Petrological constraints on seismic properties of the Slave upper mantle (Northern Canada)

Modes and compositions of minerals in Slave mantle xenoliths, together with their pressures and temperatures of equilibrium were used to derive model depth profiles of P- and S-wave velocities (Vp, Vs) for composites equivalent to peridotite, pyroxenite and eclogite. The rocks were modeled as isotropic aggregates with uniform distribution of crystal orientations, based on single-crystal elastic moduli and volume fractions of constituent minerals. Calculated seismic wave velocities are adjusted for in situ pressure and temperature conditions using (1) experimental P- and T- derivatives for bulk rocks' Vp and Vs, and (2) calculated P- and T- derivatives for bulk rocks' elastic moduli and densities. The peridotite seismic profiles match well with the globally averaged IASP91 model and with seismic tomography results for the Slave mantle. In peridotite, an observed increase of seismic wave velocities with depth is controlled by lower degrees of chemical depletion in the deeper upper mantle. In eclogite, seismic velocities increase more rapidly with depth than in peridotite. This follows from contrasting first-order pressure derivatives of bulk isotropic moduli for eclogite and peridotite, and from the lower compressibility of eclogite at high pressures. Our calculations suggest that depletion in cratonic mantle has a distinct seismic signature compared to non-cratonic mantle. Depleted mantle on cratons should have slower Vp, faster Vs and should show lower Poisson's ratios due to an orthopyroxene enrichment. For the modelled Slave craton xenoliths, the predicted effect on seismic wave velocities would be up to 0.05 km/s.     

Elastic properties, fabric and seismic anisotropy of amphibolites and their contribution to the lower crust reflectivity

In this paper the elastic properties of amphibolites from the Serie dei Laghi and the Ivrea zone (Southern Alps, N-Italy) were investigated as a function of their mineralogical composition, microfabric and density.Three orthogonal cores were cut parallel and normal to foliation and lineation; from those, bulk and grain density were measured and the interconnected porosity was calculated. Bulk density varies from 2.75 to 3.07 g/cm³ and calculated porosity ranges from 0.02 to 0.88%.The same cores were also used to measure seismic velocity of ultrasonic waves at room temperature and at increasing confining pressure up to 300 MPa. At high pressure the matrix properties are separated from the crack-induced properties. P-wave velocity varies with respect to the direction of propagation: the slowest direction is always normal to foliation and the fastest parallel to the mineral lineation. The mineral lineation is typically defined by the elongation of amphibole crystals, in which the fastest Vp direction is parallel to the c axis, that is also the elongation axis. The Vp ranges between 6.76 and 7.54 km/s in the direction parallel to lineation and between 6.32 and 7.06 km/s in the direction normal to foliation. This defines a Vp anisotropy of up to 14%, whose shape varies from orthorhombic to axially symmetric (either prolate or flattened). It was observed that both Vp and Vp anisotropy increase with the amount of amphibole and decrease with the amount of plagioclase. Moreover, the c axis distribution of amphiboles is responsible of the Vp anisotropy intensity and shape, in agreement with observations from previous studies. The seismic properties calculated with the approach of Mainprice (1990), using the fabric data, the elastic constants and the modal composition, gave results in good agreement with the measurements.Exposed rocks in the Ivrea and Serie dei Laghi zones show that amphibolites are interlayered with metapelites on a scale from 1 to 100 m. Because of the very large acoustic impedance contrast (20.34 ± 1.75 for amphibolites, 17.16 ± 0.4 for metapelites), they represent a very reflective portion in the middle-lower crust.     

高温高压下斜长角闪岩的Vp:熔体含量和形态的综合影响

在YJ3000t高压装置上,利用超声波脉冲透射-反射法测量恒压0.6GPa,1.0GPa和2.0GPa,室温至1 195℃条件下斜长角闪岩的纵波波速(Vp),统计了实验中间产物中各组分的体积百分含量和熔体形态(二面角),并根据主要矿物含量和弹性参数,利用VRH平均模型计算了高温高压下斜长角闪岩的Vp。结果显示,不同压力下,样品的Vp随温度升高首先缓慢降低,在温度达约850℃～950℃时转而快速下降。实验产物观测显示,随温度升高熔体含量显著增加,二面角不断减小,熔体由封闭囊状演变为连通薄膜,部分熔融是导致岩石Vp快速降低的主要因素。高温高压下Vp计算结果与测量结果有相同的Vp-T变化趋势,其对比研究表明,岩石初始熔融时,熔体尚未连通,此时熔体含量控制着岩石Vp的降低。部分熔融加剧导致熔体逐渐连通,此时不同压力下熔体导致Vp下降有差异,这可能与熔体连通过程中熔体薄膜的形态因子变化有关。     

南海ODP1144站深海沉积牵引体的岩石物理模型研究

ODP1144站是南海唯一钻揭深海沉积牵引体的站位,其完整的岩芯和测井资料为开展该沉积牵引体的岩石物理模型研究提供了良好的基础。此项研究对于理解南海深海沉积物中岩性参数与弹性参数间的关系具有重要意义,并可为根据反射地震资料开展定量岩性参数预测提供依据。对现有的深海沉积物岩石物理模型包括Wood悬浮模型、等球体颗粒接触模型、Sun速度一孔隙度关系模型进行了综述。根据岩芯分析资料将1144站深海沉积物的矿物组分简化为粘土矿物、碳酸盐、陆源碎屑和硅质生物4类;其中后3种组分的弹性模量及密度值分别由其代表矿物——方解石、石英及蛋白石的理论值代替,粘土矿物组分的等效弹性模量和等效密度则分别由Voigt-Reuss-Hill平均和体积平均计算得出。将3种岩石物理模型应用于1144站,计算得出深海沉积物的纵波速度并将其与声波测井纵波速度进行比较。结果表明,Sun模型计算结果与实测结果的吻合最好,误差最小;Wood模型所得结果在浅层与实测结果较吻合,在深层与实测结果出现偏差,误差较小;而等球体颗粒接触模型计算结果整体偏高,误差较大。     

P-wave anisotropy in eclogites and relationship to the omphacite crystallographic fabric

Measurements of P-wave velocity at room temperature and confining pressures up to 500 MPa were carried out on three eclogite mylonites collected from a shear zone in the Monviso area (Western Alps). P-wave velocities at a pressure of 400 MPa range from 7.7 km/s to 7.9 km/s, yielding to a maximum anisotropy of 6%. From the CPO of omphacite we estimated a maximum contribution of omphacite to the P-wave anisotropy of only 1.3%. These results suggest that primarily the compositional layering and secondary the fabric of minor constituent minerals significantly contribute to the seismic anisotropy. Because of the anisotropy, the seismic reflectivity of subduction zones may vary with the direction of observation.     

P- and S-wave velocities and densities in silicate and calcite rocks from the Peloritani Mountains, Sicily (Italy): The effect of pressure, temperature and the direction of wave propagation

The Peloritani Mountain Belt (north-eastern Sicily) represents the connection between the Southern Appenninic Range and the Appenninic Maghrebid Chain. The lithotypes outcropping in a 36 km long and approximately 8 km wide area in the eastern part of the Peloritani Mountains are considered to represent most properly the composition of the lower crust. We selected 7 representative samples of silicate rocks (amphibolite, paragneisses, augen gneiss, phyllitic quartzite, pegmatitic rock) and 3 samples of calcite rocks (calc-schist, marbles) for the petrophysical measurements. Measurements were done on sample cubes of dry rocks in a multi-anvil apparatus. Raising of pressure gives rise to velocity increase, but the rate is different in the silicate and calcite rocks and closely related to progressive closure of microcracks. Linear behaviour is approached above about 200 MPa. Increasing temperature at 600 MPa decreases velocities in most silicate and in the calcite rocks with almost linear slopes. Substantial anisotropy of P- and S-wave velocities and shear wave splitting is found in both rock types. The residual anisotropy observed above about 200 MPa is attributed to lattice preferred orientations (LPO) of major minerals. 3D velocity calculations for an amphibolite, a paragneiss and a marble sample based on the LPO of hornblende, biotite and calcite, respectively, confirm the experimental findings of a close relationship between velocity anisotropy, shear wave splitting, shear wave polarization, lattice preferred orientation and the structural frame of the rocks (foliation, lineation). In the silicate rocks, the intrinsic (600 MPa) average P-wave velocities and Poisson's (Vp / Vs) ratios exhibit a tendency for a linear increase with densities, whereas the three calcite rocks cluster at markedly higher P-wave velocities and Poisson's (Vp / Vs) ratios, compared to their densities. In the silicate rocks, there is also a linear trend for an inverse relationship between the SiO₂ content, density and the Poisson's (Vp / Vs) ratio, respectively.     

Optimization of the Rock Physical Model in Tight Sandstone Reservoir

Krief model, Nur model and Pride-Lee model are usually used to calculate dry rock modulus of sandstone reservoirs, but they are not effective for tight sandstone reservoirs. Based on Krief model and Nur model, and minimizing the difference between predicted P-wave or S-wave velocities and measured velocities, we acquireed lithologic index m in Krief model and critical porosity ?_c in Nur model by Gassmann relationship. The empirical parameters used in the models are expressed as the values changing with depth, so the accuracy of Krief and Nur models to estimate the P-wave and S-wave velocities was improved, and these two models are called as the variable parameter Krief model and the variable parameter Nur model. In addition, comparing with prediction accuracy of P-wave and S-wave velocities under different constraints, we can see that the shear modulus formulas in the three models are more accurate and more suitable in the tight sandstone reservoir. Han’s relationship about K_dry and u_dry is not affected by porosity, lithology and other factors, and the paper established dry rock model by Han’s relationship and any one of the above three models. The new dry rock model was applied in the Gassmann relationship to predict S-wave velocity of H8 tight sandstone reservoir in Sulige Gas Filed, Ordos Basin, which improved the accuracy of predicting S-wave velocity. At the same time, lithology index m in Krief model, critical porosity ?_c in Nur model and consolidation parameters c in Pride-Lee model which are corresponding to each sample can be obtained. The values of these parameters can reflect lithology difference, pore structure, compaction degree and other characteristics, which indicate the geological characteristics of the reservoir.     

苏鲁-大别超高压变质岩的弹性力学性质与密度的关系

我们采集了31块来自中国大陆科学钻探(CCSD)主孔和预先导孔岩芯以及29块苏鲁-大别地区地表露头的典型超高压变质岩,在10～850 MPa的静水压力和室温下测量了60块标本的P波与S波速度,分别建立了纵横波速和围压之间的定量关系,并在此基础上计算了不同压力下各岩石标本的弹性参数即杨氏模量(E)、剪切模量(G)、体模量(K)和泊松比(v),着重探讨了超高压变质岩的弹性力学性质与密度之间的关系.这些最新成果将为超高压变质岩地区以及新老俯冲带地震波资料的解释提供关键的理论和实验基础.     

Fabric symmetry of low anisotropic rocks inferred from ultrasonic sounding: Implications for the geomechanical models

The geomechanical models were established based on the absence or presence of certain rock fabric elements — texture (crystallographic preferred orientation), microstructure (shape preferred orientation) and microcracks (flat voids). The proposed models include both (i) the ideal material showing random texture and structure but no microcracks, i.e. the material which is hardly to be found in nature, and (ii) the materials possessing various combinations of fabric elements that show different spatial arrangements. The mutual relationship between those parameters and seismic and geomechanical properties are discussed.Selected models were experimentally verified during laboratory experiments. These consist of measurement of P-wave velocities in 132 independent directions under several confining pressures in the range 0.1–400 MPa. From measured data 3D P-wave patterns can be constructed and the influence of microcracks and of texture and structure on the rock seismic anisotropy can be determined. The seismic anisotropy established at different levels of confining pressure can be used for the interpretation of rock fabric symmetry of rocks showing low anisotropy in macroscale and for the selection of directions in which the geomechanical test can be performed. The measured P-wave velocities were then mathematically processed by using a fitting function which reflects contribution of P-wave velocity in the mineral skeleton of an ideal sample without microcracks extrapolated to the atmospheric pressure level from high confining pressure interval (ca. 200–400 MPa) (v₀), linear compressibility of the samples (k_v), and confining pressure during which most of the cracks are closed (P₀). These parameters improve the understanding of the response of various rock fabric elements on increasing confinement and corresponding changes in elasticity.The observed seismic and geomechanical anisotropies reflect intensity of the fabric of rock-forming minerals and microcracks. The magnitude of seismic anisotropy measured at atmospheric pressure corresponds to the anisotropy of static elastic modulus and is governed by the spatial arrangement of microcracks. The magnitude of strength anisotropy (uniaxial compressive strength) correlates more likely to the seismic anisotropy determined at high confining pressure and is connected to the preferred orientations (either CPO or SPO or both) of rock-forming minerals.     

Well log data analysis for lithology and fluid identification in Krishna-Godavari Basin,India

Well log analysis provides the information on petrophysical properties of reservoir rock and its fluid content. The present study depicts interpretation of well log responses such as gamma ray, resistivity, density and neutron logs from six wells, namely W-1, W-2, W-9, W-12, W-13 and W-14 under the study area of Krishna-Godavari (K-G) basin. The logs have been used primarily for identification of lithology and hydrocarbon-bearing zones. The gamma ray log trend indicates deposition of cleaning upward sediment. Coarsening upward, clayey-silty-sandy bodies have been evidenced from the gamma ray log. Gas-bearing zones are characterised by low gamma ray, high deep resistivity and crossover between neutron and density logs. Total 14 numbers of hydrocarbon-bearing zones are identified from wells W-9, W-12, W-13 and W-14 using conventional log analysis. Crossplotting techniques are adopted for identification of lithology and fluid type using log responses. Crossplots, namely P-impedance vs. S-impedance, P-impedance vs. ratio of P-wave and S-wave velocities (Vp/Vs) and lambda-mu-rho (LMR), have been analysed to discriminate between lithology and fluid types. Vp/Vs vs. P-impedance crossplot is able to detect gas sand, brine sand and shale whereas P-impedance vs. S-impedance crossplot detects shale and sand trends only. LMR technique, i.e. λρ vs. μρ crossplot is able to discriminate gas sand, brine sand, carbonate and shale. The LMR crossplot improves the detectability and sensitivity of fluid types and carbonate lithology over other crossplotting techniques. Petrophysical parameters like volume of shale, effective porosity and water saturation in the hydrocarbon-bearing zones in these wells range from 5 to 37%, from 11 to 36 and from 10 to 50% respectively. The estimated petrophysical parameters and lithology are validated with limited core samples and cutting samples from five wells under the study area.     

Effect of high-low quartz transition on compressional and shear wave velocities in rocks under high pressure

The compressional and shear wave velocities in quarzite, granite, and granulite are determined at a fixed confining pressure of 2 kb as a function of temperature up to 720° C. The high-low quartz transition of the constituent quartz minerals is associated with a pronounced decrease in velocity of the compressional waves when approaching the transition and with a significant velocity increase after the transition. In contrast, the effect of the α-β transition on shear wave velocities is small. The drop of V _P is explained by the elastic softening of structure of the constituent quartz minerals near the α-β transition and the opening of grain-boundary cracks, caused by the very high volumetric thermal expansion of the quartz relative to the other component minerals. The velocity increase in the β-field may be attributed to an elastic hardening of the quartz structure. Poisson ratios computed from the velocity data are anomalous for a solid: they become negative within the transition regime. The transition temperature, as indicated by the minimum velocities, is higher in the polycristalline rocks than is expected on grounds of single crystal behavior, and the discrepancy is more marked in granite than in quartzite. The shift of the transition temperature to higher values is explained by internal stresses that arise from the anisotropy of the thermal expansion and compressibility of individual grains and the differences in thermal expansion and compressibility between different component minerals. The role of the α-β quartz transition as a possible cause of low-velocity layers is discussed.     

大别山榴辉岩的密度和波速及其对壳—幔循环的启示

测定了大别山地区榴辉岩和麻粒岩的密度和高温高压 (至 5 .0GPa和 130 0℃ )的纵波速度 (Vp)。超高压榴辉岩具有较高的密度和Vp 及较弱的各向异性。榴辉岩的压力系数为 0 .2 2～ 0 .33km/s·GPa ,超高压榴辉岩的温度系数为 - 3.41× 10 -4 km/s·℃。榴辉岩的密度和波速的分析表明 ,地幔深部的超高压榴辉岩形成后可能包含了两个过程 ,即一部分榴辉岩通过拆沉作用进入深部地幔 ,另一部分快速折返至地壳内或地表 ,榴辉岩的形成过程代表了壳幔物质循环。现今的大别山深部可能只存在少量榴辉岩。     

First-principles study of high-pressure stability,structure, and elasticity of FeS2 polymorphs

The pressure-dependent elastic properties of the Fe–S system are important to understand the dynamic properties of the Earth’s interior. We have therefore undertaken a first-principles study of the structural and elastic properties of FeS₂ polymorphs under high pressure using a method based on plane-wave pseudopotential density function theory. The lattice constants, elastic constants, zero-pressure bulk modulus, and its pressure derivative of pyrite are in good agreement with the previous experiments and theoretical approaches; the lattice constants of marcasite are also consistent with the available experimental data. Calculations of the elastic constants of pyrite and marcasite have been determined from 0 to 200 GPa. Based on the relationship between the calculated elastic constants and the pressure, which can provide the stability of mineral, it would appear that pyrite is stable, whereas marcasite is unstable when the pressure rises above 130 GPa. Static lattice energy calculations predict the marcasite-to-pyrite phase transition to occur at 5.4 GPa at 0 K.     

Seismic properties of the upper crust in the central Friuli area (northeastern Italy) based on petrophysical data

The compressional and shear wave velocities have been measured at room temperature and pressure up to 450 MPa on 5 sedimentary rock samples, representative of the most common lithologies of the upper crust in the central Friuli area (northeastern Italy). At 400 MPa confining pressure the Triassic dolomitic rock shows the highest velocities (Vp  7 km/s, Vs  3.6 km/s), the Jurassic and Triassic limestones samples intermediate velocities (Vp  6.3 /s, Vs  3.5 km/s) and the Cenozoic and Paleozoic sandstones the lowest velocities (Vp  6.15 km/s, Vs  3.35 km/s). The Paleozoic sandstone sample is characterized by the strongest anisotropy (10%) and significant birefringence (0.2 km/s) is found only on the Cenozoic sandstone sample. We elaborated the synthetic profiles of seismic velocities, density, elastic parameters and reflection coefficient, related to 4 one-dimensional geological models extended up to 22 km depth. The synthetic profiles evidence high rheological contrasts between Triassic dolomitic rocks and the soft sandstones and the Jurassic limestones. The Vp profiles obtained from laboratory measurements match very well the in-situ Vp profile measured by sonic log for the limestones and dolomitic rocks, supporting our one-dimensional modelling of the calcareous-carbonatic stratigraphic series. The Vp and Vs values of the synthetic profiles are compared with the corresponding ones obtained from the 3-D tomographic inversion of local earthquakes. The laboratory Vp are generally higher than the tomographic ones with major discrepancies for the dolomitic lithology. The comparison with the depth location of seismicity reveals that the seismic energy is mainly released in correspondence of high-contrast rheological boundaries.     

Elastic properties of polycrystalline minerals: Comparison of theory and experiment

Literature compressional and shear wave velocities measured versus pressure and temperature on dense, isotropic polycrystals of periclase, corundum, forsterite, fayalite, alpha-quartz, rutile, germania, and cassiterite are compared with the Voigt, Reuss, and Hashin-Shtrikman bounds calculated from single-crystal elastic stiffnesses and their first pressure and temperature derivatives. The Hashin-Shtrikman bounds reduce the separation between the Voigt and Reuss bounds by factors of from 3 to 15. There is very good agreement between the Hashin-Shtrikman bounds and the experimental data when errors in the polycrystal data and in the single-crystal elastic stiffnesses are taken into account. This comparison demonstrates that the Hashin-Shtrikman bounds can be used with considerable confidence in modeling velocities in mineral assemblages, particularly mantle assemblages, and are especially useful in problems where sensitivity of the results to the uncertainties in all the input parameters is of interest.     

Direct measurement of 3D elastic anisotropy on rocks from the Ivrea zone (Southern Alps, NW Italy)

Lower crustal and upper mantle rocks exposed at the earth's surface present direct possibility to measure their physical properties that must be, in other cases, interpreted using indirect methods. The results of these direct measurements can be then used for the corrections of models based on the indirect data. Elastic properties are among the most important parameters studied in geophysics and employed in many fields of earth sciences. In laboratory, dynamic elastic properties are commonly tested in three mutually perpendicular directions. The spatial distribution of P- and S-wave velocities are then computed using textural data, modal composition, density and elastic constants. During such computation, it is virtually impossible to involve all microfabric parameters like different types of microcracking, micropores, mineral alteration or quality of grain boundaries.

In this study, complete 3D ultrasonic transmission of spherical samples in 132 independent directions at several levels of confining pressure up to 400 MPa has been employed for study of selected mafic and ultrabasic rocks sampled in and nearby Balmuccia ultrabasic massif (Ivrea zone, Southern Alps, NW Italy). This method revealed large directional variance of maximum P-wave velocity and different symmetries (orthorhombic vs. transversal isotropic) of elastic waves 3D distribution that has not been recorded on these rocks before. Moreover, one dunite sample exhibits P-wave velocity approaching to that of olivine single crystal being interpreted as influence of CPO.     

http://www.sciencedirect.com/science/article/pii/S1674987113001369

The 3-D P- and S-wave velocity models of the upper crust beneath Southwest Iberia are determined by inverting arrival time data from local earthquakes using a seismic tomo~raphy method. We used a total of 3085 P- and 2780 S-wave high quality arrival times from 886 local earthquakes recorded by a per- manent seismic network, which is operated by the Institute of Meteorology （IM）, Lisbon, Portugal. The computed P- and S-wave velocities are used to determine the 3-D distributions of Vp/Vs ratio. The 3-D velocity and Vp/Vs ratio images display clear lateral heterogeneities in the study area. Significant veloc- ity variations up to ~6% are revealed in the upper crust beneath Southwest lberia, At 4 km depth, both P- and S-wave velocity take average to high values relative to the initial velocity model, while at 12 km, low P-wave velocities are clearly visible along the coast and in the southern parts. High S-wave velocities at 12 km depth are imaged in the central parts, and average values along the coast; although some scattered patches of low and high S-wave velocities are also revealed. The Vp/Vs rztio is generally high at depths of 4 and 12 km along the coastal parts with some regions of high Vp/Vs ratio in the north at 4 km depth, and low Vp/Vs ratio in the central southern parts at a depth of 12 km, The imaged low velocity and high Vp/Vs ratios are related to the thick saturated and unconsolidated sediments covering the region; whereas the high velocity regions are generally associated with the Mesozoic basement rocks.     

矿物热分解动力学的研究方法探讨

:矿物分解动力学的研究可以大大提高我们对地质作用过程中矿物生长、元素和流体迁移等过程的了解。本文在介绍固相反应动力学原理的基础上 ,讨论了常压下研究矿物分解动力学的热重分析法和电导率法 ,指出精确确定高压下的反应分数 ,是研究高压下矿物热分解动力学的关键。提出了高压下确定反应分数的方法。     

The lithospheric mantle beneath the Kerguelen Islands (Indian Ocean): petrological and petrophysical characteristics of mantle mafic rock types and correlation with seismic profiles

Deep-seated meta-igneous xenoliths brought to the surface by alkali basaltic magmas from the Kerguelen Islands reveal that basaltic magmas have intruded the upper mantle throughout their geological evolution. These xenoliths record volcanic activity associated with their early South East Indian Ridge location and subsequent translation to an intraplate setting over the Kerguelen Plume. The meta-igneous xenoliths sample two distinctive geochemical episodes: one is tholeiitic transitional and one is alkali basaltic. Geothermobarometry calculations provide a spatial context for the rock type sequence sampled and for interpreting petrophysical data. The garnet granulites equilibrated over a pressure range of 1.15 to 1.35 GPa and the garnet pyroxenite at 1.8 GPa. Ultrasonic measurements of compressional wave speed V_P have been carried out at pressures up to 1 GPa, and densities measured for representative samples of meta-igneous xenoliths and for a harzburgite that represents the peridotitic mantle. V_P and density have also been calculated using modal proportions of minerals and appropriate elastic properties for the constituent minerals. Calculated and measured V_P agree well for rock types with microstructures not complicated by kelyphitic breakdown of garnet and/or pervasive grain-boundary cracking. Pyroxene granulites have measured and calculated V_P within the range 7.37-7.52 km/s; calculated velocities for the garnet granulites and pyroxenites range from 7.69 to 7.99 km/s, whereas measured and calculated V_P for a mantle harzburgite are 8.45 and 8.29 km/s respectively. The seismic structure observed beneath the Kerguelen Islands can be explained by (1) a mixture of underplated pyroxene granulites and ultramafic rocks responsible for the 2-3 km low velocity transitional zone below the oceanic layer 3, (2) varying proportions of granulites and pyroxenites in different regions within the upper mantle producing the lateral heterogeneities, and (3) intercalation of the granulites and pyroxenites throughout the entire upper mantle column, along with elevated temperatures, accounting for the relatively low mantle velocities (7.70-7.95 km/s).     

Teacher's Aide: Geologic Characteristics of Hole-Effect Variograms Calculated from Lithology-Indicator Variables

Variograms calculated from binary variables, such as from two lithologies, tend to show sinusoidal forms with decreasing amplitudes for increasing lag distances. This cyclicity is observed often when analyzing drill-hole data for rock sequences with alternating lithologies, and the variograms are thus labeled “hole-effect variograms.” Such variograms show a variety of forms: (1) Low to moderate variation in lithologic-body dimensions causes variograms to have strong cyclicity with decaying amplitude. (2) Variograms with one or more peaks and troughs usually result from a binary variable for which lithologies are about equally abundant but possibly large variations exist in the size of lithologic bodies. (3) Variograms show poor cyclicity if one lithology has highly variable body sizes and the other has moderately variable body dimensions. (4) Variograms that attain a plateau at short lag distances represent extremely high or low sandstone fraction, high variability in size of the most abundant lithology, and low variability in the other. Information about the dimensions of lithologic bodies makes it possible to approximate characteristics of the variogram of the lithology variable without numerous wells. Conversely, a hole-effect variogram of lithology may be used to estimate lithologic dimensions.