Velocity–depth and time–depth relationships for a decompacted uplifted unit

A linear instantaneous velocity model is used to describe the velocity variations in an uplifted unit that has been partly decompacted as a result of the reduction in overburden that often accompanies uplift. The model results in a series of equations for deriving values for the function parameters in the velocity–depth and the time– depth domains and for carrying out time‐to‐depth conversions. The formulation uses the base of the unit as a reference level to generate the reference datum from a combination of the depth of the base of the unit and a parameter that represents the decompaction factor.     

Rock physics modelling based on depositional and burial history of Barents Sea sandstones

Understanding how physical properties and seismic signatures of present day rocks are related to ancient geological processes is important for enhanced reservoir characterization. In this paper, we have studied this relationship for the Kobbe Formation sandstone in the Barents Sea. These rocks show anomalous low shear velocities and high V_P/V_S ratios, which does not agree well with conventional rock physics models for moderately to well consolidated sandstones. These sandstones have been buried relatively deeply and subsequently uplifted 1–2 km. We compared well log data of the Kobbe sandstone with velocity–depth trends modelled by integrating basin modelling principles and rock physics. We found that more accurate velocity predictions were obtained when first honouring mechanical and chemical compaction during burial, followed by generation of micro-cracks during uplift. We suspect that these micro-cracks are formed as overburden is eroded, leading to changes in the subsurface stress-field. Moreover, the Kobbe Formation is typically heterogeneous and characterized by structural clays and mica that can reduce the rigidity of grain contacts. By accounting for depositional and burial history, our velocity predictions become more consistent with geophysical observables. Our approach yields more robust velocity predictions, which are important in prospect risking and net erosion estimates.     

Mathematical simulation of geotemperature and heat flow patterns

Geotemperature and heat flow patterns in a large-scale Meso-Cenozoic basin such as the North China Basin are strongly affected by the relief of the basement, and controlled by the contrast of thermal conductivity between basement rock and sedimentary cover. Usually, heat flow observed at the surface of a basement uplift is greater than that of a basement depression. Calculation revealed, that the ratio of the former and the latter is determined by the uplifted height (H) of the bed-rock roof of the basement and the thickness (h) of the sedimentary cover. The relief of the basement also disturbs the geotemperature and, hence, the heat flow patterns at shallow depth. Consequently, the more or less “uniform” one dimensional heat flow from the deep interior of the Earth becomes two dimensional at shallow depth with great lateral and vertical variations. The extent of the disturbed zone is also controlled by the contrast of the thermal conductivity between basement rock and sedimentary cover as well as the uplifted heigh (H) of the bed-rock roof of the basement. Numerical computation demonstrated that the disturbed depth (Ze) is usually about 3–6 times of the uplifted height (H) of a basement uplift.     

Formation,uplift and dissection of planation surfaces at passive continental margins – a new approach

The usefulness of large‐scale, low‐relief, high‐level landscapes as markers of uplift events has become a subject of disagreement among geomorphologists. We argue that the formation of low‐relief surfaces over areas of large extent and cutting across bedrock of different age and resistance must have been guided by distinct base levels. In the absence of other options the most likely base level is sea level. We have analysed West Greenland landscapes in a recent study by combining the cooling history from apatite fission‐track analysis (AFTA) data with the denudation history from landscape analysis and the stratigraphic record. An important difference between our approach and that of classical geomorphology is that we now have the ability to document when thick sections of rocks have been deposited and then removed. The present‐day high‐level plateau in West Greenland is the remnant of a planation surface that was formed by denudation that lasted c. 20 million years during which up to 1 km of cover was removed after maximum burial at the Eocene–Oligocene transition. Here we present additional AFTA data to show that the planation surface is the end‐product of Cenozoic denudation even in basement areas and argue that Phanerozoic sediments – most likely of Cretaceous–Palaeogene age – must have been present prior to denudation. The planation surface was offset by reactivated faults and uplifted to present‐day altitudes of up to 2 km. The uplift occurred in two late Neogene phases that caused incision of valleys below the planation surface and their subsequent uplift. We therefore find that the elevated and deeply dissected plateau is evidence of episodic post‐rift uplift that took place millions of years after cessation of sea‐floor spreading west of Greenland. We suggest that other margins with similar morphology may also be characterized by episodic post‐rift uplift unrelated to the processes of rifting and continental separation, rather than being permanently uplifted since the time of rifting, as is commonly assumed. Copyright © 2009 John Wiley & Sons, Ltd.     

P‐wave stacking‐velocity tomography for VTI media

A major complication caused by anisotropy in velocity analysis and imaging is the uncertainty in estimating the vertical velocity and depth scale of the model from surface data. For laterally homogeneous VTI (transversely isotropic with a vertical symmetry axis) media above the target reflector, P‐wave moveout has to be combined with other information (e.g. borehole data or converted waves) to build velocity models for depth imaging. The presence of lateral heterogeneity in the overburden creates the dependence of P‐wave reflection data on all three relevant parameters (the vertical velocity V_P0 and the Thomsen coefficients ε and δ) and, therefore, may help to determine the depth scale of the velocity field. Here, we propose a tomographic algorithm designed to invert NMO ellipses (obtained from azimuthally varying stacking velocities) and zero‐offset traveltimes of P‐waves for the parameters of homogeneous VTI layers separated by either plane dipping or curved interfaces. For plane non‐intersecting layer boundaries, the interval parameters cannot be recovered from P‐wave moveout in a unique way. Nonetheless, if the reflectors have sufficiently different azimuths, a priori knowledge of any single interval parameter makes it possible to reconstruct the whole model in depth. For example, the parameter estimation becomes unique if the subsurface layer is known to be isotropic. In the case of 2D inversion on the dip line of co‐orientated reflectors, it is necessary to specify one parameter (e.g. the vertical velocity) per layer. Despite the higher complexity of models with curved interfaces, the increased angle coverage of reflected rays helps to resolve the trade‐offs between the medium parameters. Singular value decomposition (SVD) shows that in the presence of sufficient interface curvature all parameters needed for anisotropic depth processing can be obtained solely from conventional‐spread P‐wave moveout. By performing tests on noise‐contaminated data we demonstrate that the tomographic inversion procedure reconstructs both the interfaces and the VTI parameters with high accuracy. Both SVD analysis and moveout inversion are implemented using an efficient modelling technique based on the theory of NMO‐velocity surfaces generalized for wave propagation through curved interfaces.     

Denudation history of the Kiso Range,central Japan,and its tectonic implications: Constraints from low‐temperature thermochronology

Fission‐track (FT) and (U–Th–Sm)/He (He) analyses are used to constrain the denudation pattern and history of the Kiso Range, a Japanese fault‐block mountain range which has been uplifted since ca 0.8 Ma. We obtained nine zircon FT ages ranging 59.3–42.1 Ma, 18 apatite FT ages ranging 81.9–2.3 Ma, and 13 apatite He ages ranging 36.7–2.2 Ma. The apatite FT and He ages are divided into an older group comparable to the zircon FT age range and a younger group of <18 Ma. The younger ages are interpreted as a reflection of uplift of the Kiso Range because they were obtained only to the east of the Seinaiji‐touge Fault, and the event age estimated from apatite FT data is consistent with the timing of the onset of the Kiso Range uplift. On the basis of the distribution of the younger ages, we propose westward tilting uplift of the Kiso Range between the boundary fault of the Inadani Fault Zone and Seinaiji‐touge Fault, which implies a model of bedrock uplift that is intermediate between two existing models: a pop‐up model in which the Kiso Range is squeezed upward between the two faults and a tilted uplift model which assumes that the Kiso Range is uplifted and tilted to the west by the Inadani Fault Zone. The original land surface before the onset of uplift/denudation of the Kiso Range is estimated to have been uplifted to an elevation of 2700–4900 m. We estimated denudation rates at 1.3–4.0 mm/y and maximum bedrock uplift rates at 3.4–6.1 mm/y since ca 0.8 Ma. The Seinaiji‐touge fault is interpreted as a back thrust of the west‐dipping Inadani Fault Zone. The older group of apatite FT and He ages is interpreted to reflect long‐term peneplanation with a probable denudation rate of <0.1 mm/y.     

Migration velocity analysis for tilted transversely isotropic media

Tilted transversely isotropic formations cause serious imaging distortions in active tectonic areas (e.g., fold‐and‐thrust belts) and in subsalt exploration. Here, we introduce a methodology for P‐wave prestack depth imaging in tilted transversely isotropic media that properly accounts for the tilt of the symmetry axis as well as for spatial velocity variations. For purposes of migration velocity analysis, the model is divided into blocks with constant values of the anisotropy parameters ε and δ and linearly varying symmetry‐direction velocity V_P0 controlled by the vertical (k_z) and lateral (k_x) gradients. Since determination of tilt from P‐wave data is generally unstable, the symmetry axis is kept orthogonal to the reflectors in all trial velocity models. It is also assumed that the velocity V_P0 is either known at the top of each block or remains continuous in the vertical direction. The velocity analysis algorithm estimates the velocity gradients k_z and k_x and the anisotropy parameters ε and δ in the layer‐stripping mode using a generalized version of the method introduced by Sarkar and Tsvankin for factorized transverse isotropy with a vertical symmetry axis. Synthetic tests for several models typical in exploration (a syncline, uptilted shale layers near a salt dome and a bending shale layer) confirm that if the symmetry‐axis direction is fixed and V_P0 is known, the parameters k_z, k_x, ε and δ can be resolved from reflection data. It should be emphasized that estimation of ε in tilted transversely isotropic media requires using nonhyperbolic moveout for long offsets reaching at least twice the reflector depth. We also demonstrate that application of processing algorithms designed for a vertical symmetry axis to data from tilted transversely isotropic media may lead to significant misfocusing of reflectors and errors in parameter estimation, even when the tilt is moderate (30°). The ability of our velocity analysis algorithm to separate the anisotropy parameters from the velocity gradients can be also used in lithology discrimination and geologic interpretation of seismic data in complex areas.     

A note on tsunami caused by submarine slides and slumps spreading in one dimension with nonuniform displacement amplitudes

Tsunami created by spreading submarine slides and slumps with spatially variable final uplift are investigated in the near-field using a kinematic model. It is shown that for velocities of spreading comparable to and smaller than the long period tsunami velocity (g is the acceleration due to gravity and h is the ocean depth), the models with spatially uniform final uplift of the accumulation and depletion zones provide good approximation for the tsunami amplitudes in the near-field. For spreading velocities 2–5 times greater than c_T, and for applications that use wavelengths of the order of the source dimensions, the spatial variability of the final uplift has to be considered in estimation of the high-frequency tsunami amplitudes in the near-field.     

基于典型地质特征分析的大同盆地VS30预测研究

土体剪切波速是进行土层地震反应分析的动力学参数，对场地地震动参数确定具有重要意义。基于地质地貌分析，将大同盆地划分为5类典型地质单元。对盆地1429个钻孔剪切波速资料进行分析，探讨V_S30与V_S20的相关性，研究土体埋深、岩性、地质单元、标贯击数及密实度等地质特征对V_S的影响，并基于地质单元、剪切波速比、密实度系数及第四系上部覆盖层厚度相关性分析给出土体V_S30预测模型。研究结果表明，基于典型地质特征的V_S30预测模型拟合优度R2>0.90，预测精度很高，对于离散性较大、直接拟合估算较差及无剪切波速场地来说，以区分地质单元及土体类型的方式进行V_S30分解预测是良好的研究思路。首次在区分地质单元及土体类型的前提下提出剪切波速比及密实度系数，并将其与第四系上部覆盖层厚度综合应用于V_S30预测研究。研究结果可为大同盆地城市防震减灾规划、震害预测、区域性地震安全评价提供重要技术支撑。     

A note on tsunami amplitudes above submarine slides and slumps

Tsunami generated by submarine slumps and slides are investigated in the near-field, using simple source models, which consider the effects of source finiteness and directivity. Five simple two-dimensional kinematic models of submarine slumps and slides are described mathematically as combinations of spreading constant or slopping uplift functions. Tsunami waveforms for these models are computed using linearized shallow water theory for constant water depth and transform method of solution (Laplace in time and Fourier in space). Results for tsunami waveforms and tsunami peak amplitudes are presented for selected model parameters, for a time window of the order of the source duration.The results show that, at the time when the source process is completed, for slides that spread rapidly (c_R/c_T≥20, where c_R is the velocity of predominant spreading), the displacement of the free water surface above the source resembles the displacement of the ocean floor. As the velocity of spreading approaches the long wavelength tsunami velocity the tsunami waveform has progressively larger amplitude, and higher frequency content, in the direction of slide spreading. These large amplitudes are caused by wave focusing. For velocities of spreading smaller than the tsunami long wavelength velocity, the tsunami amplitudes in the direction of source propagation become small, but the high frequency (short) waves continue to be present. The large amplification for c_R/c_T1 is a near-field phenomenon, and at distances greater than several times the source dimension, the large amplitude and short wavelength pulse becomes dispersed.A comparison of peak tsunami amplitudes for five models plotted versus L/h (where L is characteristic length of the slide and h is the water depth) shows that for similar slide dimensions the peak tsunami amplitude is essentially model independent.     

Decadal‐scale gravel beach evolution on a tectonically‐uplifting coast: Wellington,New Zealand

Uplift of the shoreline in tectonically‐active areas can have a profound influence on geomorphology changing the entire process dynamics of the coast as the landforms are removed from the influence of the sea. Over decadal timescales it is possible for the landforms to return to their pre‐earthquake condition and this paper examines the re‐establishment of mixed sand and gravel beaches on the coast of Wellington, New Zealand, subsequent to an uplift event in 1855. Over 60 topographic profiles were surveyed, seven sets of aerial photographs from a 67 year period were mapped and sediment size analyses conducted in order to quantify the nature of beach change following uplift, and associated relative sea level fall. These data were supported by surveys using ground penetrating radar. It is found that uplift raised the gravel beaches out of the swash zone thereby removing them from the littoral zone. Intertidal rocky reefs which occur between each embayment were also uplifted during the same event and completely interrupted the longshore transport system. Continued input of gravel material to the littoral zone allowed beaches to re‐establish sequentially along the coast as each embayment was infilled with sediment. This reconnection of the embayments with the longshore drift system is associated with the beach planform being initially drift dominated during infill but then switching to swash alignment once the embayment becomes infilled. This has resulted in shoreline accretion of over 100 m in some places, at rates of up to 4 m/yr, covering shore protection works built in the past few decades. The ability of the shore to adjust back to its pre‐uplift condition appears to be a function of the accommodation space created during uplift and the rate of sediment supply. Copyright © 2012 John Wiley & Sons, Ltd.     

Converted-wave imaging in anisotropic media: theory and case studies

Common‐conversion‐point binning associated with converted‐wave (C‐wave) processing complicates the task of parameter estimation, especially in anisotropic media. To overcome this problem, we derive new expressions for converted‐wave prestack time migration (PSTM) in anisotropic media and illustrate their applications using both 2D and 3D data examples. The converted‐wave kinematic response in inhomogeneous media with vertical transverse isotropy is separated into two parts: the response in horizontally layered vertical transverse isotrophy media and the response from a point‐scatterer. The former controls the stacking process and the latter controls the process of PSTM. The C‐wave traveltime in horizontally layered vertical transverse isotrophy media is determined by four parameters: the C‐wave stacking velocity V_C2, the vertical and effective velocity ratios γ₀ and γ_eff, and the C‐wave anisotropic parameter χ_eff. These four parameters are referred to as the C‐wave stacking velocity model. In contrast, the C‐wave diffraction time from a point‐scatterer is determined by five parameters: γ₀, V_P2, V_S2, η_eff and ζ_eff, where η_eff and ζ_eff are, respectively, the P‐ and S‐wave anisotropic parameters, and V_P2 and V_S2 are the corresponding stacking velocities. V_P2, V_S2, η_eff and ζ_eff are referred to as the C‐wave PSTM velocity model. There is a one‐to‐one analytical link between the stacking velocity model and the PSTM velocity model. There is also a simple analytical link between the C‐wave stacking velocities V_C2 and the migration velocity V_Cmig, which is in turn linked to V_P2 and V_S2. Based on the above, we have developed an interactive processing scheme to build the stacking and PSTM velocity models and to perform 2D and 3D C‐wave anisotropic PSTM. Real data applications show that the PSTM scheme substantially improves the quality of C‐wave imaging compared with the dip‐moveout scheme, and these improvements have been confirmed by drilling.     

ADV measurements of velocity distributions in a gravel‐bed flume

Velocity measurements carried out by an acoustic doppler velocimeter (ADV) in a rectangular laboratory ?ume having a gravel bed are presented. The velocity pro?les are measured in six verticals of the channel cross‐section having an increasing distance (from 4 to 38·5 cm) from the ?ume wall. The experimental runs are carried out for ?ve different bed arrangements, characterized by different concentrations of coarser elements, and for the two conditions of small‐ and large‐scale roughness. For both hydraulic conditions, the velocity measurements are ?rst used to test the applicability of the Dean pro?le and of the logarithmic pro?le corrected by a divergence function proposed in this paper. Then, for each value of the depth sediment ratio h/d₈₄, the non‐dimensional friction factor parameter is calculated by integration of the measured velocity distributions in the different verticals of the cross‐section. Finally a semi‐logarithmic ?ow resistance equation is empirically deduced. Copyright © 2003 John Wiley & Sons, Ltd.     

P- and S-wave velocities of consolidated sediments from a seafloor seismic survey in the North Celtic Sea Basin, offshore Ireland

A geophysical survey was conducted over a hydrocarbon prospect in the North Celtic Sea Basin using a small array of ocean‐bottom seismographs (OBSs). The purpose of this study was to determine the ratio of compressional (P)‐ to shear (S)‐wave velocity of consolidated sedimentary rocks in order to constrain possible subsurface variations in pore‐fluid content. The ratio of V_P and V_S is known to be particularly sensitive to lithology, porosity and pore‐fluid content, making it a useful parameter for evaluating hydrocarbon prospects. OBSs offer a relatively cheap and time‐effective means of acquiring multi‐component data compared with ocean‐bottom cables. In this contribution, we demonstrate the ability of an OBS survey comprising three pairs of two OBSs spaced at 1.6 km to recover lateral variations in the V_P/V_S ratio. A key requirement of this type of study is that S waves will be generated by mode conversions in the subsurface, since they cannot be generated in nor travel through fluids. In this survey, the contrast in physical properties of the hard seabed of the North Celtic Sea Basin provided a means of generating converted S waves. Two‐dimensional ray‐tracing and forward modelling was used to create both V_P and V_S models along a profile crossing the Blackrock prospect in the North Celtic Sea Basin. These models comprise four layers and extend to a maximum depth of 1.1 km. The observed northward decrease in the V_P/V_S ratio at depths of 500–1000 m below the seafloor in the study area is interpreted to represent lateral variation in the amount of gas present in the pore space of Upper Cretaceous chalks and shales overlying the prospective reservoir.     

Practical and robust experimental determination of c13 and Thomsen parameter δ

We analysed the complications in laboratory velocity anisotropy measurement on shales. There exist significant uncertainties in the laboratory determination of c₁₃ and Thomsen parameter δ. These uncertainties are primarily related to the velocity measurement in the oblique direction. For reliable estimation of c₁₃ and δ, it is important that genuine phase velocity or group velocity be measured with minimum uncertainty. The uncertainties can be greatly reduced if redundant oblique velocities are measured. For industrial applications, it is impractical to make multiple oblique velocity measurements on multiple core plugs. We demonstrated that it is applicable to make multiple genuine oblique group velocity measurements on a single horizontal core plug. The measurement results show that shales can be classified as a typical transversely isotropic medium. There is a coupling relation between c₄₄ and c₁₃ in determining the directional dependence of the seismic velocities. The quasi‐P‐wave or quasi‐S‐wave velocities can be approximated by three elastic parameters.     

3D description and inversion of reflection moveout of PS‐waves in anisotropic media

Common‐midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t²(x²) conventionally used for pure modes. Here, we present concise parametric expressions for both common‐midpoint (CMP) and common‐conversion‐point (CCP) gathers of PS‐waves for arbitrary anisotropic, horizontally layered media above a plane dipping reflector. This analytic representation can be used to model 3D (multi‐azimuth) CMP gathers without time‐consuming two‐point ray tracing and to compute attributes of PS moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum. In addition to providing an efficient tool for forward modelling, our formalism helps to carry out joint inversion of P and PS data for transverse isotropy with a vertical symmetry axis (VTI media). If the medium above the reflector is laterally homogeneous, P‐wave reflection moveout cannot constrain the depth scale of the model needed for depth migration. Extending our previous results for a single VTI layer, we show that the interval vertical velocities of the P‐ and S‐waves (V_P0 and V_S0) and the Thomsen parameters ε and δ can be found from surface data alone by combining P‐wave moveout with the traveltimes of the converted PS(PSV)‐wave. If the data are acquired only on the dip line (i.e. in 2D), stable parameter estimation requires including the moveout of P‐ and PS‐waves from both a horizontal and a dipping interface. At the first stage of the velocity‐analysis procedure, we build an initial anisotropic model by applying a layer‐stripping algorithm to CMP moveout of P‐ and PS‐waves. To overcome the distorting influence of conversion‐point dispersal on CMP gathers, the interval VTI parameters are refined by collecting the PS data into CCP gathers and repeating the inversion. For 3D surveys with a sufficiently wide range of source–receiver azimuths, it is possible to estimate all four relevant parameters (V_P0, V_S0, ε and δ) using reflections from a single mildly dipping interface. In this case, the P‐wave NMO ellipse determined by 3D (azimuthal) velocity analysis is combined with azimuthally dependent traveltimes of the PS‐wave. On the whole, the joint inversion of P and PS data yields a VTI model suitable for depth migration of P‐waves, as well as processing (e.g. transformation to zero offset) of converted waves.     

贵州西部多流域水库区地壳三维速度结构

使用基于机器学习构建的贵州西部多流域水库区地震目录和震相报告,采用波速比一致性约束的双差层析成像方法联合反演得到了该地区的地震位置和三维v_p、v_s、v_p/v_s结构。结果显示,研究区内的地壳速度结构具有明显的不均匀性,不同大地构造变形分区展现出不同的速度结构特征。在10km以上深度,横穿黔西中部NW向的威宁构造变形区显示出显著的低速异常条带,揭示了威宁—水城深大断裂带的影响深度和范围。受库区岩性和流体渗透的影响,0km深度的速度结构显示普遍的低波速和高波速比特征,包括夹岩、平寨、光照和马马崖水库区域。重定位后,地震的空间分布勾勒出大量隐伏断层的几何展布特征,结合三维速度结构,推测该区域的地震活动与水库周围的断层活化有关。     

Two-step interface and velocity inversion

This paper studies the computation method of two-step inversion of interface and velocity in a region. The 3-D interface is described by a segmented incomplete polynomial; while the reconstruction of 3-D velocity is accomplished by the principle of least squares in functional space. The computation is carried out in two steps. The first step is to inverse the shape of 3-D interface; while the second step is to do 3-D velocity inversion by distributing the remaining residual errors of travel time in accordance with their weights. The data of seismic sounding in the Tangshan-Luanxian seismic region are processed, from which the 3-D structural form in depth of the Tangshan seismic region and the 3-D velocity distribution in the crust below the Tangshan-Luanxian seismic region are obtained. The result shows that the deep 3-D structure in the Tangshan seismic region trends NE on the whole and the structure sandwiched between the NE-trending Fengtai-Yejituo fault and the NE-trending Tangshan fault is an uplifted zone of the Moho. In the 3-D velocity structure of middle-lower crust below that region, there is an obvious belt of low-velocity anomaly to exist along the NE-trending Tangshan fault, the position of which tallies with that of the Tangshan seismicity belt. The larger block of low-velocity anomaly near Shaheyi corresponds to a denser earthquake distribution. In that region, there is an NW-trending belt of high-velocity anomaly, probably a buried fault zone. The lower crust below the epicentral region of the Tangshan M _S=7.8 earthquake is a place where the NE-trending belt of low-velocity anomaly meets the NW-trending belt of high-velocity anomaly. The two sets of structures had played an important role in controlling the preparation and occurrence of the M _S=7.8 Tangshan earthquake. Contribution RCEG97006, Research Center of Exploration Geophysics, China Seismological Bureau, China. This project is supported by the Chinese Joint Seismological Science Foundation.     

Seismic anisotropy of shales

Shales are a major component of sedimentary basins, and they play a decisive role in fluid flow and seismic‐wave propagation because of their low permeability and anisotropic microstructure. Shale anisotropy needs to be quantified to obtain reliable information on reservoir fluid, lithology and pore pressure from seismic data, and to understand time‐to‐depth conversion errors and non‐hyperbolic moveout. A single anisotropy parameter, Thomsen's δ parameter, is sufficient to explain the difference between the small‐offset normal‐moveout velocity and vertical velocity, and to interpret the small‐offset AVO response. The sign of this parameter is poorly understood, with both positive and negative values having been reported in the literature. δ is sensitive to the compliance of the contact regions between clay particles and to the degree of disorder in the orientation of clay particles. If the ratio of the normal to shear compliance of the contact regions exceeds a critical value, the presence of these regions acts to increase δ, and a change in the sign of δ, from the negative values characteristic of clay minerals to the positive values commonly reported for shales, may occur. Misalignment of the clay particles can also lead to a positive value of δ. For transverse isotropy, the elastic anisotropy parameters can be written in terms of the coefficients W₂₀₀ and W₄₀₀ in an expansion of the clay‐particle orientation distribution function in generalized Legendre functions. For a given value of W₂₀₀, decreasing W₄₀₀ leads to an increase in δ, while for fixed W₄₀₀, δ increases with increasing W₂₀₀. Perfect alignment of clay particles with normals along the symmetry axis corresponds to the maximum values of W₂₀₀ and W₄₀₀, given by and . A comparison of the predictions of the theory with laboratory measurements shows that most shales lie in a region of the (W₂₀₀, W₄₀₀)‐plane defined by W₄₀₀/W₂₀₀≤W^max₄₀₀/W^max₂₀₀ .