Rheological information from geological structures

The contrast in rheological properties between layers of different composition or texture, and between stiff inclusions and their matrix, gives rise to perturbations in flow that result in structures. Theory and modeling allow us to understand the conditions necessary for such structures to form and, conversely, we can use the form of the structures to infer possible rheological conditions for the rocks during natural deformation. We review here several structures and their use as indicators of rheological behavior, based on theory, numerical and experimental models, and observations on naturl structures.Theory predicts that a dominant wavelength/thickness (L _d /h) exists for both folding and boudinage that depends on the ratio of viscosities of layer to matrix, the homogeneous shortening undergone by the layer, and the exponent,n, in a flow law of power-law type. The measurement of averageL/h, and of the shortening within the layers allows an estimate of the power-law exponent of the stiff layer to be made. Also, numerical modeling shows that fold hinges become sharper asn increases and the limbs become relatively longer and straighter. The dynamic growth of pinch and swell instabilities only overcomes the kinematic decay in nonlinear flow, thus the existence of pinch and swell is by itself evidence of nonlinear behavior.Strain rate and strain, increase more rapidly away from the neutral surface for a layer of power-law rheology (withn>1) than for a layer of Newtonian rheology. Thus, strain gradient across a fold hinge, at fixed amplitude or limb dip, increases with increasingn.Porphyroclasts in mylonites develop characteristic rims of recrystallized grains that are drawn out into trails of or ° shape by the perturbed flow of the, material around the clast. Experimental evidence suggests that shapes occur if flow is linear, whereas nonlinear flow may give rise to the shape.The inference of rheological behavior from structures is complementary to the determination of rheological properties of rocks in the laboratory. What data there is suggest that constitutive relations for rocks undergoing ductile deformation in which many structures develop are highly nonlinear. There is general qualitative agreement between flow laws inferred on the basis of experimental results and those inferred from observation of structural characteristics.     

An experimental study on semi-brittle and plastic rheology of Panzhihua gabbro

Rheological properties of the crust and upper mantle are essential data that are needed in modelling the mechanical behaviour of the shallow part of the earth. The importance of such data has been seen in discussions about the strength profile of continen…     

Roughness scale dependence of the relationship between tracer longitudinal dispersion and Peclet number in variable‐aperture fractures

The relationship between the longitudinal dispersion (D_L) and Peclet number (Pe) is crucial for predicting and simulating tracer through the variable‐aperture fracture. In this study, the roughness of the self‐affine fracture wall was decomposed into primary roughness (relatively large‐scale waviness) and secondary roughness (relatively small‐scale waviness) by a multiscaled wavelet analysis technique. Based on the complete dispersion mechanism (diffusion, macrodispersion, and Taylor dispersion) in the variable‐aperture fracture, three relationships (second‐order, power‐law, and linear relationships) between the D_L and Pe were investigated at large and small scales, respectively. Our results showed that the primary roughness mostly controlled the Taylor dispersion mechanism, whereas the secondary roughness was a dominant factor for the macrodispersion mechanism. Increasing the Hurst exponent and removing the secondary roughness led to the decreasing range of Pe where macrodispersion mechanism dominated the solute transport. It was found that estimating the D_L from the power‐law relationship based on Taylor dispersion theory resulted in considerable errors, even in the range of Pe where the Taylor dispersion mechanism dominated. The exponent of the power‐law relationship increased as the secondary roughness was removed. Analysing the linear relationship between the D_L and Pe revealed that the longitudinal dispersivity α_L increased linearly. However, this linear increase became weak as the Taylor dispersion mechanism dominated. In the range of Pe where the macrodispersion mechanism dominated, increasing the Hurst exponent caused the increase of α_L and the secondary roughness played a significant role in enhancing the α_L. As the Taylor dispersion mechanism dominated, the α_L was insensitive to the influence of multiscale roughness in variable‐aperture fractures.     

Mechanical analysis of en echelon structure and its significance of controlling earthquakes

The paper deals with the mechanical origin and rules ofen echelon folds and their secondary fractures by means of elastic stability theory and nonlinear fracture criterion. Obtains the quantitative relations amongen echelon angles ofen echelon folds, ratios of boundary stresses anden echelon pitches of shear zone under an action of general boundary forces (tension shear, pure shear or compression shear). As an applied example, the paper researches the displacement field, stress field, distortion energy distribution, state of secondary fractures and energy released by fracturing ofen echelon fold structure developed at the east foot of Taihang Mountain. The results of research show that maximum principal (compressive) stresses, maximum shear stresses, high value area of distortion energy are in the nuclear parts ofen echelon folds. In these parts compressive fractures were easily developed in approximately parallel with fold axis. So it is verified that the secondary fracture ofen echelon folds is a mechanism controlling a strong earthquake.     

Lg magnitude determination for the eastern six Provinces of China (part 2)

Any pair ofm _{L gz} ,m _{L g} b,mmxz andmm x h in the eastern six provinces of China show good linear relation this makes it easy to convert from one scale to another.mm x h may replaceM _L (ECH) as the local earthquake magnitude scale for the eastern six provinces, yet retaining the level ofM _L (ECH). The scalemm x h is 0.36 magnitude units higher thanM _L (SC) for southern California. By comparingRm a x (Δ) withR ₃ (Δ) of Yunnan, it is found that the γ-value ofMAX phase of about 1 section in Yunnan region is half as large as that in the eastern six provinces of China. Observation indicates thatmm x h≈mb for magnitude 4–5. It follows therefore thatmb (ECH)≈mb (WUS). This is supported by the result that the attenuation coefficient, the γ-value in eastern China is the same as in western United States.     

Permeability Evolution During Non-linear Viscous Creep of Calcite Rocks

Permeability, storage capacity and volumetric strain were measured in situ during deformation of hot-pressed calcite aggregates containing 10, 20, and 30 wt% quartz. Both isostatic and conventional triaxial loading conditions were used. The tests were performed at confining pressure of 300 MPa, pore pressures between 50 to 290 MPa, temperatures from 673 to 873 K and strain rates of 3 × 10⁻⁵ s⁻¹. Argon gas was used as the pore fluid. The initial porosities of the starting samples varied from 5% to 9%, with higher porosity correlated to higher quartz content. Microstructural observations after the experiment indicate two kinds of pores are present: 1) Angular, crack-like pores along boundaries between quartz grains or between quartz and calcite grains and 2) equant and tubular voids within the calcite matrix. Under isostatic loading conditions, the compaction rate covaries with porosity and increases with increasing effective pressure. Most of the permeability reduction induced during compaction is irreversible and probably owes to plastic processes. As has been found in previous studies on hot-pressed calcite aggregates, permeability, k, is nonlinearly related to porosity, ϕ. Over small changes in porosity, the two parameters are approximately related as k ∝ ϕⁿ. The exponent n strongly increases as porosity decreases to a finite value (from about 4 to 6% depending on quartz content), suggesting a porosity percolation threshold. When subjected to triaxial deformation, the calcite-quartz aggregates exhibit shear-enhanced compaction, but permeability does not decrease as rapidly as it does under isostatic conditions. During triaxial compaction the exponent n only varies between 2 and 3. Non-isostatic deformation seems to reduce the percolation threshold, and, in fact, enhances the permeability relative to that at the same porosity during isostatic compaction. Our data provide constraints on the governing parameters of the compaction theory which describes fluid flow through a viscous matrix, and may have important implications for expulsion of sedimentary fluids, for fluid flow during deformation and metamorphism, and melt extraction from partially molten rocks.     

Depth of the brittle-ductile transition in a transcurrent boundary zone

A model is proposed which describes the boundary zone between two transcurrent plates as a viscoelastic body, with rheological properties changing with depth. In this model, the brittle-ductile transition is defined as the depth at which the time derivative of shear stress changes from positive to negative values. Variations of this depth are studied as functions of geothermal gradient, rheological parameters and strain rate, using a power law rheology with exponent ranging from 1 to 4. Stress relaxation in the ductile zone is controlled by a local characteristic time, which depends on petrology, temperature and, in the case of non-Newtonian rheology, on strain rate. The composition and the hydration degree of crustal rocks may also sensibly influence the depth of the brittle-ductile transition. The model predictions are compared with observations regarding the San Andreas, Imperial Valley and North Anatolian Faults: it is found that values ofn from 1 to 3 are more appropriate to reproduce the transition depth inferred by the seismicity distribution.     

Seismicity induced by gas production: II. Lithology correlated events,induced stresses and deformation

A 3D relocation technique permits precise locations of induced earthquakes. Geostatistical processing using the data of 87 boreholes provides the basis of a precise 3D structure, with a dome geometry. Conventional laboratory mechanical tests performed on deep rock samples (1000 m to 5000 m) define the rock properties at depths similar to those of the seismic events (1<M _L<4.2) that range from 1 to 7 km.In the studied period, most (85%), of the events were located above the gas reservoir, with very few located in the reservoir itself. Because the production parameters (50 MPa depletion of the gas pressure reservoir) are homogeneous throughout the gas field, the lateral inhomogeneity of the seismic rupture locations are a consequence of variations in the rheological response of the dome to the deformation induced by gas production.Here a ratio of two is found between the elastic modulus of the seismic rock matrix and the elastic modulus of the aseismic rock matrix. The contrast in strength is at least as great, if not greater. Repeated measured surface deformations involve the whole structure. Spatial and temporal deformations indicate that aseismic deformation is quantitatively the main process of this structural deformation. The heterogeneous stress pattern inferred fromP-axes of induced earthquakes disagrees with the tectonic regional stress field. The radial distribution ofP-axes towards the gas reservoir probably reflects the production induced deformation. The inferred deformation of the dome occurs in response to weak induced stresses.     

A visco-elastoplastic model for fault rocks and its application to earthquake research

In the light of the rheological properties of crustal rocks and some features of earthquakes, a rheological model for fault rocks is suggested in the paper and the possibility of applying the suggested model to the study of earthquake mechanism is discussed. The results show that it is reasonable to take the suggested model as a physical simplification of fault rocks and to apply it to the numerical calculation and simulation of 2-D problems. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 129–136, 1992.     

The lunar barometric tide,its global distribution and annual variation

Summary The global distribution of the lunar barometric tideL ₂ is investigated by spherical harmonic analysis, based on 104 stations for the annual mean, and on 85 stations for the three seasons. The main wave ofL ₂ is the one with wave number 2, but for a detailed study of the irregularities of the global distribution ofL ₂, waves with other wave numbers have also to be considered. Even the main wave ofL ₂ is asymmetric to the equator with the two lunar-daily pressure maxima occurring earlier in the Southern than in the Northern Hemisphere. The amplitudes at the same distances from the equator are greater in the Southern than in the Northern Hemisphere. These hemispheric differences are most pronounced during the D season. As found in earlier investigations the phase consiant ofL ₂ is always greater during the J season than during the D season. But the amplitudes are greatest during the J season only north of 30^oS. Farther south the amplitude maximum occurs during the D season.sponsored by the National Science Foundation     

Variations in the upper mantle structure as derived fromP n andS n waves

Summary Observed travel-times ofP _n andS _n waves are used to determine the ratio ofP _n toS _n velocities, Poisson's ratio and the ratio of incompressibility to shear modulus for Europe, Japan, North America and Scandinavia. The analysis of the data reveals that theP _n toS _n velocity ratio decreases when theP _n velocity increases for Scandinavia and North America, while the velocity ratio increases when theP _n velocity increases for Europe and Japan.     

Distribution of<Emphasis Type="Italic">L</Emphasis><Subscript>g</Subscript> coda<Emphasis Type="Italic">Q</Emphasis> in the Chinese continent and its adjacent regions

785 traces of vertical components from shallow earthquakes recorded by 10 CDSN (Chinese Digital Seismographic Network) stations and 5 GSN (Global Seismographic Network) stations were collected to study the attenuation characteristics ofL _g coda in the Chinese continent and its adjacent regions. The records were processed first using the stack spectral ratio method to obtain the average values ofQ ₀ (Q at 1Hz) and η, the frequency dependence, ofL _g coda in the ellipses corresponding to the paths. The back-projection technique was then employed to obtain the tomographic maps ofQ ₀ and η values, and the distribution of their errors. Results indicate that in the studied areaQ ₀ varies between 200 and 500. The lowest value ofQ ₀ exists in the Yun-nan-Tibetan region, while the highest value ofQ ₀ occurs in the southern edge of Siberian platform. η varies between 0.3 and 0.8. For most part of the studied area η varies inversely withQ ₀.     

Strain and kinematic vorticity analysis: An indicator for sinistral transpressional strain-partitioning along the Lancangjiang shear zone,western Yunnan,China

This work deals with the preliminary relationship between strain path and strain partitioning pattern in a sinistral transpressional zone,Lancangjiang shear zone,located to the southeast of Tibet.Various ductile rocks provide an opportunity to investigate quantitative finite strain(Rs),kinematic vorticity values(Wm),and proportions of simple and pure shear components.The mean kinematic vorticity values(Wm) were evaluated based on three methods,such as Rs-θ,prophyroclast hyperbolic distribution method(PHD),a...     

On the seismic phasesP n andS n as recorded in Fennoscandia

Summary P _n velocities determined from seismic refraction measurements, show significant differences between Southern Finland (7.96 km/sec) and Southeastern Norway (8.20 km/sec). TheP _n/S_n velocity ratios (k) were determined from earthquake and explosion data, and the observed variation ofk indicates lateral variations in theP _n and/orS _n velocities in Fennoscandia.     

Time domain solution for multiple scattering and the coda envelopes

This article summarizes work on multiple scattering based on models of media with randomly distributed scatterers. The scatterers are isotropic and statistically uniform. Measuring distance in terms of mean-free pathL _s and time in terms of the mean-free timesL _s/V, whereV is the velocity of scattered waves, we have more convenient dimensionless distance and time. It can be shown that after the dimensionless time equals 0.65 energy contributed from multiple scattering becomes predominant. Thus the later coda reflects the effect of multiple scattering rather than single scattering. Treating the seismic record, including starting and tail parts, as a whole, the diffusion theory predicts that at a dense distribution of scatterers and a small distance between source and receiver, codas reflect mainly intrinsicQ _i. Of course, this conclusion is coincident with the presumption of the diffusion theory,Q _s>Q _i. However, from a new integral equation of multiple scattering, which deals with the scattered waves and primary waves separately, the conclusion is similar but clearer. This article quotes the new expression for coda energy in two-dimensional space. It shows that if the receiver is close to the source, the coda decay reflects only intrinsicQ _i, then as the distance increases, effects of scatteringQ _s, are involved in the decay feature. The theoretical plots of coda decay show that it seems in most cases in the earthQ _i should not be smaller than one tenth ofQ _s.Project Sponsored by the Joint Earthquake Science Foundation of China.     

V p /V s anomalies in dilatant rock samples

Summary In a series of triaxial experiments we have measuredV _p ,V _s and volumetric strain simultaneously in dilating dry and saturated rocks. For the first time these data permit quantitative comparison of seismic velocities or their ratio and dilatant volumetric strain. In air-dry samplesV _p /V _s decreases by a few per cent at strains of 10^–3; in saturated materials with high pore pressure,V _p /V _s increases by a comparable amount. Decreases in seismic velocity ratio are difficult to generate in initially saturated rocks even with low pore pressures and at strain rates of 10^–4/sec. A liquid-vapor transition will not produce a significant drop inV _p /V _s . If dilatancy and fluid flow are responsible for seismic travel time anomalies prior to earthquakes, our results suggest that such anomalies will occur only in regions where pore fluid source to sink dimensions are of the order of 10 km or more, or in regions where the rocks are not saturated to begin with.     

A concise parameterization of the hydraulic conductivity of unsaturated soils

The parameter n in the well-known expression for hydraulic conductivity K=K₀S_eⁿ (where K₀ is its value at satiation and S_e the effective saturation) is determined as a function of the exponent in the power form of the soil–water retention relationship. The result is validated with an extensive experimental database comprising some 43 soils, collected by Mualem.     

Testing the Universal Soil Loss Equation‐MB equation in plots in Central and South Italy

Planning soil conservation strategies requires predictive techniques at event scale because a large percentage of soil loss over a long‐time period is due to relatively few large storms. Considering runoff is expected to improve soil loss predictions and allows relation of the process‐oriented approach with the empirical one, furthermore, the effects of detachment and transport on soil erosion processes can be distinguished by a runoff component. In this paper, the empirical model USLE‐MB (USLE‐M based), including a rainfall‐runoff erosivity factor in which the event rainfall erosivity index EI₃₀ of the Universal Soil Loss Equation (USLE) multiplies the runoff coefficient Q_R raised to an exponent b₁ > 1 is tested by the measurements carried out for the Masse (10 plots) and Sparacia (22 plots) experimental stations in Italy. For the Masse experimental station, an exponent b₁ > 1 was also estimated by tests carried out by a nozzle‐type rainfall simulator. For each experimental site in fallow conditions, the effect of the sample size of the plot soil loss measurements on the estimate of the b₁ coefficient was also studied by the extraction of a fixed number N of randomly obtained pairs of the normalized soil loss and runoff coefficient. The analysis showed that the variability of b₁ with N is low and that 350 pairs are sufficient to obtain a stable estimate of b₁. A total of 1,262 soil loss data were used to parameterize the model both locally and considering the two sites simultaneously. The b₁ exponent varied between the two sites (1.298–1.520), but using a common exponent (1.386) was possible. Using a common b₁ exponent for the two experimental areas increases the practical interest for the model and allows the estimation of a baseline component of the soil erodibility factor, which is representative of the at‐site soil intrinsic and quasi‐static properties. Development of a single USLE‐MB model appears possible, and sampling other sites is advisable to develop a single USLE‐MB model for general use.     

岩石破裂强度的温度和应变率效应及其对岩石圈流变结构的影响

研究了温度和应变率对岩石破裂强度的影响,得到了岩石圈中一些典型岩石破裂强度的新的经验规律.新的经验规律除考虑围压和标本尺度的影响外,还考虑了温度和应变率的影响,并增加了新岩石的结果,所以更能反映岩石圈内岩石破裂的真实状态.通过对鄂尔多斯平均流变结构的计算和对比研究表明：传统的忽略脆性破裂的流变模型过高地估计了流变强度,流变机制的分布也不尽合理.而考虑了脆性破裂机制的流变模型的结果表明脆性区分为两部分,浅部以摩擦滑动机制控制,深部以脆性破裂机制控制.由于新的经验规律考虑的代表性岩石更全面,并考虑了应变率的影响,得到的脆性区的范围进一步增大,流变强度进一步降低.     

Modeling of the runup heights of the Hokkaido-Nansei-Oki tsunami of 12 July 1993

The Hokkaido-Nansei-Oki earthquake (M _w 7.7) of July 12, 1993, is one of the largest tsunamigenic events in the Sea of Japan. The tsunami magnitudeM _t is determined to be 8.1 from the maximum amplitudes of the tsunami recorded on tide gauges. This value is larger thanM _w by 0.4 units. It is suggested that the tsunami potential of the Nansei-Oki earthquake is large forM _w . A number of tsunami runup data are accumulated for a total range of about 1000 km along the coast, and the data are averaged to obtain the local mean heightsH _n for 23 segments in intervals of about 40 km each. The geographic variation ofH _n is approximately explained in terms of the empirical relationship proposed byAbe (1989, 1993). The height prediction from the available earthquake magnitudes ranges from 5.0–8.4 m, which brackets the observed maximum ofH _n , 7.7 m, at Okushiri Island.