Elastic wave velocities in a granitic geothermal reservoir

Geothermal resources have potential for providing cost-effective and sustainable energy. Monitoring of production-induced changes in geothermal reservoirs using seismic waves requires understanding of the elastic properties of the rock and how they change due to injection of fluids and opening and closing of natural and hydraulic fractures. P- and S-wave velocities measured in a granitic geothermal reservoir using sonic logging are systematically lower than those predicted using the composition of the rock. Cracks may occur in granitic rocks from tectonic stresses and from the thermal expansion mismatch between differently oriented anisotropic crystals. An isotropic orientation distribution of microcracks causes a significant reduction in both the P- and S-velocities, consistent with the observed sonic P- and S-velocities. Vertical fractures cause a difference in the velocity of vertically propagating shear waves polarized parallel and perpendicular to the fractures. An assumption that the lower measured velocities are caused by the presence of vertical fractures is inconsistent with the sonic data. This is because vertical fractures cause a decrease in slow S-wave velocity that greatly exceeds the decrease in P-wave velocity, in contrast to the observed data. The growth of vertical fractures in the geothermal reservoir may be monitored using the difference in velocity of the fast and slow shear waves, while the change in P-velocity in a crossplot of measured P- and slow S-velocities is useful for estimating the ratio of the normal-to-shear compliance of the fractures.     

岩石的纵、横波速度与密度的规律研究

选择了济阳坳陷第三系地层四类不同岩性、237块典型岩心样品,在变温变压条件下进行超声波纵、横波速度及密度的测定,样品的孔隙度范围从2％到27％.根据变温变压测试数据,得出纵横波速度的压力、温度校正公式,将高温高压条件下测量的弹性参数校正到60 MPa条件,再进行密度、Vp和Vs数据分析.分析结果表明：Vp、Vs具有很好的线性相关性,得到新的密度与Vp关系式.同时将Vp、Vs关系融入到Gardner公式中,将Gardner函数推广为〖JP2〗ρ=CVApVBs的函数形式（称为广义Gardner公式）,拟合出砂岩的密度、Vp和Vs间的新关系式：ρ=1.575 8V0.287 9pV0.019 7s.〖JP〗文中讨论了该公式在横波速度预测、岩石物理模拟和AVO正反演等的作用,指出这些规律性认识可服务于油气勘探和开发.     

Field measurements of compressional wave velocities in common crystalline rocks

Field measurements of seismic P-wave velocities have been carried out by surface to surface refraction measurements for five different rock types. Subweathering velocities are surprisingly high and range from 5.0 km/sec in quartz monzonite to 6.2 km/sec in amphibolite in agreement with the proposal of Nur and Simmons for water-saturated low-porosity rocks. Maximum velocities found are 6.1 km/sec for quartz monzonite, 5.8 km/sec for granite gneiss, 6.4 km/sec for syenite, 6.4 km/sec for anorthosite, and 7.0 km/sec for amphibolite, and maximum depth for these velocities is 1.3 km. We conclude as follows: (1) field measurements correspond well with laboratory measurements but true velocity may be slightly higher than laboratory measurements, (2) shallow velocities are much higher than older laboratory measurements but agree well with recent laboratory measurements on water-saturated samples, (3) velocities much less than 6 km/sec seem unlikely in the crust unless in an area of extreme tectonic activity, (4) velocities of 6.5–6.7 km/sec commonly reported for the lower continental crust probably correspond to rocks less mafic than basalt or gabbro.     

Elastic wave propagation and scattering in prestressed porous rocks

Poro-acoustoelastic theory has made a great progress in both theoretical and experimental aspects, but with no publications on the joint research from theoretical analyses, experimental measurements, and numerical validations. Several key issues challenge the joint research with comparisons of experimental and numerical results, such as digital imaging of heterogeneous poroelastic properties, estimation of acoustoelastic constants, numerical dispersion at high frequencies and strong heterogeneities, elastic nonlinearity due to compliant pores, and contamination by boundary reflections. Conventional poroacoustoelastic theory, valid for the linear elastic deformation of rock grains and stiff pores, is modified by incorporating a dualporosity model to account for elastic nonlinearity due to compliant pores subject to high-magnitude loading stresses. A modified finite-element method is employed to simulate the subtle effect of microstructures on wave propagation in prestressed digital cores. We measure the heterogeneity of samples by extracting the autocorrelation length of digital cores for a rough estimation of scattering intensity. We conductexperimental measurements with a fluid-saturated sandstone sample under a constant confining pressure of 65 MPa and increasing pore pressures from 5 to 60 MPa. Numerical simulations for ultrasound propagation in the prestressed fluid-saturated digital core of the sample are followed based on the proposed poro-acoustoelastic model with compliant pores. The results demonstrate a general agreement between experimental and numerical waveforms for different stresses, validating the performance of the presented modeling scheme. The excellent agreement between experimental and numerical coda quality factors demonstrates the applicability for the numerical investigation of the stress-associated scattering attenuation in prestressed porous rocks.     

Modeling of mineralogical composition,density and elastic wave velocities in anhydrous magmatic rocks

We use the technique of direct minimization of the Gibbs free energy of the 8-component (K₂O-Na₂O-Fe₂O₃-FeO-CaO-MgO-Al₂O₃-SiO₂) multiphase system in order to determine the equilibrium mineral assemblages of rocks of different bulk chemical compositions equilibrated at various P-T conditions. The calculated modal compositions of rocks and experimental data on elastic moduli of single crystals are then used to calculate densities and isotropic elastic wave velocities of rocks together with their pressure and temperature derivatives. Sufficient accuracy of the calculations is confirmed by comparison with experimental data on the gabbro-eclogite transformation and precise ultrasonic measurements of elastic wave velocities in a number of magmatic and metamorphic rocks.We present calculated phase diagrams with isolines of density, elastic wave velocities, and their pressure and temperature derivatives for several anhydrous magmatic rocks, from granite to lherzolite. Density and elastic properties of rocks are controlled by their chemical compositions, especially the SiO₂ content, and by P-T of equilibration, and they increase with pressure due to mineral reactions changing mineral assemblages from plagioclase-bearing and garnet-free to garnetbearing and plagioclase-free. TheV _p -density correlation is high, and shows two clear trends: one for iron-poor ultramafic rocks and another for all the other rocks considered. Mineral reactions, which occur at high pressures, changeV _p and density of anhydrous magmatic rocks following the well-known Birch (or a similar) law.Felsic, intermediate and mafic rocks can be well distinguished in theV _p -V _p /V _s - diagram, although their values ofV _p can be close to one another. TheV _p -V _p /V _s -density diagrams together with calculated phase diagrams can serve as efficient instruments for petrologic interpretation of seismic velocities.     

Crustal model based on aeromagnetic profiles,gravity studies and wave velocities in rocks and crust

Summary Regional airborne magnetic profiles from India and U.S.A. are analyzed. Profiles are i) 130 km offshore Manglore to 60 km offshore Madras (India) along 13th parallel; ii) Washington to San Francisco (U.S.A.): iii) Brownsville (Texas) to Guatemala City (Mexico). Depth to the sources of magnetic anomalies along Manglore-Madras profile and Washington-San Francisco profiles is calculated either by elementary approximation ofSmellie or Prism model method ofVacquier et al. It is significant that depth values for some of the anomalies obtained by these methods are in very good agreement with those based on drilling data. The magnetic pictures along these profiles are compared with Bouguer gravity anomaly maps and it is shown that in almost all cases where magnetic bodies lie below 5 km (approximately) from sea level they are not reflected in gravity maps whereas all the magnetic bodies which are above 5 km (approximately) produce a markable feature in Bouguer gravity anomaly. This indicates that density of material below this level is almost equal to that of normal basic rocks (2.80 gm/cm³) and those above 5 km have a density less than this. Based on these results the top most layer in crust is considered to be metasedimentary including intrusive rocks and below this it is tentatively taken as Quartz-diorite accounting for the quartz rich Archean formations. Curves representing the variation of compressional wave velocity in i) granite; ii) quartz-diorite; iii) gabbro and iv) dunite, with pressure and temperature as reported from measurements in laboratory, are studied in the light of the general variation of P-wave velocity in the earth's crust reported from seismic sounding studies. It is found that a change in composition from metasedimentary zone to quartz diorite at about 5 km below sea level is supported by this study. It is found that further increase in compressional wave velocity in earth's crust can be explained by a compositional change from quartz diorite to gabbro. At certain places an unusual high velocity for compressional wave at the base of the crust is reported. This can be explained by considering that gabbro merges to Dunite in those areas. Based on this crustal model a probable explanation for the origin of granite masses is attempted.     

Comparative experimental study on several methods for measuring elastic wave velocities in rocks at high pressure

To measure elastic wave velocities in rocks at high temperature and high pressure is an important way to acquire the mechanics and thermodynamics data of rocks in the earth's interior and also a substantial approach to studying the structure and composition of materials there. In recent years, a rapid progress has been made in methodology pertaining to the measurements of elastic wave velocities in rocks at high temperature and high pressure with solids as the pressure-transfer media. However, no strict comparisons have been made of the elastic wave velocity data of rocks measured at high temperature and high pressure by various laboratories. In order to compare the experimental results from various laboratories, we have conducted a comparative experimental study on three measuring methods and made a strict comparison with the results obtained by using the transmission method with fluid as the pressure-transfer medium. Our experimental results have shown that the measurements obtained by the three methods are comparable in the pressure ranges of their application. The cubic sample pulse transmission method used by Kern is applicable to measuring elastic wave velocities in crustal rocks at lower temperature and lower pressure. The prism sample pulse reflection-transmission method has some advantages in pressure range, heating temperature and measuring precision. Although the measurements obtained under relatively low pressure conditions by the prism sample pulse transmission method are relatively low in precision, the samples are large in length and their assemblage is simple. So this method is suitable to the experiments that require large quantities of samples and higher pressures. Therefore, in practical application the latter two methods are usually recommended because their measurements can be mutually corrected and supplemented.     

Seismic wave velocities in the lower mantle

Summary The vertical velocity variations of longitudinal and transverse waves in the earth's interior in the depth range of 413 to 2800 km are put into mathematical form. Expressions of the velocities in terms of power functions of the radius are found to conform closely to the given velocities, as well as to be very simple in applications. Examples of the use of such formulas are given, including calculations of travel times and of radial velocity gradients.     

Determination of the elastic wave velocities in porous rocks with the change of overburden pressure and its universal significance

Typical rock samples with different lithologic characteristics were collected from exploring wells drilled in sandstone-conglomerate sedimental reservoirs with positive rhythm. In different pore fluid states (fully saturated with gas, water and oil), the velocities of compressional and shear waves (Vp, Vs) were measured under different overburden pressure in laboratory. The effects of pore fluid and different fluid types on the velocities were analyzed. The velocities (Vp, Vs) of the samples fully saturated with water were calculated by use of Gassmann's formula that is suitable for low frequency. The calculated values were compared with the experimental values obtained at high frequency. The result shows that Gassmann's theory can be used to calculate elastic wave velocities in porous rocks saturated with fluid. By this result, the change of elastic velocities with the change of fluid can be predicted. The error is allowable in petroleum engineering. This conclusion is useful for sonic logging interpretation and seismic datum processing.     

Shear wave velocities from down-hole measurements

Shear wave velocities of soils, which provide shear moduli for earthquake response calculations, can be measured clearly and accurately using the down-hole method. Such a method has been used at a number of sites in California with good results to depths of 200 ft. Seismic waves from hammer blows, delivered to the ends of a heavy plank loaded by the front wheels of a vehicle, are received by a three-component geophone in a carefully prepared vertical hole and recorded at 1 mm/ms with a six-channel seismograph. A series of records are obtained at various measured depths in the hole, allowing calculation of interval velocities. Shear waves are easily identified by a clear 180 degrees phase difference between waves generated by blows on the opposite ends of the plank. Compressional waves are routinely logged by a vertical hammer blow at each recording depth. Shear velocities are reproducible to about 5 per cent in surveys of neighbouring holes. The reading uncertainty of ± 1 msec for the S arrival gives a resolution sufficient to detect a buried layer 5–10 ft thick with a velocity contrast of only 20 per cent.     

Elastic wave inverse scattering in nondestructive evaluation

Ultrasonic detection and characterization of flaws in metals and ceramics is of considerable technological interest. Scattering and inverse scattering theories have recently been applied to these tasks in a systematic manner and considerable progress has resulted. This paper first reviews briefly the development of scattering and inverse scattering methods in the AF/DARPA Program in Quantitative Nondestructive Evaluation.² Then one particular inverse method studied in that program, the inverse Born approximation, is discussed in detail. Progress is reviewed and the ability of the method to distinguish volumetric and crack-like flaws is demonstrated in simple cases.This work was sponsored by the Center for Advanced Nondestructive Evaluation, operated by the Ames Laboratory, USDOE, for the Air Force Wright Aeronautical Laboratories/Materials Laboratory under Contract No. W-7405-ENG-82 with Iowa State University.     

Elastic wave propagation in inhomogeneous anisotropic media

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The Western Bohemia uppermost crust shear wave velocities from Love wave dispersion

We present a detailed study of Western Bohemia Love waves generated by blasts with an intention to estimate the uppermost crust structure for a more detailed layer distribution than previous studies have used. The use of short-period (4 s and shorter) Love waves represents a new approach in the studied region. Properties of multiple filtering as a tool of frequency–time analysis are discussed. A new method of selecting the dispersion ridges is introduced. Tests of filtering are provided by analyzing signals with analytically known dispersion. The isometric algorithm for the inversion problem is applied, the problem of non-uniqueness is discussed, and tests of reliability of the inversion are presented. During the inversion, the forward problem is solved by use of the matrix method. Six records of blasts from the Western Bohemia region are analyzed to separate the fundamental modes of Love wavegroups, and shear wave velocity distributions down to a depth of 3.0 km are inferred. Modal summation is used to compute synthetic velocigrams, which are compared to measured ones. The lateral heterogeneity of the region is discussed and the presented models are compared to those of previous studies and to the geological setting of the region.     

Shear and dilatational wave velocities for unsaturated soils

The primary objective of this study is for presenting some simple-to-use expressions relating the shear and dilatational wave velocities (V_S and V_P) to some physical and constitutive parameters of unsaturated soils. To this purpose, a simplified formulation is developed using the theory of linear poroelasticity in conjunction with some constitutive parameters widely used in geotechnical engineering. The derived expressions are of practical interest in view of the fact that they could be employed for evaluating the involved soil parameters from V_S and V_P measurements by in-situ or laboratory geophysical tests.     

Seismic wave velocities in the lower mantle — Part II

Summary In an earlier paper the author developed mathematical expressions for the longitudinal and transverse wave velocities in the lower mantle in the form of power functions of the radius. In the present paper we shall instead develop the velocities as power series or polynomials of the radius. The two procedures are compared with regard to accuracy and convenience in applications. The power series expansion can permit higher accuracy in the representation of the velocities, but often entails greater complications in applications.     

弹性波逆散射微扰论

本文将普遍声逆散射微扰论应用于弹性波层析成像问题,在Born变换下推出了以旋转角为补偿参数的各阶微扰重建公式,实现了对非均匀各向同性散射体内3个参数（质量密度ρ和两个Lamé系数λ,μ）的同时重建. 对于层析成像问题,在弹性波的传播过程中P波与SV波有耦合,但它们不会和SH波发生耦合,于是可以得到3个形式相对简单的标量方程. 在Born变换下,在散射波中引入微扰参数,将散射体的3个参数分别按该微扰参数展开,然后利用二维自由空间的Green函数分别得到散射的P波、SV波和SH波的积分表示. 最后,经一维傅氏变换后,得到Born变换下散射体3个参数的各阶微扰重建公式.