A seismic reflection from isotropic‐fractured fluid‐saturated layer

Average elastic properties of a fluid‐saturated fractured rock are discussed in association with the extremely slow and dispersive Krauklis wave propagation within individual fractures. The presence of the Krauklis wave increases P‐wave velocity dispersion and attenuation with decreasing frequency. Different laws (exponential, power, fractal, and gamma laws) of distribution of the fracture length within the rock show more velocity dispersion and attenuation of the P‐wave for greater fracture density, particularly at low seismic frequencies. The results exhibit a remarkable difference in the P‐wave reflection coefficient for frequency and angular dependency from the fractured layer in comparison with the homogeneous layer. The biggest variation in behaviour of the reflection coefficient versus incident angle is observed at low seismic frequencies. The proposed approach and results of calculations allow an interpretation of abnormal velocity dispersion, high attenuation, and special behaviour of reflection coefficients versus frequency and angle of incidence as the indicators of fractures.     

Attenuation tomography: An application to gas-hydrate and free-gas detection

We estimate the quality factor (Q) from seismic reflections by using a tomographic inversion algorithm based on the frequency‐shift method. The algorithm is verified with a synthetic case and is applied to offshore data, acquired at western Svalbard, to detect the presence of bottom‐simulating reflectors (BSR) and gas hydrates. An array of 20 ocean‐bottom seismographs has been used. The combined use of traveltime and attenuation tomography provides a 3D velocity–Q cube, which can be used to map the spatial distribution of the gas‐hydrate concentration and free‐gas saturation. In general, high P‐wave velocity and quality factor indicate the presence of solid hydrates and low P‐wave velocity and quality factor correspond to free‐gas bearing sediments. The Q‐values vary between 200 and 25, with higher values (150–200) above the BSR and lower values below the BSR (25–40). These results seem to confirm that hydrates cement the grains, and attenuation decreases with increasing hydrate concentration.     

Frequency‐dependent anisotropy of porous rocks with aligned fractures

Naturally fractured reservoirs are becoming increasingly important for oil and gas exploration in many areas of the world. Because fractures may control the permeability of a reservoir, it is important to be able to find and characterize fractured zones. In fractured reservoirs, the wave‐induced fluid flow between pores and fractures can cause significant dispersion and attenuation of seismic waves. For waves propagating normal to the fractures, this effect has been quantified in earlier studies. Here we extend normal incidence results to oblique incidence using known expressions for the stiffness tensors in the low‐ and high‐frequency limits. This allows us to quantify frequency‐dependent anisotropy due to the wave‐induced flow between pores and fractures and gives a simple recipe for computing phase velocities and attenuation factors of quasi‐P and SV waves as functions of frequency and angle. These frequency and angle dependencies are concisely expressed through dimensionless velocity anisotropy and attenuation anisotropy parameters. It is found that, although at low frequencies, the medium is close to elliptical (which is to be expected as a dry medium containing a distribution of penny‐shaped cracks is known to be close to elliptical); at high frequencies, the coupling between P‐wave and SV‐wave results in anisotropy due to the non‐vanishing excess tangential compliance.     

基于地震剖面瞬时峰值能量频率的衰减分析与气藏预测方法

由于流体本身的粘滞性和摩擦性,使得地震波在含油气地层中传播时衰减形成低频阴影.通过对叠后地震资料做时频分解,分析地层衰减特征,是当前除了AVO技术之外,比较流行的直接识别流体和气藏的技术.本文基于波动方程正演,模拟了地震波对含油气地层的响应.然后采用连续小波变换分析不同尺度剖面的瞬时能量特征,提取分频剖面上每一个点的峰值能量对应的频率,得到瞬时峰值能量频率剖面.通过分析瞬时峰值能量频率剖面,分析了地震波在地下介质中传播时的衰减特征.最后应用此方法对实际地震剖面进行了分析,验证了其有效性.     

Extension of White's layered model to the full frequency range

The low‐frequency theory of the White model to predict the dispersion and intrinsic attenuation in a single porous skeleton saturated with periodic layers of two immiscible fluids is extended to the full frequency range using the Biot theory. The extension is similar to the Dutta–Odé model for spherical inhomogeneities. Below the layer resonance frequency, the acoustic bulk properties for several gas–water fractions are in good agreement with the original White model. Deviations start to occur at higher frequencies due to the growing importance of resonance phenomena that were neglected in the original White model. The full model predicts significantly higher damping at sonic frequencies than the original White model. We also show that attenuation is significantly dependent on porosity variations. With realistic rock and fluid properties, a maximum attenuation of about 0.3 is found at seismic frequencies.     

Modulus defect,velocity dispersion and attenuation in partially-saturated reservoirs of Jurassic sandstone,Indus Basin,Pakistan

Partially saturated reservoirs are one of the major sources of seismic wave attenuation, modulus defect and velocity dispersion in real seismic data. The main attenuation and dispersion phenomenon is wave induced fluid flow due to the heterogeneity in pore fluids or porous rock. The identification of pore fluid type, saturation and distribution pattern within the pore space is of great significance as several seismic and petrophysical properties of porous rocks are largely affected by fluid type, saturation and fluid distribution pattern. Based on Gassmann-Wood and Gassmann- Hill rock physics models modulus defect, velocity dispersion and attenuation in Jurassic siliclastic partially-saturated rocks are studied. For this purpose two saturation patterns - uniform and patchy - are considered within the pore spaces in two frequency regimes i.e., lower frequency and higher frequency. The results reveal that at low enough frequency where saturation of liquid and gas is uniform, the seismic velocity and bulk modulus are lower than at higher frequency where saturation of fluid mixture is in the form of patches. The velocity dispersion and attenuation is also modeled at different levels of gas saturation. It is found that the maximum attenuation and velocity dispersion is at low gas saturation. Therefore, the dispersion and attenuation can provide a potential way to predict gas saturation and can be used as a property to differentiate low from high gas saturation.     

地震低频伴影的数值模拟与应用

Strong low-frequency energy beneath a hydrocarbon reservoir is called a seismic low-frequency shadow and can be used as a hydrocarbon indicator （Tarter et al., 1979） bu the physical mechanism of the observed low-frequency shadow is still unclear. To stud） the mechanism, we performed seismic numerical simulation of geological models with a hydrocarbon-bearing zone using the 2-D diffusive-viscous wave equation which car effectively model the characteristics of velocity dispersion and transform the seismic dat~ centered in a target layer slice within a time window to the time-frequency domain by usinl time-frequency signal analysis and sort the frequency gathers to common frequency cubes. Then, we observe the characteristics of the seismic low-frequency shadow in the common frequency cubes. The numerical simulations reveal that the main mechanism of seismic lowfrequency shadows is attributed to high attenuation of the medium to high seismic frequency components caused by absorption in the hydrocarbon-filled reservoir. Results from a practical example of seismic low-frequency shadows show that it is possible to identify the reservoir by the low-frequency shadow with high S/N seismic data.     

Interaction of multiple courses of wave‐induced fluid flow in layered porous media

Different theoretical and laboratory studies on the propagation of elastic waves in layered hydrocarbon reservoir have shown characteristic velocity dispersion and attenuation of seismic waves. The wave‐induced fluid flow between mesoscopic‐scale heterogeneities (larger than the pore size but smaller than the predominant wavelengths) is the most important cause of attenuation for frequencies below 1 kHz. Most studies on mesoscopic wave‐induced fluid flow in the seismic frequency band are based on the representative elementary volume, which does not consider interaction of fluid flow due to the symmetrical structure of representative elementary volume. However, in strongly heterogeneous media with unsymmetrical structures, different courses of wave‐induced fluid flow may lead to the interaction of the fluid flux in the seismic band; this has not yet been explored. This paper analyses the interaction of different courses of wave‐induced fluid flow in layered porous media. We apply a one‐dimensional finite‐element numerical creep test based on Biot's theory of consolidation to obtain the fluid flux in the frequency domain. The characteristic frequency of the fluid flux and the strain rate tensor are introduced to characterise the interaction of different courses of fluid flux. We also compare the behaviours of characteristic frequencies and the strain rate tensor on two scales: the local scale and the global scale. It is shown that, at the local scale, the interaction between different courses of fluid flux is a dynamic process, and the weak fluid flux and corresponding characteristic frequencies contain detailed information about the interaction of the fluid flux. At the global scale, the averaged strain rate tensor can facilitate the identification of the interaction degree of the fluid flux for the porous medium with a random distribution of mesoscopic heterogeneities, and the characteristic frequency of the fluid flux is potentially related to that of the peak attenuation. The results are helpful for the prediction of the distribution of oil–gas patches based on the statistical properties of phase velocities and attenuation in layered porous media with random disorder.     

Acoustic properties of sediments saturated with gas hydrate, free gas and water

We obtain the wave velocities and quality factors of gas‐hydrate‐bearing sediments as a function of pore pressure, temperature, frequency and partial saturation. The model is based on a Biot‐type three‐phase theory that considers the existence of two solids (grains and gas hydrate) and a fluid mixture. Attenuation is described with the constant‐Q model and viscodynamic functions to model the high‐frequency behaviour. We apply a uniform gas/water mixing law that satisfies Wood's and Voigt's averages at low and high frequencies, respectively. The acoustic model is calibrated to agree with the patchy‐saturation theory at high frequencies (White's model). Pressure effects are accounted by using an effective stress law for the dry‐rock moduli and permeabilities. The dry‐rock moduli of the sediment are calibrated with data from the Cascadia margin. Moreover, we calculate the depth of the bottom simulating reflector (BSR) below the sea floor as a function of sea‐floor depth, geothermal gradient below the sea floor, and temperature at the sea floor.     

Wave velocities and attenuation of shaley sandstones as a function of pore pressure and partial saturation

We obtain the wave velocities and quality factors of clay‐bearing sandstones as a function of pore pressure, frequency and partial saturation. The model is based on a Biot‐type three‐phase theory that considers the coexistence of two solids (sand grains and clay particles) and a fluid mixture. Additional attenuation is described with the constant‐Q model and viscodynamic functions to model the high‐frequency behaviour. We apply a uniform gas/fluid mixing law that satisfies the Wood and Voigt averages at low and high frequencies, respectively. Pressure effects are accounted for by using an effective stress law. By fitting a permeability model of the Kozeny– Carman type to core data, the model is able to predict wave velocity and attenuation from seismic to ultrasonic frequencies, including the effects of partial saturation. Testing of the model with laboratory data shows good agreement between predictions and measurements.     

Laboratory measurements of seismic attenuation and Young's modulus dispersion in a partially and fully water‐saturated porous sample made of sintered borosilicate glass

We measured the extensional‐mode attenuation and Young's modulus in a porous sample made of sintered borosilicate glass at microseismic to seismic frequencies (0.05–50 Hz) using the forced oscillation method. Partial saturation was achieved by water imbibition, varying the water saturation from an initial dry state up to ～99%, and by gas exsolution from an initially fully water‐saturated state down to ～99%. During forced oscillations of the sample effective stresses up to 10 MPa were applied. We observe frequency‐dependent attenuation, with a peak at 1–5 Hz, for ～99% water saturation achieved both by imbibition and by gas exsolution. The magnitude of this attenuation peak is consistently reduced with increasing fluid pressure and is largely insensitive to changes in effective stress. Similar observations have recently been attributed to wave‐induced gas exsolution–dissolution. At full water saturation, the left‐hand side of an attenuation curve, with a peak beyond the highest measured frequency, is observed at 3 MPa effective stress, while at 10 MPa effective stress the measured attenuation is negligible. This observation is consistent with wave‐induced fluid flow associated with mesoscopic compressibility contrasts in the sample's frame. These variations in compressibility could be due to fractures and/or compaction bands that formed between separate sets of forced‐oscillation experiments in response to the applied stresses. The agreement of the measured frequency‐dependent attenuation and Young's modulus with the Kramers–Kronig relations and additional data analyses indicate the good quality of the measurements. Our observations point to the complex interplay between structural and fluid heterogeneities on the measured seismic attenuation and they illustrate how these heterogeneities can facilitate the dominance of one attenuation mechanism over another.     

AVO study of a gas-hydrate deposit, offshore Costa Rica

Amplitude variation with offset (AVO) analysis and waveform inversion are techniques used to determine qualitative or quantitative information on gas hydrates and free gas in sediments. However, the quantitative contribution of gas hydrates to the acoustic impedance contrast observed at the bottom‐simulating reflector and the reliability of quantitative AVO analyses are still topics of discussion. In this study, common‐midpoint gathers from multichannel wide‐angle reflection seismic data, acquired offshore Costa Rica, have been processed to preserve true amplitude information at the bottom‐simulating reflector for a quantitative AVO analysis incorporating angles of incidence of up to 60°. Corrections were applied for effects that significantly alter the observed amplitudes, such as the source directivity. AVO and rock‐physics modelling indicate that free gas immediately beneath the gas‐hydrate stability zone can be detected and low concentrations can be quantified from AVO analysis, whereas the offset‐dependent reflectivity is not sensitive to gas‐hydrate concentrations of less than about 10% at the base of the gas‐hydrate stability zone. Bulk free‐gas saturations up to 5% have been determined from the reflection seismic data assuming a homogeneous distribution of free gas in the sediment. Assuming a patchy distribution of free gas increases the estimated concentrations up to 14%. There is a patchy occurrence of bottom‐simulating reflectors south‐east of the Nicoya Peninsula on the continental margin, offshore Costa Rica. AVO analysis indicates that this phenomenon is related to the local presence of free gas beneath the gas‐hydrate stability zone, probably related to a focused vertical fluid flow. In areas without bottom‐simulating reflectors, the results indicate that no free gas is present.     

Ground-roll attenuation using a 2D time-derivative filter

We present a new filtering method for the attenuation of ground-roll. The method is based on the application of a bi-dimensional filter for obtaining the time-derivative of the seismograms. Before convolving the filter with the input data matrix, the normal moveout correction is applied to the seismograms with the purpose of flattening the reflections. The method can locally attenuate the amplitude of data of low frequency (in the ground-roll and stretch normal moveout region) and enhance flat events (reflections). The filtered seismograms can reveal horizontal or sub-horizontal reflections while vertical or sub-vertical events, associated with ground-roll, are attenuated. A regular set of samples around each neighbourhood data sample of the seismogram is used to estimate the time-derivative. A numerical approximation of the derivative is computed by taking the difference between the interpolated values calculated in both the positive and the negative neighbourhood of the desired position. The coefficients of the 2D time-derivative filter are obtained by taking the difference between two filters that interpolate at positive and negative times. Numerical results that use real seismic data show that the proposed method is effective and can reveal reflections masked by the ground-roll. Another benefit of the method is that the stretch mute, normally applied after the normal moveout correction, is unnecessary. The new filtering approach provides results of outstanding quality when compared to results obtained from the conventional FK filtering method.     

Analysis of the traveltime sensitivity kernels for an acoustic transversely isotropic medium with a vertical axis of symmetry

In anisotropic media, several parameters govern the propagation of the compressional waves. To correctly invert surface recorded seismic data in anisotropic media, a multi‐parameter inversion is required. However, a tradeoff between parameters exists because several models can explain the same dataset. To understand these tradeoffs, diffraction/reflection and transmission‐type sensitivity‐kernels analyses are carried out. Such analyses can help us to choose the appropriate parameterization for inversion. In tomography, the sensitivity kernels represent the effect of a parameter along the wave path between a source and a receiver. At a given illumination angle, similarities between sensitivity kernels highlight the tradeoff between the parameters. To discuss the parameterization choice in the context of finite‐frequency tomography, we compute the sensitivity kernels of the instantaneous traveltimes derived from the seismic data traces. We consider the transmission case with no encounter of an interface between a source and a receiver; with surface seismic data, this corresponds to a diving wave path. We also consider the diffraction/reflection case when the wave path is formed by two parts: one from the source to a sub‐surface point and the other from the sub‐surface point to the receiver. We illustrate the different parameter sensitivities for an acoustic transversely isotropic medium with a vertical axis of symmetry. The sensitivity kernels depend on the parameterization choice. By comparing different parameterizations, we explain why the parameterization with the normal moveout velocity, the anellipitic parameter η, and the δ parameter is attractive when we invert diving and reflected events recorded in an active surface seismic experiment.     

Caustics in a periodically layered transversely isotropic medium with vertical symmetry axis

Wave propagation in a finely layered medium is a very important topic in seismic modelling and inversion. Here we analyse non‐vertical wave propagation in a periodically layered transversely isotropic (VTI) medium and show that the evanescent (attenuation) zones in the frequency‐horizontal slowness domain result in caustics in the group velocity domain. These caustics, which may appear for both the quasi‐compressional (qP) and quasi‐shear (qSV) wave surfaces are frequency dependent but display weak dependence at low frequencies. The caustics computed for a specific frequency differ from those observed at the low‐ and high‐frequency limits. We illustrate these caustics with a few numerical examples and snapshots computed for both qP‐ and qSV‐wave types.     

Seismic attenuation and velocity dispersion in fractured rocks: The role played by fracture contact areas

The presence of fractures in fluid‐saturated porous rocks is usually associated with strong seismic P‐wave attenuation and velocity dispersion. This energy dissipation can be caused by oscillatory wave‐induced fluid pressure diffusion between the fractures and the host rock, an intrinsic attenuation mechanism generally referred to as wave‐induced fluid flow. Geological observations suggest that fracture surfaces are highly irregular at the millimetre and sub‐millimetre scale, which finds its expression in geometrical and mechanical complexities of the contact area between the fracture faces. It is well known that contact areas strongly affect the overall mechanical fracture properties. However, existing models for seismic attenuation and velocity dispersion in fractured rocks neglect this complexity. In this work, we explore the effects of fracture contact areas on seismic P‐wave attenuation and velocity dispersion using oscillatory relaxation simulations based on quasi‐static poroelastic equations. We verify that the geometrical and mechanical details of fracture contact areas have a strong impact on seismic signatures. In addition, our numerical approach allows us to quantify the vertical solid displacement jump across fractures, the key quantity in the linear slip theory. We find that the displacement jump is strongly affected by the geometrical details of the fracture contact area and, due to the oscillatory fluid pressure diffusion process, is complex‐valued and frequency‐dependent. By using laboratory measurements of stress‐induced changes in the fracture contact area, we relate seismic attenuation and dispersion to the effective stress. The corresponding results do indeed indicate that seismic attenuation and phase velocity may constitute useful attributes to constrain the effective stress. Alternatively, knowledge of the effective stress may help to identify the regions in which wave induced fluid flow is expected to be the dominant attenuation mechanism.     

地震复谱分解技术及其在烃类检测中的应用

谱分解技术在地震解释领域已得到广泛应用,但常用的谱分解方法存在两方面的不足.一是时间分辨率低,难以对薄层进行刻画;二是在烃类检测中多解性强,难以区分流体类型.为了改善该问题,本文提出一种基于地震复谱分解技术的烃类检测方法.复谱分解是指用一个包含多个不同频率Ricker子波的复子波库对地震道进行分解,从而得到时变子波频率和相位信息的过程.借助稀疏反演技术复谱分解可以获得高分辨率的时频能量谱和时频相位谱.本文首先通过拟合算例验证了复谱分解方法刻画薄层的能力以及求取子波频率和相位的准确性.然后利用基于Kelvin-Voigt模型的黏弹波动方程数值模拟对衰减引起子波相位改变的原因进行了分析.最后通过实际资料应用展示了本文方法在储层预测中的高时间分辨率优势,验证了利用子波相位信息识别气藏的有效性.     

Research note: Seismic attenuation due to wave‐induced fluid flow at microscopic and mesoscopic scales

Wave‐induced fluid flow at microscopic and mesoscopic scales arguably constitutes the major cause of intrinsic seismic attenuation throughout the exploration seismic and sonic frequency ranges. The quantitative analysis of these phenomena is, however, complicated by the fact that the governing physical processes may be dependent. The reason for this is that the presence of microscopic heterogeneities, such as micro‐cracks or broken grain contacts, causes the stiffness of the so‐called modified dry frame to be complex‐valued and frequency‐dependent, which in turn may affect the viscoelastic behaviour in response to fluid flow at mesoscopic scales. In this work, we propose a simple but effective procedure to estimate the seismic attenuation and velocity dispersion behaviour associated with wave‐induced fluid flow due to both microscopic and mesoscopic heterogeneities and discuss the results obtained for a range of pertinent scenarios.     

Foldback reflectors near methane hydrate bottom‐simulating reflectors: Indicators of gas distribution from 3D seismic images in the eastern Nankai Trough

Understanding of fluid behavior and gas distribution in the shallow subsurface are important considerations in gas hydrate formation and the global carbon cycle. Estimation of gas distribution based on reflection seismic surveys, however, is difficult because the boundary of a gas‐bearing zone is indistinct and not systematically defined. This study reports distinctive features related to gas‐hydrate distribution and possible fluid migration in high‐resolution 3D seismic‐reflection data from sediments of the eastern Nankai Trough. These features, here termed foldback reflectors (FBRs), descend in accordion shaped reflectors near the edges of bottom‐simulating reflectors (BSRs). FBRs generally correspond to lateral boundaries between two seismic facies, a ‘dimmed’ facies with relatively low amplitude and subdued high‐frequency components beneath the BSR and the contrasting facies around the BSR. The dimmed facies corresponds to areas of anomalously low velocity consistent with a small amount of free gas. FBR is mostly developed in well‐stratified formations in uplifted regions. Dip directions of the FBR appear to be restricted by orientation of the host formations. Edges of the FBR often correspond to high‐amplitude layers. Such occurrences of FBR suggest that regional uplift and layer‐parallel fluid migration are related to the formation of FBR as well as BSR.     

基于常规测井数据的纵波本征衰减估计

地震波本征衰减反映了地层及其所含流体的一些特性,对油气勘探开发有重要意义.已有的理论研究与实验发现,地震频带内的衰减主要与中观尺度(波长与颗粒尺度之间)的斑状部分饱和、完全饱和岩石弹性非均匀性情况下波诱导的局部流体流有关.这种衰减与岩石骨架、孔隙度及充填流体的性质密切相关.本文着重讨论均匀流体分布、斑状或非均匀流体分布两种情况下部分饱和岩石的纵波模量差异.以经典岩石物理理论和衰减机制认识为基础,通过分析低频松弛状态、高频非松弛状态岩石的弹性模量,讨论储层参数(如孔隙度、泥质含量以及含水饱和度等)与纵波衰减之间的确定性关系.上述方法与模型在陆相砂泥岩地层与海相碳酸盐岩地层中的适用性通过常规测井资料得到了初步验证.