Solving the Buckley–Leverett equation with gravity in a heterogeneous porous medium

Immiscible two‐phase flow in porous media can be described by the fractional flow model. If capillary forces are neglected, then the saturation equation is a non‐linear hyperbolic conservation law, known as the Buckley–Leverett equation. This equation can be numerically solved by the method of Godunov, in which the saturation is computed from the solution of Riemann problems at cell interfaces. At a discontinuity of permeability this solution has to be constructed from two flux functions. In order to determine a unique solution an entropy inequality is needed. In this article an entropy inequality is derived from a regularisation procedure, where the physical capillary pressure term is added to the Buckley‐Leverett equation. This entropy inequality determines unique solutions of Riemann problems for all initial conditions. It leads to a simple recipe for the computation of interface fluxes for the method of Godunov. This revised version was published online in July 2006 with corrections to the Cover Date.     

Implications of gravity data from East Kalimantan and the Makassar Straits: a solution to the origin of the Makassar Straits?

Recent free-air gravity data covering the Makassar Straits is integrated with Bouguer gravity data from onshore East Kalimantan to provide new insights into the basement structure of the region. Onshore Kalimantan, gravity highs on the northern margin of the Kutai Basin trend NNE–SSW and N–S and correspond with the axes of inverted Eocene half-grabens. NW–SE trending lows correspond to deep seated basement weaknesses reactivated as normal faults during the Tertiary. An intra-basin gravity high trending NNE–SSW, the Kutai Lakes Gravity High, is modelled as folded high density Paleogene sediments flanked by syn-inversion synclines infilled with low density sediments. Offshore Kalimantan, the Makassar Straits include two basins offset by an en-echelon fault zone, suggestive of an extensional origin. The regional signature of the free-air anomaly data mirrors the bathymetry, but this effect can be reduced by the use of filters in order to examine the basin architecture. The free-air gravity minimum in the Makassar Strait is only −20 mGal, much smaller than that appropriate for a foreland basin, and more indicative of an extensional basin. The steepness of the gradients on the flanks of the basins indicates fault control of their margins. A regional 2D profile across the North Makassar Basin suggests the presence of attenuated crust (<14 km) in the basin axis at the present day, whereas flexural backstripping implies the presence of oceanic crust of middle Eocene age. The presence of oceanic crust in the North Makassar Straits Basin has implications for regional plate tectonic models.     

Moho depth determination beneath the Zagros Mountains from 3D inversion of gravity data

Due to its geological and economic importance, the Zagros Mountains have been investigated by many researchers during the last decades. Nevertheless, in spite of all the studies conducted on the region, there are still some controversial problems concerning the structure of the Zagros Mountains, including crustal depths, demanding more insights into understanding the crustal constraints of the region. Accordingly, we have conducted a gravity study to determine Moho depth map of the Zagros Mountains region, including its major structural domains from the coastal plain of the Persian Gulf to central Iran. The employed data are the densest and most accurate terrestrial gravity data set observed until now with the precision of 5 μGal and resolution of 5 arc-minute by 5 arc-minute. To image Moho depth variations, gravity inversion software GROWTH2.0 is used, proposing the possibility to model stratified structures by means of a semi-objective exploratory 3D inversion approach. The obtained results reveal the crustal thickness of ~?30–35 km underneath the southwestern most Zagros Fold-Thrust Belt increasing northeastward to 48 km. The maximum Moho depth is estimated ~?62 km below the Zagros Mountains belt along the Main Zagros Thrust. Northeast of the study area, an average crustal thickness of 46 km is computed beneath Urumieh–Dokhtar magmatic arc and central Iran.     

Crustal structure of the Alpine–Pannonian transition zone: a combined seismic and gravity study

 The crustal structure of the transition zone between the Eastern Alps and the western part of the Pannonian depression (Danube basin) is traditionally interpreted in terms of subvertical Tertiary strike-slip and normal faults separating different Alpine tectonic units. Reevaluation of approximately 4000-km-long hydrocarbon exploration reflection seismic sections and a few deep seismic profiles, together with data from approximately 300 wells, suggests a different structural model. It implies that extensional collapse of the Alpine orogene in the Middle Miocene was controlled by listric normal faults, which usually crosscut Alpine nappes at shallow levels, but at depth merge with overthrust planes separating the different Alpine units. The alternative structural model was tested along a transect across the Danube basin by gravity model calculations, and the results show that the model of low-angle extensional faulting is indeed viable. Regarding the whole lithosphere of the western Pannonian basin, gravity modelling indicates a remarkable asymmetry in the thickness minima of the attenuated crust and upper mantle. The approximately 160 km lateral offset between the two minima suggests that during the Miocene extension of the Pannonian basin detachment of the upper crust from the mantle lithosphere took place along a rheologically weak lower crust. Received: 13 July 1998 / Accepted: 18 March 1999     

Interpretation of gravity profiles across the northern Oaxaca terrane,its boundaries and the Tehuacán Valley,southern Mexico

A gravity study was conducted across the northern Oaxaca terrane and its bounding faults: the Caltepec and Oaxaca Faults to the west and east, respectively. These faults juxtapose the Oaxaca terrane against the Mixteca and Juarez terranes, respectively. The Oaxaca Fault also forms the eastern boundary of the Cenozoic Tehuacán depression. On the west, at depth, the Tehuacán valley is limited by the normal buried Tehuacán Fault. This gravity study reveals that the Oaxaca Fault system gives rise to a series of east tilted basamental blocks (Oaxaca Complex). The tectonic depression is filled with Phanerozoic rocks and has a deeper depocenter to the west. The gravity data also indicate that on the west, the Oaxaca Complex, the Caltepec and Santa Lucia faults continue northwestwards beneath Phanerozoic rocks. A major E–W to NE–SW discontinuity is inferred to exist between profiles 1 and 2.     

Development of the negative gravity anomaly of the 85°E Ridge,northeastern Indian Ocean – A process oriented modelling approach

The 85°E Ridge extends from the Mahanadi Basin, off northeastern margin of India to the Afanasy Nikitin Seamount in the Central Indian Basin. The ridge is associated with two contrasting gravity anomalies: negative anomaly over the north part (up to 5°N latitude), where the ridge structure is buried under thick Bengal Fan sediments and positive anomaly over the south part, where the structure is intermittently exposed above the seafloor. Ship-borne gravity and seismic reflection data are modelled using process oriented method and this suggest that the 85°E Ridge was emplaced on approximately 10–15 km thick elastic plate (Te) and in an off-ridge tectonic setting. We simulated gravity anomalies for different crust-sediment structural configurations of the ridge that were existing at three geological ages, such as Late Cretaceous, Early Miocene and Present. The study shows that the gravity anomaly of the ridge in the north has changed through time from its inception to present. During the Late Cretaceous the ridge was associated with a significant positive anomaly with a compensation generated by a broad flexure of the Moho boundary. By Early Miocene the ridge was approximately covered by the post-collision sediments and led to alteration of the initial gravity anomaly to a small positive anomaly. At present, the ridge is buried by approximately 3 km thick Bengal Fan sediments on its crestal region and about 8 km thick pre- and post-collision sediments on the flanks. This geological setting had changed physical properties of the sediments and led to alter the minor positive gravity anomaly of Early Miocene to the distinct negative gravity anomaly.     

Metallogeny of deep structures of the Earth’s crust in Southern Sikhote-Alin: Evidence from gravity data

The spatial relations between ore deposits in Sikhote-Alin and deep density inhomogeneities of the Earth??s crust down to a depth of 30 km have been examined. The ore areas and regions show a discrete correlation with the anomalies of the normalized density of the equivalent spherical sources of gravity anomalies at depths of 1 to 2, 4 to 5, 10?C12, and 24 km presumably provoked by magmatic bodies of different compositions. The depth of the magmatic bodies with the intermediate-to-basic composition of the initial magmas and the southeastward-decreasing vertical range of their correlation with the ore regions depend on their structural position. In the case of magmatic bodies of felsic and mixed compositions, the metallogenic specialization of the corresponding ore-magmatic systems is correlated with their inferred vertical range. Tin ore systems are characterized by a smaller vertical range (5?C10 km) of the correlation with density inhomogeneities, whereas tin-tungsten-gold ore systems are marked by a wider range (20?C25 km). Tin-lead-zinc systems occupy an intermediate position (12?C20 km). The ore-controlling role of the boundaries between the lithostructural complexes of the Earth??s crust and the central-type structures in the distribution of deep sources of ore mineralization is shown.     

Tectonic evolution of the North Patagonian Andes from field and gravity data (39–40°S)

This paper analyzes the style, distribution, mechanics and timing of deformation of the Andean retroarc zone between 39° and 40°S, in the North Patagonian Andes. Field recognition and interpretation of the main structures, constrained by new gravity data allowed establishing a structural control for the main sedimentary successions that coexisted with Andean development. A balanced cross section is constructed, where the westernmost segment is characterized by a thick-skinned structure associated with a deep decollment, over which Late Paleozoic rocks are uplifted on top of Cenozoic successions. To the east, a central segment was formed by Late Miocene inversion of a late Oligocene backarc basin controlled by a shallower decollment. A new K/Ar age of 29 Ma constrains the age of these synextensional deposits. Gravity data show the rhomboedric geometry and depth of these depocenters affecting the basement in the western orogenic front area. Finally, an eastern sector is characterized by the inversion of Late Triassic structures and development of primary faults over a deeper decollment, producing a west-vergent deformational belt. The restoration of the structural profile has yielded a total shortening of less than 10 km produced in more than one contractional stage. The complex structure described in this work results from the interaction of NW structures related to the typical Andean deformation, and ENE structures related to the intraplate Huincul high. Finally, previous works had visualized in seismic tomographies an area of relatively low velocities in the orogenic front area, interpreting it as a mantle-derived magmatic-hydrothermal crustal reservoir. Computed elastic thicknesses performed in this work from gravity data show a good correlation between areas of low flexural rigidity and areas of low seismic velocities. These anomalies coincide at surface with Pliocene to Quaternary retroarc mafic eruptions that could have a connection to slab tearing processes proposed for the last 5–2 Ma from seismic data.     

Detailed gravity studies over Jabera — Damoh region of the Vindhyan basin (Central India) and crustal evolution

Vindhyan Basin of Central India situated just north of SONATA rift zone, forms one of the major geotectonic segment of the Indian subcontinent which is associated with complex thermo-tectonic history. Southern part of this basin is known to contain favorable conditions for hydrocarbon entrapment. Keeping this in view, a detailed gravity survey network comprising 40 gravity bases and 1500 data points in an area of about 110 × 100 km² was planned in and around Jabera-Damoh region. Analysis of Bouguer and free air gravity anomaly maps, prepared using fractal based gridding method, indicates presence of two sedimentary basins (Jabera and Damoh) faulted on either sides beside ridge like features. However, well-known Jabera domal structure appeared to be a shallow feature only. Inversion of gravity data further reveals presence of 5 to 6 km thick Vindhyan sediments in the Jabera basin which are underlain by Mahakoshal/Bijawar group of rocks, resting directly over the lower crust, thereby indicating almost total absence of granitic crust from this region. It appears that due to an underlying thermal anomaly, the entire region may have been subjected to sustained uplift, deformation, erosion and consequent crustal extension during early to mid Proterozoics which brought high velocity mafic crust to such shallow levels.     

Variscan Sn–W–Mo metallogeny in the gravity picture of the Krušné hory/Erzgebirge granite batholith (Central Europe)

Late Variscan wolframite (± molybdenite) and cassiterite–wolframite greisen, skarn and vein deposits occur in a close spatial association with the granites of the Krušné hory/Erzgebirge batholith (KHEB) in Central Europe. We examined the distribution of the deposits in relation to the gravity field affected by Late Variscan granites using the data from previous gravity and metallogenic studies. Late Variscan granites are differentiated into earlier biotite monzogranites (low-F granites) and later biotite or lithium mica syenogranites (high-F granites) in accordance with the previous classifications. All the outcrops of granites in the KHEB region and their hidden continuation are confined to the Bouguer anomaly contour of − 20 mGal. The Sn–W–Mo (rare metal) deposits and occurrences are within the gravity contour of − 30 mGal with the exception of the Grossschirma stratiform tin deposit in the Freiberg polymetallic ore district. We constructed a geological model based on the gravity data along two profiles across the KHEB showing the position of some rare metal deposits and of outcropping and hidden granite bodies. The models show that the overlapping of earlier and later granites is in the areas of the most intense regional gravity minima. These coincide with the Eastern Volcano-Plutonic Complex (Altenberg minimum), which encloses large volumes of felsic extrusives, microgranite dikes and granites, and the Western Plutonic Complex (Eibenstock minimum), with small volumes of felsic dikes and predominance of earlier and later granites, with no extrusives preserved. There is no distinct relationship between the masses of Late Variscan granites and the distribution and the sizes of associated W ± Mo and Sn–W deposits. We prefer the idea that rare metal mineralization was formed by hydrothermal fluids derived from outside of presently outcropping granites. It originated in two cycles: one connected with the formation of earlier granites producing W ± Mo associations and the other one associated with later granites connected with Sn–W mineralization. Mineralizing fluids were probably generated by mantle–crustal interaction in the crust near the mantle–crust boundary as also indicated by lamprophyric intrusions coeval with the Late Variscan granitic magmatism.     

Seismic, gravity, and wire line logging characterization of the Zéramdine fault corridor and its influence in the deep Miocene aquifers distribution (east-central Tunisia)

In the Jemmel?CZéramdine region, the combined analysis of petroleum well data, seismic reflection profiles, and gravity data show the presence of the Zéramdine fault corridor, which was activated in the Neogene period. Both tectonic activity and fluvio-deltaic sedimentation are the origin of the lithologic and hydrodynamic heterogeneities. Thus, the Zéramdine fault corridor constitutes a limit between two hydraulic systems formed by Miocene sandy reservoir layers. These reservoirs have not been exploited yet and could be new water resources which can extremely benefit the region; only the upper one is exploited in the Jemmel?CBembla and Zéramdine?CBéni Hassen deep aquifers. The wire line logging, seismic reflection, and gravity interpretations show the distribution of the Miocene layers which formed the Sahel Miocene deep aquifers. The Zéramdine fault corridor leads to a spatial variability in number, distribution, depths, and thicknesses of these reservoir layers. In the northern part of the Zéramdine fault corridor, seven layers were highlighted; their thicknesses range between 15 and 105?m. However, in the southern part, only four strata were deposited: their thicknesses vary between 45 and 53?m. The total porosity of the studied aquifers is about 30%.     

A multidisciplinary study of the emplacement mechanism of the Qingyang–Jiuhua massif in Southeast China and its tectonic bearings. Part II: Amphibole geobarometry and gravity modeling

The Late Mesozoic geology of the Lower Yangtze area is characterized by extensional sedimentary basins, numerous granitic plutons and several world-class ore deposits. Regionaly, the coeval tectonic and geodynamic framework remains inadequately investigated. In order to provide a more comprehensive understanding of the regional tectonic context, we performed a multidisciplinary study of the emplacement mechanism of the Qingyang–Jiuhua massif. It consists of the granodioritic Qingyang and the monzogranitic Jiuhua plutons, U–Pb dated at 142 ± 1.0 Ma and 131 ± 2.6 Ma, respectively. Biotite and amphibole cooling ages are 5–8 myr younger. Results deduced from field structural observation, petrographic and magnetic fabrics, paleomagnetism show that this massif was probably vertically emplaced by permissive intrusion coeval with weak regional extension. However, detailed information on the characteristics of this tectonic event and its emplacement depth was not documented. Therefore, we carried out an investigation of amphibole geobarometry and gravity modeling in order to address the emplacement mode of the plutons within their regional tectonic framework. Amphibole data show that the Qingyang–Jiuhua massif was emplaced in the upper crust at a depth between 5 and 12 km. Gravity modeling indicates that the massif is laccolithic. It is characterized by several NE–SW-striking linear thickening zones that we interpret as the feeder roots of the massif. These results led us to conclude that (1) the Qingyang–Jiuhua massif was fed by vertical, NE–SW striking tension gashes; (2) consequently the late Early Cretaceous tectonics in the study area was characterized by NW–SE extension.     

Spectral harmonic analysis and synthesis of Earth’s crust gravity field

We developed and applied a novel numerical scheme for a gravimetric forward modelling of the Earth’s crustal density structures based entirely on methods for a spherical analysis and synthesis of the gravitational field. This numerical scheme utilises expressions for the gravitational potentials and their radial derivatives generated by the homogeneous or laterally varying mass density layers with a variable height/depth and thickness given in terms of spherical harmonics. We used these expressions to compute globally the complete crust-corrected Earth’s gravity field and its contribution generated by the Earth’s crust. The gravimetric forward modelling of large known mass density structures within the Earth’s crust is realised by using global models of the Earth’s gravity field (EGM2008), topography/bathymetry (DTM2006.0), continental ice-thickness (ICE-5G), and crustal density structures (CRUST2.0). The crust-corrected gravity field is obtained after modelling and subtracting the gravitational contribution of the Earth’s crust from the EGM2008 gravity data. These refined gravity data mainly comprise information on the Moho interface and mantle lithosphere. Numerical results also reveal that the gravitational contribution of the Earth’s crust varies globally from 1,843 to 12,010 mGal. This gravitational signal is strongly correlated with the crustal thickness with its maxima in mountainous regions (Himalayas, Tibetan Plateau and Andes) with the presence of large isostatic compensation. The corresponding minima over the open oceans are due to the thin and heavier oceanic crust.     

2D geological–geophysical model of the Timok Complex (Serbia,SE Europe): a new perspective from aeromagnetic and gravity data

The study reports new aeromagnetic and gravity data for the northern part of the Timok Magmatic Complex (TMC), East Serbia. The TMC is part of the Tethyan Eurasian metallogenic zone well known for hosting large copper and gold deposits. The complex formed by continuous volcanic activity 90–78 Ma ago, that developed in roughly three phases: Turonian andesites, Santonian–Campanian andesites/basaltic andesites (both mostly volcanic) and Campanian latites/monzonites (mostly shallow intrusive). The aeromagnetic measurements included acquiring total magnetic intensity data that were corrected for diurnal variations, leveling, microleveling, calculated normal field values, calculated anomaly values of total magnetic field intensity and reduction to the pole. The gravity measurements were carried out in an irregular grid with relative gravity values obtained using a Worden gravity meter. 2D modeling reveals that the subsurface extension of the Campanian Valja Str? pluton is ten times larger than it is indicated by its surface outcrops. This implies that the area south and southeast from the pluton can be interesting in terms of finding new porphyry systems. The model indicates that this intrusive body should not be considered as a deeply dissected pluton. This sheds new light onto its potential with respect to epithermal gold mineralization, as well. The model also suggests that there are larger non-exposed bodies of Santonian–Campanian volcanics and near-surface hydrothermally altered rocks than it is inferred from geological maps. The results of our study suggest that further interdisciplinary investigations in the TMC, in particular those integrating geophysics and geology, may have potential of advancing the existing exploration models.     

The Central Andean gravity high, a relic of an old subduction complex?

The Central Andean gravity high (CAGH) is a positive anomaly in isostatic residual gravity with its center located at the western flank of the Central Andes at about 24°S. The gravity was analyzed by various methods to draw quantitative conclusions about the sources of this anomaly and their process of formation. Methods include the analysis of the gravity gradients, power spectrum, wavelength filters, and Euler deconvolution.Numerical investigations of gravity field in the area of the CAGH indicate the presence of a dense body of nearly 400 km length and about 100–140 km width, that masses lie at varying depths between 10 and 38 km. A correlation between the location of the residual anomalies and the topographic lows in the area between the Salars de Atacama and Pipanaco is observed, which indicates the strong influence of the anomalous-causing rocks of the CAGH within the formation process of the Andean orogen. An influence of these causing bodies of rock on the trend of Holocene volcanic arc is likely. Genesis of the anomalous dense formations of rock could be traced back to Ordovician–Silurian time when a pre-Andean subduction zone is postulated in the region of northern Chile with its corresponding volcanic arc in the region of the CAGH.

Zusammenfassung

El campo de gravedad alto de los Andes Centrales (CAGH) consiste en una pronunciada anomalía positiva de la gravedad isostática, cuyo centro se encuentra en el borde oeste de los Andes Centrales a los 24°S. En este estudio se analizó el campo de gravedad mediante distintos métodos, de manera de poder establecer conclusiones cuantitativas sobre el causante de esta anomalía y el proceso de formación de este causante.La investigación numérica de las anomalías gravimétricas del CAGH indica la presencia de un cuerpo de alta densidad con aproximadamente 400 km de largo y 100–140 km de ancho, que se encuentra a profundidades variables entre 10 y 38 km. Se observa una correlación entre la posición de la anomalía residual y los bajos topográficos en los areas de Salares de Atacama, Arizaro, Antofalla y Pipanaco, la cual indica una fuerte influencia de rocas productoras de la anomalía en el CAGH, dentro del proceso de formación del orógeno andino. Es probable que estos cuerpos de rocas causantes de la anomalía tengan incluso influencia en el alineamiento del arco volcánico holocénico. La generación de cuerpos de rocas con una densidad anómala puede remontarse al Ordovícico–Silúrico, tiempo para el que postula una subducción pre-Andina en la región del norte de Chile y que corresponde con el arco volcánico en la región del CAGH.     

A basic study on the application of LRFD in “the technical standard for port and harbour facilities in Japan”: a case of gravity type quay wall in a persistent design situation

ABSTRACT

The Partial Factor Method (PFM) based on the Level 1 reliability design method was introduced in 2007 to the Technical Standards for Port and Harbour Facilities (TSPHF-2007) in Japan. After nearly 10 years of practical use of TSPHF-2007, the design standard has been revised based on requests from the practitioners who recommend the transition from the PFM to the Load Resistance Factor Design (LRFD). In this paper, we discuss the setting method of the target failure probability to determine the partial factors based on code calibration. Furthermore, we examine the impacts of implementing the LRFD concept to the TSPHF by taking the sliding and overturning of a gravity type quay wall as an example to represent port and harbour facilities. We found no practical difference in caisson width derived using the LRFD and the PFM, whereas the degree of matching of the target failure probability was somewhat more precise for the PFM. This finding indicates that the LRFD is a more reasonable design method than the PFM in terms of the simplicity of the performance function itself and the ease of engineering interpretation during the design procedure.