Stochastic inversion of pressure and saturation changes from time-lapse multi component data

Knowledge about saturation and pressure distributions in a reservoir can help in determining an optimal drainage pattern, and in deciding on optimal well designs to reduce risks of blow‐outs and damage to production equipment. By analyzing time‐lapse PP AVO or time‐lapse multicomponent seismic data, it is possible to separate the effects of production related saturation and pressure changes on seismic data. To be able to utilize information about saturation and pressure distributions in reservoir model building and simulation, information about uncertainty in the estimates is useful. In this paper we present a method to estimate changes in saturation and pressure from time‐lapse multicomponent seismic data using a Bayesian estimation technique. Results of the estimations will be probability density functions (pdfs), giving immediate information about both parameter values and uncertainties. Linearized rock physical models are linked to the changes in saturation and pressure in the prior probability distribution. The relationship between the elastic parameters and the measured seismic data is described in the likelihood model. By assuming Gaussian distributed prior uncertainties the posterior distribution of the saturation and pressure changes can be calculated analytically. Results from tests on synthetic seismic data show that this method produces more precise estimates of changes in effective pressure than a similar methodology based on only PP AVO time‐lapse seismic data. This indicates that additional information about S‐waves obtained from converted‐wave seismic data is useful for obtaining reliable information about the pressure change distribution.     

Geomechanical property estimation of unconventional reservoirs using seismic data and rock physics

An extension of a previously developed rock physics model is made that quantifies the relationship between the ductile fraction of a brittle/ductile binary mixture and the isotropic seismic reflection response. By making a weak scattering (Born) approximation and plane wave (eikonal) approximation, with a subsequent ordering according to the angles of incidence, singular value decomposition analyses are performed to understand the stack weightings, number of stacks, and the type of stacks that will optimally estimate two fundamental rock physics parameters – the ductile fraction and the compaction and/or diagenesis. It is concluded that the full PP stack, i.e., sum of all PP offset traces, and the “full” PS stack, i.e., linear weighted sum of PS offset traces, are the two optimal stacks needed to estimate the two rock physics parameters. They dominate over both the second‐order amplitude variation offset “gradient” stack, which is a quadratically weighted sum of PP offset traces that is effectively the far offset traces minus the near offset traces, and the higher order fourth order PP stack (even at large angles of incidence). Using this result and model‐based Bayesian inversion, the seismic detectability of the ductile fraction (shown by others to be the important rock property for the geomechanical response of unconventional reservoir fracking) is demonstrated on a model characteristic of the Marcellus shale play.     

Utilizing spectral decomposition to determine the distribution of injected CO2 at the Snøhvit Field

Time‐lapse 3D seismic reflection data, covering the CO₂ storage operation at the Snøhvit gas field in the Barents Sea, show clear amplitude and time‐delay differences following injection. The nature and extent of these changes suggest that increased pore fluid pressure contributes to the observed seismic response, in addition to a saturation effect. Spectral decomposition using the smoothed pseudo‐Wigner–Ville distribution has been used to derive discrete‐frequency reflection amplitudes from around the base of the CO₂ storage reservoir. These are utilized to determine the lateral variation in peak tuning frequency across the seismic anomaly as this provides a direct proxy for the thickness of the causative feature. Under the assumption that the lateral and vertical extents of the respective saturation and pressure changes following CO₂ injection will be significantly different, discrete spectral amplitudes are used to distinguish between the two effects. A clear spatial separation is observed in the distribution of low‐ and high‐frequency tuning. This is used to discriminate between direct fluid substitution of CO₂, as a thin layer, and pressure changes that are distributed across a greater thickness of the storage reservoir. The results reveal a striking correlation with findings derived from pressure and saturation discrimination algorithms based on amplitude versus offset analysis.     

Sensitivity of the elastic anisotropy and seismic reflection amplitude of the Eagle Ford Shale to the presence of kerogen

The Eagle Ford Shale of Central and South Texas is currently of great interest for oil and gas exploration and production. Laboratory studies show that the Eagle Ford Shale is anisotropic, with a correlation between anisotropy and total organic carbon. Organic materials are usually more compliant than other minerals present in organic‐rich shales, and their shapes and distribution are usually anisotropic. This makes organic materials an important source of anisotropy in organic‐rich shales. Neglecting shale anisotropy may lead to incorrect estimates of rock and fluid properties derived from inversion of amplitude versus offset seismic data. Organic materials have a significant effect on the PP and PS reflection amplitudes from the Austin Chalk/Upper Eagle Ford interface, the Upper Eagle Ford/Lower Eagle Ford interface, and the Lower Eagle Ford/Buda Limestone interface. The higher kerogen content of the Lower Eagle Ford compared with that of the Upper Eagle Ford leads to a negative PP reflection amplitude that dims with offset, whereas the PS reflection coefficient increases in magnitude with increasing offset. The PP and PS reflection coefficients at the Austin Chalk/Upper Eagle Ford interface, the Upper Eagle Ford/Lower Eagle Ford interface, and the Lower Eagle Ford/Buda Limestone interface all increase in magnitude with increasing volume fraction of kerogen.     

Lithology and hydrocarbon mapping from multicomponent seismic data

Elastic rock properties can be estimated from prestack seismic data using amplitude variation with offset analysis. P‐wave, S‐wave and density ‘reflectivities’, or contrasts, can be inverted from angle‐band stacks. The ‘reflectivities’ are then inverted to absolute acoustic impedance, shear impedance and density. These rock properties can be used to map reservoir parameters through all stages of field development and production. When P‐wave contrast is small, or gas clouds obscure reservoir zones, multicomponent ocean‐bottom recording of converted‐waves (P to S or Ps) data provides reliable mapping of reservoir boundaries. Angle‐band stacks of multicomponent P‐wave (Pz) and Ps data can also be inverted jointly. In this paper Aki‐Richards equations are used without simplifications to invert angle‐band stacks to ‘reflectivities’. This enables the use of reflection seismic data beyond 30° of incident angles compared to the conventional amplitude variation with offset analysis. It, in turn, provides better shear impedance and density estimates. An important input to amplitude variation with offset analysis is the V_s/V_p ratio. Conventional methods use a constant or a time‐varying V_s/V_p model. Here, a time‐ and space‐varying model is used during the computation of the ‘reflectivities’. The V_s/V_p model is generated using well log data and picked horizons. For multicomponent data applications, the latter model can also be generated from processing V_s/V_p models and available well data. Reservoir rock properties such as λρ, μρ, Poisson's ratio and bulk modulus can be computed from acoustic impedance, shear impedance and density for pore fill and lithology identification. λ and μ are the Lamé constants and ρ is density. These estimations can also be used for a more efficient log property mapping. V_p/V_s ratio or Poisson's ratio, λρ and weighted stacks, such as the one computed from λρ and λ/μ, are good gas/oil and oil/water contact indicators, i.e., pore fill indicators, while μρ mainly indicates lithology. μρ is also affected by pressure changes. Results from a multicomponent data set are used to illustrate mapping of gas, oil and water saturation and lithology in a Tertiary sand/shale setting. Whilst initial log crossplot analysis suggested that pore fill discrimination may be possible, the inversion was not successful in revealing fluid effects. However, rock properties computed from acoustic impedance, shear impedance and density estimates provided good lithology indicators; pore fill identification was less successful. Neural network analysis using computed rock properties provided good indication of sand/shale distribution away from the existing wells and complemented the results depicted from individual rock property inversions.     

2D PP/PS-stereotomography: Application to a real 2D-OBC dataset

It has been shown on an ‘ideal’ synthetic dataset that PP/PS‐stereotomography can estimate an accurate velocity model without any pairing of PP‐ and PS‐events. The P‐wave velocity model is first estimated using PP data and then, fixing this velocity field, the S‐wave velocity is estimated using the PS data. This method needed to be evaluated further and we present here the first application of PP/PS‐stereotomography to a real dataset: the 2D East‐West Mahogany OBC line (Gulf of Mexico). We are here confronted with data which do not fit our working assumptions: coherent noise (due to an approximate separation of PP‐ and PS‐events and some remaining multiples), probably some anisotropy and 3D effects. With a careful selection of the stereotomographic picks, which allows one to decrease the effect of the picked coherent noise by the automatic picker, our application can demonstrate the relevance of our approach in the upper part of the profile, where anisotropy and 3D effects might be low. We can thus estimate, without any pairing of PP‐ and PS‐events, a velocity field which provides not only flat common image gathers, but also PP‐ and PS‐depth migrated images located at the same positions. For the deeper part of the profile, a significant shift in depth appears. In addition to possible anisotropy, 3D effects and a more complex velocity field (‘salt body’), this is due to the quality of the PZ‐ and X‐components profiles: The PZ‐component profile where the PP‐stereotomographic picking is performed, is polluted by conflicting converted or multiple events and the X‐component profile, where the PS‐stereotomographic picking is performed, is highly noisy. This study emphasizes the need to develop accurate selection criteria for the stereotomographic picks.     

Seepage erosion in layered stream bank material

Current stream restoration practices often require anthropogenic manipulation of natural field soils to reconstruct stream banks in the absence of stabilizing vegetation. For this study, researchers conducted laboratory experiments on reconstructed, non‐vegetated stream banks with layered soils experiencing seepage. The objective of the study was to determine the effect of seepage, pore water pressure, and bank geometry on erosion and bank stability of layered streambanks. The experimental design consisted of an intermediate‐size soil lysimeter packed with a sandy clay loam top soil and an underlying fine sand layer at three bank slopes (90°, 45° and 26°). Shallow groundwater flow and seepage resulted in bank failure of geometrically stable banks. Pop out failures, liquid deformation, and piping were all observed failure mechanisms in the underlying sand material, dependent on the bank angle. Groundwater seepage processes created small‐scale failures of the underlying sand leading to larger‐scale failures of the overlying sandy clay loam. The underlying sand layer eroded according to the initial bank angle and change in overburden loading. The overlying loam layer failed along linear failure planes. The gradually sloped bank (i.e. 26° slope) failed faster, hypothesized to be due to less confining pressure and greater vertical seepage forces. Researchers analyzed the laboratory experiments using the Bank Stability and Toe Erosion Model, version 4·1. The model calculated an accurate shear surface angle similar to the failure angle observed in the lysimeter tests. The model predicted failure only for the undercut 90° bank slope, and indicated stable conditions for the other geometries. Steeper initial bank slopes and undercut banks decreased the bank factor of safety. The observed failure mechanisms and measured saturation data indicated an interaction between overburden pressure, seepage forces, and bank slope on bank stability. Future bank stability modeling would benefit by incorporating lateral seepage erosion and soil liquefaction prediction calculations. Copyright © 2009 John Wiley & Sons, Ltd.     

Fracture characterization using converted waves

We present a method for inversion of fracture compliance matrix components from wide‐azimuth noisy synthetic PS reflection data and quantitatively show that reflection amplitude variations with offset and azimuth for converted PS‐waves are more informative than P‐waves for fracture characterization. We consider monoclinic symmetry for fractured reservoir (parameters chosen from Woodford Shale), which can be formed by two or more sets of vertical fractures embedded in a vertically transverse isotropic background. Components of effective fracture compliance matrices for a medium with monoclinic symmetry are related to the characteristics of the fractured medium. Monte Carlo simulation results show that inversion of PS reflection data is more robust than that of PP reflection data to uncertainties in our a priori knowledge (vertically transverse isotropic parameters of unfractured rock) than PP reflection data. We also show that, while inversion of PP reflections is sensitive to contrasts in elastic properties of upper and lower media, inversion of PS reflections is robust with respect to such contrasts.     

The added value of joint PP–PS inversion for reservoir characterization: A case study using Jubarte PRM seismic data (offshore Brazil)

The added value of the joint pre-stack inversion of PP (incident P-wave and reflected P-wave) and PS (incident P-wave and reflected S-wave) seismic data for the time-lapse application is shown. We focus on the application of this technique to the time-lapse (four-dimensional) multicomponent Jubarte field permanent reservoir monitoring seismic data. The joint inversion results are less sensitive to noise in the input data and show a better match with the rock physics models calibrated for the field. Further, joint inversion improves S-impedance estimates and provides a more robust quantitative interpretation, allowing enhanced differentiation between pore pressure and fluid saturation changes, which will be extremely useful for reservoir management. Small changes in reservoir properties are expected in the short time between the time-lapse seismic acquisitions used in the Jubarte project (only 1 year apart). The attempt to recover subtle fourth-dimensional effects via elastic inversion is recurrent in reservoir characterization projects, either due to the small sensitivity of the reservoirs to fluid and pressure changes or the short interval between the acquisitions. Therefore, looking for methodologies that minimize the uncertainty of fourth-dimensional inversion outputs is of fundamental importance. Here, we also show the differences between PP only and joint PP–PS inversion workflows and parameterizations that can be applied in other projects. We show the impact of using multicomponent data as input for elastic seismic inversions in the analysis of the time-lapse differences of the elastic properties. The larger investment in the acquisition and processing of multicomponent seismic data is shown to be justified by the improved results from the fourth-dimensional joint inversion.     

基于精确Zoeppritz方程的非线性AVO三参数反演

常规AVO三参数反演通常存在密度反演不准确的问题,而密度参数对常规油气藏中的流体识别、流体饱和度计算、孔隙度计算以及非常规油气藏中TOC含量计算、裂缝预测等都至关重要,因此对于研究如何利用大偏移距振幅信息和富含密度信息的PS波地震资料来提高密度反演结果的稳定性和精度显得尤为重要.研究基于贝叶斯反演理论框架,引入三变量Cauchy分布先验约束,利用精确Zoeppritz方程构建了AVO三参数联合反演的目标函数,对目标函数进行Taylor二阶非线性简化,得到模型参数的迭代更新公式,实现了大偏移距地震振幅信息的利用和PP波、PS波联合反演.合成数据和实际地震数据的方法测试结果表明,新方法不仅可以直接反演纵波速度、横波速度和密度,而且还具有很高的精度,尤其是密度反演结果.基于合成数据的PP波、PS波单独反演结果与PP波和PS波联合反演结果对比显示,联合反演稳定性更好,精度更高,抗噪能力更强,验证了该方法的可行性和有效性.与基于Aki-Richards近似公式的反演结果对比表明,该反演方法具有更高的反演精度和更好的抗噪性.     

Analysis of time‐lapse travel‐time and amplitude changes to assess reservoir compartmentalization

Fluid depletion within a compacting reservoir can lead to significant stress and strain changes and potentially severe geomechanical issues, both inside and outside the reservoir. We extend previous research of time‐lapse seismic interpretation by incorporating synthetic near‐offset and full‐offset common‐midpoint reflection data using anisotropic ray tracing to investigate uncertainties in time‐lapse seismic observations. The time‐lapse seismic simulations use dynamic elasticity models built from hydro‐geomechanical simulation output and a stress‐dependent rock physics model. The reservoir model is a conceptual two‐fault graben reservoir, where we allow the fault fluid‐flow transmissibility to vary from high to low to simulate non‐compartmentalized and compartmentalized reservoirs, respectively. The results indicate time‐lapse seismic amplitude changes and travel‐time shifts can be used to qualitatively identify reservoir compartmentalization. Due to the high repeatability and good quality of the time‐lapse synthetic dataset, the estimated travel‐time shifts and amplitude changes for near‐offset data match the true model subsurface changes with minimal errors. A 1D velocity–strain relation was used to estimate the vertical velocity change for the reservoir bottom interface by applying zero‐offset time shifts from both the near‐offset and full‐offset measurements. For near‐offset data, the estimated P‐wave velocity changes were within 10% of the true value. However, for full‐offset data, time‐lapse attributes are quantitatively reliable using standard time‐lapse seismic methods when an updated velocity model is used rather than the baseline model.     

3D simultaneous joint PP‐PS prestack seismic inversion at Schiehallion field,United Kingdom Continental Shelf

A workflow for simultaneous joint PP‐PS prestack inversion of data from the Schiehallion field on the United Kingdom Continental Shelf is presented and discussed. The main challenge, describing reasonable PS to PP data registration before any prestack or joint PP‐PS inversion, was overcome thanks to a two‐stage process addressing the signal envelope, then working directly on the seismic data to estimate appropriate time‐variant time‐shift volumes. We evaluated the benefits of including PS along with PP prestack seismic data in a joint inversion process to improve the estimated elastic property quality and also to enable estimation of density compared with other prestack and post‐stack inversion approaches. While the estimated acoustic impedance exhibited a similar quality independent of the inversion used (PP post‐stack, PP prestack or joint PP‐PS prestack inversion) the shear impedance estimation was noticeably improved by the joint PP‐PS prestack inversion when compared to the PP prestack inversion. Finally, the density estimated from joint PP and PS prestack data demonstrated an overall good quality, even where not well‐controlled. The main outcome of this study was that despite several data‐related limitations, inverting jointly correctly processed PP and PS data sets brought extra value for reservoir delineation as opposed to PP‐only or post‐stack inversion.     

When 4D seismic is not applicable: Alternative monitoring scenarios for the Arab-D reservoir in the Ghawar Field

Ghawar, the largest oilfield in the world, produces oil from the Upper Jurassic Arab‐D carbonate reservoir. The high rigidity of the limestone–dolomite reservoir rock matrix and the small contrast between the elastic properties of the pore fluids, i.e. oil and water, are responsible for the weak 4D seismic effect due to oil production. A feasibility study was recently completed to quantify the 4D seismic response of reservoir saturation changes as brine replaced oil. The study consisted of analysing reservoir rock physics, petro‐acoustic data and seismic modelling. A seismic model of flow simulation using fluid substitution concluded that time‐lapse surface seismic or conventional 4D seismic is unlikely to detect the floodfront within the repeatability of surface seismic measurements. Thus, an alternative approach to 4D seismic for reservoir fluid monitoring is proposed. Permanent seismic sensors could be installed in a borehole and on the surface for passive monitoring of microseismic activity from reservoir pore‐pressure perturbations. Reservoir production and injection operations create these pressure or stress perturbations. Reservoir heterogeneities affecting the fluid flow could be mapped by recording the distribution of epicentre locations of these microseisms or small earthquakes. The permanent borehole sensors could also record repeated offset vertical seismic profiling surveys using a surface source at a fixed location to ensure repeatability. The repeated vertical seismic profiling could image the change in reservoir properties with production.     

PP and PS joint AVO inversion and fluid prediction

The technique of amplitude variation with offset or angle (AVO or AVA) can be used to extract fluid and lithology information from prestack seismic data. Based on three-term AVO equations, three elastic parameters can be inverted for by linear AVO inversion. However, many theoretical and numerical studies have demonstrated that by using offset limited data, a three-term AVO inversion may have problems of instability and inaccuracy while inverting for the density term. We have searched for an elastic parameter that contains density information and inverted this parameter in a more stable manner using offset limited data. First, we test the sensitivity of elastic parameters to hydrocarbon reservoirs and select the optimal fluid factor (ρf) that contains density information and has an excellent performance as an inversion parameter used to detect hydrocarbons. Then, we derive approximate PP and PS reflection coefficient equations in terms of the fluid factor. The derived equations allow us to directly estimate the fluid factor of the reservoir. Finally, we apply these equations to synthetic data by employing a joint AVO inversion technique. The results show that the method is stable and unambiguous.     

Tectonic reconstruction of batholith formation based on the spatiotemporal distribution of Cretaceous–Paleogene granitic rocks in southwestern Japan

The spatiotemporal distribution of Cretaceous–Paleogene granitic rocks in southwestern Japan is investigated to understand the origin of the granitic batholith belt and to reconstruct the tectonic setting of emplacement. New U–Pb zircon ages for 92 samples collected from a region measuring 50 km (E–W) by 200 km (N–S) reveals a stepwise northward younging of granitic rocks aged between 95 and 30 Ma with an age‐data gap between 60 and 48 Ma. Based on the spatiotemporal distribution of granite ages, we examine two plausible models to explain the pattern of magmatic activity: (i) subduction of a segmented spreading ridge and subsequent slab melting (ridge‐subduction model), and (ii) subduction with a temporally variable subduction angle and corresponding spatial distribution of normal arc magmatism (subduction angle model). We optimize the model parameters to fit the observed magmatism in time and space, and compare the best‐fit models. As to ridge subduction model, the best‐fit solution indicates that the spreading ridge started to subduct at approximately 100 Ma, and involved a 45‐km‐wide section of the ridge segment, a subduction obliquity of 30°, and a slow migration velocity (～1.6 cm/y) of the ridge. These values are within the ranges of velocities observed for present‐day ridge subduction at the Chile trench. On the other hand, the best‐fit solution of subduction angle model indicates that the subduction angle decreases stepwise from 37° at 95 Ma, 32° at 87 Ma, 22° at 72 Ma, to 20° at 65 Ma, shifting magmatic region towards the continental side. These results and comparison, together with constraints on the geometry of the tectonic setting provided by previous studies, suggest that the ridge subduction model better explains the limited duration of magmatism, although both models broadly fit the data and cannot be ruled out.     

Effects of the sea floor topography on the 1D inversion of time‐domain marine controlled source electromagnetic data

Time‐domain marine controlled source electromagnetic methods have been used successfully for the detection of resistive targets such as hydrocarbons, gas hydrate, or marine groundwater aquifers. As the application of time‐domain marine controlled source electromagnetic methods increases, surveys in areas with a strong seabed topography are inevitable. In these cases, an important question is whether bathymetry information should be included in the interpretation of the measured electromagnetic field or not. Since multi‐dimensional inversion is still not common in time‐domain marine controlled source electromagnetic methods, bathymetry effects on the 1D inversion of single‐offset and multi‐offset joint inversions of time‐domain controlled source electromagnetic methods data are investigated. We firstly used an adaptive finite element algorithm to calculate the time‐domain controlled source electromagnetic methods responses of 2D resistivity models with seafloor topography. Then, 1D inversions are applied on the synthetic data derived from marine resistivity models, including the topography in order to study the possible topography effects on the 1D interpretation. To evaluate the effects of topography with various steepness, the slope angle of the seabed topography is varied in the synthetic modelling studies for deep water (air interaction is absent or very weak) and shallow water (air interaction is dominant), respectively. Several different patterns of measuring configurations are considered, such as the systems adopting nodal receivers and the bottom‐towed system. According to the modelling results for deep water when air interaction is absent, the 2D topography can distort the measured electric field. The distortion of the data increases gradually with the enlarging of the topography's slope angle. In our test, depending on the configuration, the seabed topography does not affect the 1D interpretation significantly if the slope angle is less or around 10°. However, if the slope angle increases to 30° or more, it is possible that significant artificial layers occur in inversion results and lead to a wrong interpretation. In a shallow water environment with seabed topography, where the air interaction dominates, it is possible to uncover the true subsurface resistivity structure if the water depth for the 1D inversion is properly chosen. In our synthetic modelling, this scheme can always present a satisfactory data fit in the 1D inversion if only one offset is used in the inversion process. However, the determination of the optimal water depth for a multi‐offset joint inversion is challenging due to the various air interaction for different offsets.     

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.     

平均入射角道集PP波与PS波联合反演

在界面两侧地层的弹性参数弱反差的假设难以成立的情况下,本文提出用平均入射角道集进行PP波与PS波的联合反演.首先,在PP波与PS波AVA(amplitude versus angle,振幅随入射角变化)道集的基础上,分别选择小入射角范围与大入射角范围的AVA道集进行局部加权叠加,以获得由两个角度组成的平均入射角道集,并作为后续反演的输入数据.然后,再通过最小二乘原理建立了PP波与PS波联合反演目标函数,推导了模型修改量的向量公式,建立了平均入射角道集联合反演的流程.模型数据与实际数据的测试结果表明:在信噪比较低、地层弹性参数反差较大、层厚较薄的情况下,该反演方法的精度在很大程度上超过了基于近似反射系数的反演方法,为复杂油气藏勘探提供了新的思路.     

Elastic behaviour of North Sea chalk: A well-log study

We present two different elastic models for, respectively, cemented and uncemented North Sea chalk well‐log data. We find that low Biot coefficients correlate with anomalously low cementation factors from resistivity measurements at low porosity and we interpret this as an indication of cementation. In contrast, higher Biot coefficients and correspondingly higher cementation factors characterize uncemented chalk for the same (low) porosity. Accordingly, the Poisson's ratio–porosity relationship for cemented chalk is different from that of uncemented chalk. We have tested the application of the self‐consistent approximation, which here represents the unrelaxed scenario where the pore spaces of the rock are assumed to be isolated, and the Gassmann theory, which assumes that pore spaces are connected, as tools for predicting the effect of hydrocarbons from the elastic properties of brine‐saturated North Sea reservoir chalk. In the acoustic impedance–Poisson's ratio plane, we forecast variations in porosity and hydrocarbon saturation from their influence on the elastic behaviour of the chalk. The Gassmann model and the self‐consistent approximation give roughly similar predictions of the effect of fluid on acoustic impedance and Poisson's ratio, but we find that the high‐frequency self‐consistent approach gives a somewhat smaller predicted fluid‐saturation effect on Poisson's ratio than the low‐frequency Gassmann model. The Gassmann prediction for the near and potentially invaded zone corresponds more closely to logging data than the Gassmann prediction for the far, virgin zone. We thus conclude that the Gassmann approach predicts hydrocarbons accurately in chalk in the sonic‐frequency domain, but the fluid effects as recorded by the acoustic tool are significantly affected by invasion of mud filtrate. The amplitude‐versus‐angle (AVA) response for the general North Sea sequence of shale overlying chalk is predicted as a function of porosity and pore‐fill. The AVA response of both cemented and uncemented chalk generally shows a declining reflectivity coefficient versus offset and a decreasing normal‐incidence reflectivity with increasing porosity. However, for the uncemented model, a phase reversal will appear at a relatively lower porosity compared to the cemented model.