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1.
Summary. A fluid-saturated cubic packing of like elastic spheres is taken to be in equilibrium under the effect of gravity and the effects of a superimposed low-frequency elastic wave are considered. In the first place, expressions for the wave velocity, dispersion and attenuation are derived for the dry packing. This dynamic theory leads to the result that, for very low frequencies, the wave velocity is proportional to the third root of the depth and not the sixth root as is obtained by using the effective elastostatic modulus of the packing. For the fluid-saturated packing, two waves, termed respectively the 'solid wave' and the 'fluid wave', are found to propagate. The 'solid wave' has the characteristics of a wave propagating within a dry packing whose parameters differ in a specified way from those of the original packing, whereas the 'fluid wave' has those of a wave within a homogeneous fluid with similarly modified parameters.  相似文献   

2.
The phase velocity and the attenuation coefficient of compressional seismic waves, propagating in poroelastic, fluid-saturated, laminated sediments, are computed analytically from first principles. The wavefield is found to be strongly affected by the medium heterogeneity. Impedance fluctuations lead to poroelastic scattering; variations of the layer compressibilities cause inter-layer flow (a 1-D macroscopic local flow). These effects result in significant attenuation and dispersion of the seismic wavefield, even in the surface seismic frequency range, 10–100 Hz. The various attenuation mechanisms are found to be approximately additive, dominated by inter-layer flow at very low frequencies. Elastic scattering is important over a broad frequency range from seismic to sonic frequencies. Biot's global flow (the relative displacement of solid frame and fluid) contributes mainly in the range of ultrasonic frequencies. From the seismic frequency range up to ultrasonic frequencies, attenuation due to heterogeneity is strongly enhanced compared to homogeneous Biot models. Simple analytical expressions for the P -wave phase velocity and attenuation coefficient are presented as functions of frequency and of statistical medium parameters (correlation lengths, variances). These results automatically include different asymptotic approximations, such as poroelastic Backus averaging in the quasi-static and the no-flow limits, geometrical optics, and intermediate frequency ranges.  相似文献   

3.
Hyaloclastites develop where lava interacts with water resulting in deposits that have a unique and often complex range of petrophysical properties. A combination of eruptive style and emplacement environment dictates the size, geometry and distribution of different hyaloclastite facies and their associated primary physical properties such as porosity, permeability and velocity. To date, links between the 3D facies variability within these systems and their petrophysical properties remain poorly understood. Hjörleifshöfði in southern Iceland presents an exceptional outcrop exposure of an emergent hyaloclastite sequence >1 km wide by >200 m high and enables an investigation of the distribution of the hyaloclastite deposits at seismic scale. Within this study we present a photogrammetry-based 3D model from part of this recent hyaloclastite delta and incorporate previous work by Watton et al. (Journal of Volcanology and Geothermal Research, 2013, 250, 19) to undertake detailed facies interpretation and quantification. Laboratory petrophysical analyses were performed on 34 core plugs cut from key field facies samples, including P- and S-wave velocity, density, porosity and permeability at both ambient and confining pressure. Integration of the 3D model with the petrophysical data has enabled the production of pseudo-wireline logs and property distribution maps which demonstrate the variability of physical properties within hyaloclastite sequences at outcrop to seismic scale. Through comparison of our data with examples of older buried hyaloclastite sequences we demonstrate that the wide-ranging properties of young hyaloclastites become highly uniform in older sequences making their identification by remote geophysical methods for similar facies variations more challenging. Our study provides an improved understanding of the petrophysical property distribution within hyaloclastite sequences and forms a valuable step towards improving the understanding of similar subsurface sequences and their implications for imaging and fluid flow.  相似文献   

4.
It is quantified the properties of seismic waves in fully saturated homogeneous porous media within the framework of Sahay's modified and reformulated poroelastic theory. The computational results comprise amplitude attenuation, velocity dispersion and seismic waveforms. They show that the behaviour of all four waves modelled as a function of offset, frequency, porosity, fluid viscosity and source bandwidth depicts realistic dissipation within the sonic–ultrasonic band. Therefore, it appears that there is no need to include material heterogeneity to model attenuation. By inference it is concluded that the fluid viscosity effects may be enhanced by dynamic porosity.  相似文献   

5.
Summary. A fluid-saturated packing of like elastic spheres is used as a model of an oceanic sediment and a method is presented for calculating the effective velocities of elastic waves in such a medium. In particular the method is applied to low-frequency waves travelling vertically down a cubic packing, saturated with an inviscid fluid and initially at rest under a uniform compressive force. It is found that two waves propagate and moreover, that their velocities are not related through the usual equations of classical elasticity to the effective elastic moduli for static deformation of the packing. For a dry packing, there is found to exist a 'cut-off' frequency above which the wave decays with depth. An extension of the method to slightly viscous fluids is also given.  相似文献   

6.
Wave propagation is studied in a general anisotropic poroelastic solid. The presence of dissipation due to fluid-viscosity as well as hydraulic anisotropy of pore permeability are also considered. Biot's theory is used to derive a system of modified Christoffel equations for the propagation of plane harmonic waves in porous media. A non-trivial solution of this system is ensured by a determinantal equation. This equation is separated into two different polynomial equations. One is the quartic equation whose roots represent the complex velocities of four attenuating waves in the medium. The other is a eighth-degree polynomial whose roots represent the vertical slowness values for the four waves propagating upward and downward in a finite porous medium. Procedure is explained to associate the numerically obtained roots with the waves propagating in the medium. The slowness surfaces of waves reflected at the boundary of the medium are computed for a realistic numerical model. The behaviours of phase velocity surfaces are analysed with the help of numerical examples.  相似文献   

7.
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8.
We show that seismic shear waves may be used to monitor the in situ stress state of deep inaccessible rocks in the crust. The most widespread manifestation of the stress-related behaviour of seismic waves is the shear-wave splitting (shear-wave birefringence) observed in almost all rocks, where the polarizations of the leading split shear waves are usually subparallel to the direction of the local maximum horizontal stress. It has been recognized that such shear-wave splitting is typically the result of propagation through distributions of stress-aligned fluid-filled microcracks and pores, known as extensive-dilatancy anisotropy or EDA. This paper provides a quantitative basis for the EDA hypothesis. We model the evolution of anisotropic distributions of microcracks in triaxial differential stress, where the driving mechanism is fluid migration along pressure gradients between neighbouring microcracks and pores at different orientations to the stress field. This leads to a non-linear anisotropic poroelasticity (APE) model for the stress-sensitive behaviour of fluid-saturated microcracked rocks. A companion paper shows that APE modelling matches a range of observed phenomena and is a good approximation to the equation of state of a stressed fluid-saturated rock mass.  相似文献   

9.
Effects of fractures on seismic-wave velocity and attenuation   总被引：1，自引：0，他引：1  
The effects of fractures on the seismic velocity and attenuation of a rock are investigated using theoretical results and experimental data. Fractures in a rock mass influence the traveltimes and amplitudes of seismic waves that have propagated through them. The displacement discontinuity model, recently employed in fracture investigations, is modified to describe the effect of fractures on seismic-wave velocity and attenuation. This new model, the modified displacement discontinuity model (MDD), is formulated in a way analogous to transmission-line analysis. The fractures are treated as transmission lines for the passage of seismic waves. The MDD takes into consideration realistic fracture parameters which include the fracture length, the fractional area of a fracture surface in contact, and the nature of the infilling material. A single fracture of varying geometric and material properties is shown to affect dramatically the transmission properties of a propagating waveform, and hence the seismic velocity and attenuation. These effects have been shown to result in a frequency-dependent velocity and attenuation. The sensitivity of the fracture parameters to seismic-wave velocity and attenuation was investigated and interesting results were obtained. Fracture parameters used in designing experimental models consisting of synthetically manufactured cracks were fed into the MDD and a well-known crack model, Hudson's model, for comparison. Velocities as a function of the incident-wave angle were obtained from both numerical models and were compared with the results from the experimental modelling. For P waves, the MDD model results show better agreement with those of the experimental model for all crack densities investigated than those from Hudson's model.  相似文献   

10.

Incised valleys form excellent stratigraphic pinch-out traps. Traditional seismic data analysis techniques fail to predict quantitatively the porous and low-velocity sand-fills for incised valleys. The 3D quantitative seismic inverted porosity–velocity (3DQSIPV) analysis was applied in the Indus Basin, SW Pakistan. The reflection strength attribute better portrayed the reservoir sandstone and faults compared to seismic amplitude attribute. The sweetness-based continuous wavelet transform authenticated the development of the stratigraphic play. The 17 Hz amplitude delineated the non-porous seal and porous reservoirs of sand-filled incised valley and strand plain, and faults. The integrated model of seismic attributes categorizes the reservoir and seal constituents. The petrophysical modeling corroborated the gas-bearing “sweet-spots” within the stratigraphic-based dynamical system. The facies modeling predicted the for coarse-grained sandstone and fine-grained shales, depositional environments, fluctuations of sea level and their impacts on the overall development of stratigraphic plays. The predicted density and P-wave velocity for the sandstone-filled incised valley of the lowstand system tract were?~?1.4–1.75 g/cc and?~?3217–3802 m/s, respectively. The predicted density and P-wave velocity for the sealing shales facies of strand plain of transgressive system tract were?~?1.9–2.1 g/cc and 2.55–2.7 g/cc and 3900–4700 m/s, respectively. The 3DQSIPV predicted?>?25% porosity and?~?3300 m/s velocity of reservoirs in the west. The eastern zones shows?<?12% porosity and high velocity of?~?4580 m/s. Cross-plots of porosity, velocity, and thickness showed correlation coefficients of R2?>?0.90 for inverted velocity. This workflow may serve as an analogue for the remaining oil and gas fields of the Indus Basins of Pakistan and similar geological settings of divergent plate margins.

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11.
Natural Resources Research - The joint modeling of the petrophysical properties (i.e., porosity, permeability) from wells in the presence of one or more seismic attributes (i.e., impedance) may be...  相似文献   

12.
Summary. Theoretical developments of Hudson demonstrate how to calculate the variations of velocity and attenuation of seismic waves propagating through solids containing aligned cracks. The analysis can handle a wide variety of crack configurations and crack geometries. Hudson associates the velocity variations with effective elastic constants. In this paper we associate the variation of attenuation with the imaginary parts of complex effective elastic constants. These complex elastic constants permit the simulation of wave propagation through two-phase materials by the calculation of wave propagation through homogeneous anisotropic solids.  相似文献   

13.
Summary. The response of a stratified elastic medium can be conveniently characterized by the Green's tensor for the medium. For coupled seismic wave propagation ( P—SV or fully anisotropic), the Green's tensor may be constructed directly from two matrices of linearly independent displacement solutions. Rather simple forms for the Green's tensor can be found if each displacement matrix satisfies one of the boundary conditions on the seismic field. This approach relates directly to 'reflection matrix' representations of the seismic field.
For a stratified elastic half space the Green's tensor is used to give a spectral representation for coupled seismic waves. By means of a contour integration a general completeness relation is obtained for the 'body wave' and 'surface wave' parts of the seismic field. This relation is appropriate for SH and P–SV waves in an isotropic medium and also for full anisotropy.  相似文献   

14.
《Basin Research》2018,30(5):895-925
Kilometre‐scale geobodies of diagenetic origin have been documented for the first time in a high‐resolution 3D seismic survey of the Upper Cretaceous chalks of the Danish Central Graben, North Sea Basin. Based on detailed geochemical, petrographic and petrophysical analyses, it is demonstrated that the geobodies are of an open‐system diagenetic origin caused by ascending basin fluids guided by faults and stratigraphic heterogeneities. Increased amounts of porosity‐occluding cementation, contact cement and/or high‐density/high‐velocity minerals caused an impedance contrast that can be mapped in seismic data, and represent a hitherto unrecognized, third type of heterogeneity in the chalk deposits in addition to the well‐known sedimentological and structural features. The distribution of the diagenetic geobodies is controlled by porosity/permeability contrasts of stratigraphic origin, such as hardgrounds associated with formation tops, and the feeder fault systems. One of these, the Top Campanian Unconformity at the top of the Gorm Formation, is particularly effective and created a basin‐wide barrier separating low‐porosity chalk below from high‐porosity chalk above (a Regional Porosity Marker, RPM). It is in particular in this upper high‐porosity unit (Tor and Ekofisk Formations) that the diagenetic geobodies occur, delineated by “Stratigraphy Cross‐cutting Reflectors” (SCRs) of which eight different types have been distinguished. The geobodies have been interpreted as the result of: (i) escaping pore fluids due to top seal failure, followed by local mechanical compaction of high‐porous chalks, paired with (ii) ascension of basinal diagenetic fluids along fault systems that locally triggered cementation of calcite and dolomite within the chalk, causing increased contact cements and/or reducing porosity. The migration pathway of the fluids is marked by the SCRs, which are the outlines of high‐density bodies of chalk nested in highly porous chalks. This study, thus, provides new insights into the 3D relationship between fault systems, fluid migration and diagenesis in chalks and has important applications for basin modelling and reservoir characterization.  相似文献   

15.
Numerical simulation of the propagation of P waves in fractured media   总被引：1，自引：0，他引：1  
We study the propagation of P waves through media containing open fractures by performing numerical simulations. The important parameter in such problems is the ratio between crack length and incident wavelength. When the wavelength of the incident wavefield is close to or shorter than the crack length, the scattered waves are efficiently excited and the attenuation of the primary waves can be observed on synthetic seismograms. On the other hand, when the incident wavelength is greater than the crack length, we can simulate the anisotropic behaviour of fractured media resulting from the scattering of seismic waves by the cracks through the time delay of the arrival of the transmitted wave. The method of calculation used is a boundary element method in which the Green's functions are computed by the discrete wavenumber method. For simplicity, the 2-D elastodynamic diffraction problem is considered. The rock matrix is supposed to be elastic, isotropic and homogeneous, while the cracks are all empty and have the same length and strike direction. An iterative method of calculation of the diffracted wavefield is developed in the case where a large number of cracks are present in order to reduce the computation time. The attenuation factor Q −1 of the direct waves passing through a fractured zone is measured in several frequency bands. We observe that the attenuation factor Q −1 of the direct P wave peaks around kd = 2, where k is the incident wavenumber and d the crack length, and decreases proportionally to ( kd ) −1 in the high-wavenumber range. In the long-wavelength domain, the velocity of the direct P wave measured for two different crack realizations is very close to the value predicted by Hudson's theory on the overall elastic properties of fractured materials.  相似文献   

16.
Summary. The paper gives the results of a study of the anisotropy of seismic wave velocities within the Ashkhabad test field in Central Asia. The anisotropy was studied by analysing variations in the values of apparent velocities of first arrivals for epicentral distances ranging from 30 to 130 km and by analysing the delays (Δ ts1-s2 ) between the arrival times of shear waves with different polarizations.
The velocities of P -waves vary with azimuth from 5.3 to 6.27 km s-1 and the velocities of S -waves vary from 3.15 to 3.5 km s-1.
The delay times Δ tS1 - S2 depend on the direction of the propagation. The character of the variation of the propagation velocity of the longitudinal wave, the presence of two differently polarized shear waves S 1 and S 2 propagating at different velocities, and the character of the distribution of Δ tS1 - S2 on the stereogram suggest that the symmetry of the anisotropic medium is close to hexagonal with a nearly horizontal symmetry axis coinciding with the direction of maximal velocity. The azimuth of the symmetry axis of the medium is 140° and coincides with the direction of geological faults.  相似文献   

17.
Summary. Using a single scattering approximation, we derive equations for the scattering attenuation coefficients of P- and S -body waves. We discuss our results in the light of some recent energy renormalization approaches to seismic wave scattering. Practical methods for calculating the scattering attenuation coefficients for various earth models are emphasized. The conversions of P - to S -waves and S- to P -waves are included in the theory. The earth models are assumed to be randomly inhomogeneous, with their properties known only through their average wavenumber power spectra. We approximate the power spectra with piecewise constant functions, each segment of which contributes to the net, frequency-dependent, scattering attenuation coefficient. The smallest and largest wavenumbers of a segment can be plotted along with the wavevectors of the incident and scattered waves on a wavenumber diagram. This diagram gives a geometric interpretation for the frequency behaviour associated with each spectral segment, including a 'transition' peak that is due entirely to the wavenumber limits of the segment. For regions of the earth where the inhomogeneity spectra are concentrated in a band of wavenumbers, it should be possible to observed such a peak in the apparent attenuation of seismic waves. We give both the frequency and distance limits on the accuracy of the theoretical results.  相似文献   

18.
Summary. A normal mode superposition approach is used to synthesize complete seismic codas for flat layered earth models and the P-SV phases. Only modes which have real eigenwavenumbers are used so that the search for eigenvalues in the complex wavenumber plane is confined to the real axis. In order to synthesize early P -wave arrivals by summing a number of'trapped'modes, an anomalously high velocity cap layer is added to the bottom of the structure so that most of the seismic energy is contained in the upper layers as high-order surface waves. Causality arguments are used to define time windows for which the resulting synthetic seismograms are close approximations to the exact solutions without the cap layer. The traditional Thomson—Haskell matrix approach to computing the normal modes is reformulated so that numerical problems encountered at high frequencies are avoided and numerical results of the locked mode approximation are given.  相似文献   

19.
Summary. Numerical modelling is one of the most efficient methods for an investigation of the relationship between structural features and peculiarities of observed wavefields. It is practically the only method for 2-D and 3-D inhomogeneous media.
An algorithm based on ray theory has been developed for calculations of travel times and amplitudes of seismic waves in 3-D inhomogeneous media with curved interfaces. It was applied for numerical modelling of kinematic and dynamic characteristics of seismic waves propagating in laterally inhomogeneous media.
Travel-time and amplitude patterns were studied in the 2-D and 3-D models of a geosyncline, in which velocity distribution was given by an analytical function of the coordinates. For a more complicated model representing a subducting high-velocity lithospheric plate in a transition zone between oceanic and continental upper mantle, the velocity distribution was given by discrete values on a 2-D non-rectangular grid. It was shown that when a source was placed above the lithospheric plate, a shadow zone appeared along a strike of the structure, i.e. in the direction which is perpendicular to a strong lateral velocity gradient. Travel-time residuals were calculated along the seismological profile for a 3-D velocity distribution in the upper mantle beneath Central Asia, obtained as a result of inversion of travel times by the Backus-Gilbert method. They were found to be in a good agreement with the observed data.  相似文献   

20.
Summary. Asymptotic ray theory is applied to surface waves in a medium where the lateral variations of structure are very smooth. Using ray-centred coordinates, parabolic equations are obtained for lateral variations while vertical structural variations at a given point are specified by eigenfunctions of normal mode theory as for the laterally homogeneous case. Final results on wavefields close to a ray can be expressed by formulations similar to those for elastic body waves in 2-D laterally heterogeneous media, except that the vertical dependence is described by eigenfunctions of 'local' Love or Rayleigh waves. The transport equation is written in terms of geometrical-ray spreading, group velocity and an energy integral. For the horizontal components there are both principal and additional components to describe the curvature of rays along the surface, as in the case of elastic body waves. The vertical component is decoupled from the horizontal components. With complex parameters the solutions for the dynamic ray tracing system correspond to Gaussian beams: the amplitude distribution is bell-shaped along the direction perpendicular to the ray and the solution is regular everywhere, even at caustics. Most of the characteristics of Gaussian beams for 2-D elastic body waves are also applicable to the surface wave case. At each frequency the solution may be regarded as a set of eigenfunctions propagating over a 2-D surface according to the phase velocity mapping.  相似文献   

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