high moisture content was considered as a material with fluid features, which will be examined for fluid–solid coupling analysis with a Hall anchor by means of a constraint algorithm with a penalty function. The predicted value of the maximal penetration depth is reasonable and reliable compared with the empirical formula, which is crucial to evaluate the burial depth of underwater pipelines. A research approach for the penetration depth of a Hall anchor in riverbed silt was proposed and demonstrated by considering the entire anchor process through a combination of experimental, theoretical, and computational analyses.

A laboratory study of wave-induced local scour at an emergent pile breakwater

A pile breakwater is a row of closely-spaced piles, placed in a side-by-side arrangement, to dissipate wave energy and prevent coastal erosion. It is important to understand the local scour at a pile breakwater for its foundation design. This paper reports a set of wave-flume tests on the local scour around the piles in regular waves. A laser scanner was used to measure the change in the three-dimensional bed elevation. Five values of Keulegan–Carpenter number were examined in this study. Scour holes near the pile breakwater were developed due to the oscillatory jet flow through the gaps between adjacent piles, and sand ripples were observed on both sides of the structure. The migration of the sand ripples was either onshore or offshore, depending on the wave conditions. The maximum scour-hole depth had an exponential growth with the duration of wave attack, and the equilibrium depth was found to be deeper than that for a standalone pile. Both the scour-hole depth and length were found to be scaled by the pile diameter. The ripple length and steepness were in general agreement with recent empirical formulas in the literature in spite of the presence of a pile breakwater.

Numerical Investigations on Scour and Flow around Two Crossing Pipelines on a Sandy Seabed

When a pipeline is laid on the seabed, local scour often occurs below it due to sea currents. In practical engineering, there are some cases that two pipelines laid on the seabed need to cross with each other. The complex flow structures around two crossing pipelines make the scour characteristics different from that of an isolated single pipeline. In this study, scour below two crossing pipelines was simulated numerically using the CFD software Flow-3D. The study is focused on the effect of the intersecting angle on the equilibrium depth and time scale of scour below the crossing position. Five intersecting angles, i.e., α = 0°, 15°, 30°, 45° and 90°, are considered, where α = 0° and 90° represent two pipelines parallel and perpendicular to each other, respectively. The results show that the equilibrium depth and the time scale of scour below the two crossing pipelines are greater than those of an isolated single pipeline. The equilibrium depth and time scale of scour have the largest values at α = 0° and decrease with the increase of the intersecting angle. Finally, the flow structures around the crossing pipelines are presented to explain the scour process.

Geochemical exploration in Mesillas geothermal area, Mexico

This work presents results of geochemical exploration in the promising geothermal area of Mesillas, Nayarit, in the western border of the Mexican Volcanic Belt. The assessment of the geothermal resource was based on a geochemical approach which consisted in: (i) mapping and geological survey, (ii) chemical characterization of geothermal manifestations, (iii) diffuse flux analysis (CO2 and H2S), (iv) temperature at depth calculations using both classical and integrated multicomponent geothermometry.. Additional to the technical work, social dissemination of geochemical issues was attempted by designing and distributing a geomap among local people. The geological survey identified five andesitic units in an area of ∼1.5 km2, where 25 thermal springs discharge Na–CO3 water with temperatures between 47 and 90 °C, and pH ∼9. Geothermometric calculations indicate a bottom temperature between 125 °C and 130 °C. Andesites show high permeability generated by intense fracturing related with normal fault systems with trend NW-SE, SW-NE, NS, and EW. Surface hydrothermal alteration is mainly argillic with silicification. CO2 and H2S hydrothermal degassing are mainly restricted to thermal springs aligned in the NW-SE direction. Thermal springs with high temperature, highest degassing and high presence of hydrothermal alteration occur in the south-southwest zone of the geothermal area (MOL10, MOL13, MOL14 and MOL15); they correspond with NW-SE structural alignment. Furthermore, the estimated range of temperature at depth using geothermometers is 125–130 °C, and the surface temperature is on average 20 °C; considering local thermal gradient, it was estimated an equilibrium depth of 2.0–2.1 km. These results indicate that the Mesillas geothermal prospect may be classified as a medium temperature system with good permeability that may be exploited for electricity production as well as direct uses.

On the Representation of Mediterranean Overflow Waters in Global Climate Models

Abstract Accurate representation of the Atlantic–Mediterranean exchange in climate models is important for a reliable simulation of the circulation in the North Atlantic Ocean. We evaluate the performance of 10 global climate models in representing Mediterranean Overflow Water (MOW) over the recent period 1986–2005 by using various performance metrics. The metrics are based on the representation of the climatological mean state and the spatiotemporal variability of temperature, salinity, and volume transports. On the basis of analyses and observations, we perform a model ranking by calculating absolute, relative, and total relative errors Ej over each performance metric and model. The majority of models simulate at least six metrics well. The equilibrium depth of the MOW, the mean Atlantic–Mediterranean exchange flow, and the dominant pattern of the MOW are represented reasonably well by most of the models. Of those models considered, MPI-ESM-MR, MPI-ESM-LR, CSIRO Mk3.6.0, and MRI-CGCM3 provide the best MOW representation (Ej = 0.14, 0.19, 0.19, and 0.25, respectively). They are thus likely to be the most suitable choices for studies of MOW-dependent processes. However, the models experience salinity, temperature, and transport biases and do not represent temporal variability accurately. The implications of our results for future model analysis of the Mediterranean Sea overflow are discussed.

Assessment of measurement accuracy in 210Pb dating sediment methods

Working on an experimental dataset to derive descriptive parameters with well-known procedures appears to be a straightforward process. However, due to the complexity of environmental systems, the procedures cannot be completely defined, and commonly hypothesis are required to obtain final results. These degrees of freedom cause a spread in results that is often wider than the experimental uncertainties and that should be taken into account in the measurement accuracy estimation. As an example of this issue, the sources of uncertainty, including reproducibility, that occur in dating marine and lacustrine sediment cores with the 210Pb methodology are discussed in this paper. The IAEA Coordinated Research Project (CRP) “Study of Temporal Trends of Pollution in Selected Coastal Areas by the application of Isotopic and Nuclear Tools” promoted this discussion, its main objective being the determination of a streamlined, harmonised and validated methodology for marine sediment dating. The uncertainties estimated from experimental data and mathematical propagated must be complemented with reproducibility contribution: some elements are specific for the 210Pb method (mixed layer, finite thickness of layers and identification of the equilibrium depth), while others are more general (exponential fitting and data interpolation). The final spreading of results can be mainly controlled by reproducibility, and efforts are needed to standardise procedures to reduce the effect of reproducibility and to better estimate the overall uncertainty of measurements. It is necessary to underline the importance of a thorough (a-priori) cost-effective analysis of the uncertainty evaluation of the measurement results in relation to the aim of the study, taking primarily into account the overall accuracy required case by case.

Bubbles rising through a layer of Carbopol capped with water

Air bubbles are injected into a Carbopol column capped with water to mimic ebullition from lake sediments. The first bubble sets an invisible path as it rises through the Carbopol. Subsequent bubbles rise along this path and, unlike the first bubble, break up into two separate bubbles. The leading bubble rises through the water column, while the smaller breakup bubble separates and remains trapped within the Carbopol. A conduit that forms above this breakup bubble gradually fills with water from the upper layer. After a period of growth this conduit reaches an equilibrium depth, and then starts to shrink. Inside the conduit, the rising bubbles resemble Taylor bubbles, but have velocities approximately 5–7 times the maximum velocity of standard Taylor bubbles. The variation in rise velocity depends on the interaction of the rising bubble with previous breakup bubbles. In addition, rising bubbles expel water from the conduit and water flows back after bubbles escape. This process can enhance the transport of heat and contaminants to and from aquatic sediments during ebullition events. • A damaged pathway forms inside Carbopol due to the passage of bubbles. • Bubbles break up as they cross the Carbopol–water interface. • Upper portion of the damaged pathway evolves into a water-filled conduit. • Bubbles rise much faster inside the conduit than standard Taylor bubbles. • Water flows in and out of the conduit, enhancing mixing in aquatic sediments.

The Shoreline Deformation in Convex Beach due to Sea Level Rise

Sea level rise (SLR) is become more serious on a global scale and has become one of the main reasons causes shoreline changes, and erosion, even on an extreme scale can cause the sinking of coastal areas and islands. It was recorded that many big cities were damaged by SLR. The Bruun rule is the most widely used method for predicting the horizontal translation of the shoreline associated with a given rise in sea level. In this study, however, the change in the average shoreline at the convex beach, which is more vulnerable to erosion due to sea level rise, is investigated. The increase in water depth by sea level rise causes a change in the wave crestline, ultimately leading to a linearization of the shoreline. In general, it is assumed that the annual average shoreline is parallel to the annual mean wave crestline. Moreover, assuming that the equilibrium depth contour is formed according to the crestline, the retreat of the shoreline is predicted. The shoreline change is indirectly predicted through the wave crestline deformation obtained from a wave model and this method is applied to the convex beach. Our result showed that for a convex beach with a length of 1 km has open ends with free littoral drift at both ends, the sea level rise of 1 m cause the erosion of 10 m in the protruding area, and the sea level rise of 2 m causes erosion of 23 m. However, if the convex beach is blocked at both ends, sea level rise of 1 m causes the erosion of 6.3 m in the convex area, but the shoreline advance of 3.8 m at both ends, and if the sea level rise of 2 m occurs, the erosion of 14.3 m can occur in the convex area and shoreline advance of 8.6 m can occur at both ends.

The equilibrium depth of wave scour around both slender and large piles

The equilibrium stage of the scour caused by the wave effect around the marine piles was investigated experimentally for both slender and large piles. Unlike the experimental studies in the literature, some of the experiments were carried out under clear water scour condition, since the coarse bed material was used in the present study. While the effective parameter on scour for slender piles is only the Keulegan-Carpenter number, it is understood that the diffraction parameter is also effective for large piles. It has been determined that when the steady-streaming structure around a large pile is effective, the scour increases with the increase in the Keulegan-Carpenter number and the diffraction parameter. For the estimation of the relative equilibrium scour depth around the slender piles, the results were evaluated together with the previous experimental study results and a new empirical equations based on the Keulegan-Carpenter number (KC > 4) was proposed. A new empirical correlation is derived, which includes the Keulegan-Carpenter number and the diffraction parameter (10−3<D/L < 3·10−1) for both slender and large piles. In addition, alternatively, a new equation is proposed using the modified Ursell parameter (Urp<105). The nominal limit of the relative scour depth according to the diffraction parameter was determined as 0.0082·(D/L)−1.

Dose divergence between monte carlo simulation and experimental measurements in the build-up region for a photon beam

The aim of this work was to study the divergence between simulation and experimental measurements in the build-up region using two types of medical accelerators Elekta Synergy MLCi2 and Varian clinac 2100C and also for two types of ionization chambers. The Monte Carlo simulation was performed using the G4Linac-MT code. By demonstrating the variation of the particles in the build-up region, this work allows us to give an exact conclusion on the divergence between the Monte Carlo simulation and the experimental measurements.Using multi-threading code G4Linac-MT and the performance of the HPC-Marwan computing grid, we carried out simulations of large events with a saving in computing time. After optimizing the initial beam parameters, we looked for the ideal voxel size which corresponds to a better agreement between simulation and measurements to avoid simulation errors. The divergence between simulation and measurements in the build-up region is studied according to the type of ionization chamber, the irradiation fields, the source-to-surface distance (SSD) and the photon energy.The results obtained indicate that the dose divergence in the build-up region increases with the appearance of the contamination particles. The secondary particles detected in the build-up region are electrons and positrons for the 6 MV photon beam and other particles are added for the high energy beam 18 MV, including protons and neutrons. The dose accuracy of the comparison between the simulation and the measurements of the Varian 2100C and Elekta Synergy MLCi2 accelerators increases if the voxel size is small. A good agreement between the simulation and the experimental measurements in the build-up region is that which shows almost stable contamination of the particles up to the depth of electronic equilibrium.

Warming and Freshening of the Pacific Inflow to the Arctic From 1990‐2019 Implying Dramatic Shoaling in Pacific Winter Water Ventilation of the Arctic Water Column

AbstractThe Pacific inflow to the Arctic traditionally brings heat in summer, melting sea ice; dense waters in winter, refreshing the Arctic’s cold halocline; and nutrients year‐round, supporting Arctic ecosystems. Bering Strait moorings from 1990 to 2019 find increasing (0.010 ± 0.006 Sv/yr) northward flow, reducing Chukchi residence times by ∼1.5 months over this period (record maximum/minimum ∼7.5 and ∼4.5 months). Annual mean temperatures warm significantly (0.05 ± 0.02°C/yr), with faster change (∼0.1°C/yr) in warming (June/July) and cooling (October/November) months, which are now 2°C to 4°C above climatology. Warm (≥0°C) water duration increased from 5.5 months (the 1990s) to over 7 months (2017), mostly due to earlier warming (1.3 ± 0.7 days/yr). Dramatic winter‐only (January–March) freshening (0.03 psu/yr) makes winter waters fresher than summer waters. The resultant winter density change, too large to be compensated by Chukchi sea‐ice processes, shoals the Pacific Winter Water (PWW) equilibrium depth in the Arctic from 100–150 to 50–100 m, implying PWW no longer ventilates the Arctic’s cold halocline at 33.1 psu.

Control and Spread of Contagion in Networks

We study proliferation of an action in a network coordination game that is generalized to include a tractable, model-based measure of virality to make it more realistic. We present new algorithms to compute contagion thresholds and equilibrium depth of contagion and prove their theoretical properties. These algorithms apply to arbitrary connected networks and starting sets, both with and without virality. Our algorithms are easy to implement and help to quantify relationships previously inaccessible due to computational intractability. Using these algorithms, we study the spread of contagion in scale-free networks with 1,000 players using millions of Monte Carlo simulations. Our results highlight channels through which contagion may spread in networks. Small starting sets lead to greater depth of contagion in less connected networks. Virality amplifies the effect of a larger starting set and may make full network contagion inevitable in cases where it would not occur otherwise. It also brings contagion dynamics closer to a type of singularity. Our model and analysis can be used to understand potential consequences of policies designed to control or spread contagion in networks.