Well tie,fluid substitution and AVO modelling: a North Sea example

Accurate well ties are essential to practical seismic lithological interpretation. As long as the geology in the vicinity of the reservoir is not unduly complex, the main factors controlling this accuracy are the processing of the seismic data and the construction of the seismic model from well logs. This case study illustrates how seismic data processing to a near-offset stack, quality control of logs and petrophysical modelling improved a well tie at an oil reservoir. We demonstrate the application of a predictive petrophysical model in the preparation and integration of the logs before building the seismic model and we quantify our improvements in well-tie accuracy. The data for the study consisted of seismic field data from a 3D sail line through a well in a North Sea oilfield and a suite of standard logs at the well. A swathe of fully processed 3D data through the well was available for comparison. The well tie in the shallow section from first-pass seismic data processing and a routinely edited sonic log was excellent. The tie in a deeper interval containing the reservoir was less satisfactory: the phase errors within the bandwidth of the seismic wavelet were of the order of 20°, which we consider too large for subsequent transformation of the data to seismic impedance. Reprocessing the seismic data and revision of the well-log model reduced these phase errors to less than 10° and improved the consistency of the deep and shallow well ties. The reprocessing included densely picked iterative velocity analysis, prestack migration, beam-forming multiple attenuation, stacking the near-offset traces and demigration and remigration of the near-offset data. The petrophysical model was used to monitor and, where necessary, replace the P-wave sonic log with predictions consistent with other logs and to correct the sonic log for mud-filtrate invasion in the hydrocarbon-bearing sand. This editing and correction of the P-wave transit times improved the normal-incidence well tie significantly. The recordings from a monopole source severely underestimated the S-wave transit times in soft shale formations, including the reservoir seal, where the S-wave velocity was lower than the P-wave velocity in the drilling mud. The petrophysical model predicted an S-wave log that matched the valid recordings and interpolated between them. The subsequent seismic modelling from the predicted S-wave log produced a class II AVO anomaly seen on the CDP gathers around the well.     

SHEAR-WAVE VELOCITY ESTIMATION IN POROUS ROCKS: THEORETICAL FORMULATION,PRELIMINARY VERIFICATION AND APPLICATIONS1

Shear-wave velocity logs are useful for various seismic interpretation applications, including bright spot analyses, amplitude-versus-offset analyses and multicomponent seismic interpretations. Measured shear-wave velocity logs are, however, often unavailable. We developed a general method to predict shear-wave velocity in porous rocks. If reliable compressional-wave velocity, lithology, porosity and water saturation data are available, the precision and accuracy of shear-wave velocity prediction are 9% and 3%, respectively. The success of our method depends on: (1) robust relationships between compressional- and shear-wave velocities for water-saturated, pure, porous lithologies; (2) nearly linear mixing laws for solid rock constituents; (3) first-order applicability of the Biot–Gassmann theory to real rocks. We verified these concepts with laboratory measurements and full waveform sonic logs. Shear-wave velocities estimated by our method can improve formation evaluation. Our method has been successfully tested with data from several locations.     

Backus averaging,scattering and drift1

Differences between traveltimes from sonic to seismic frequencies, commonly known as drift, can be attributed to a combination of multiple scattering and absorption. The portion due to scattering can be estimated directly by calculating synthetic seismograms from sonic logs. A simple alternative approach is suggested by the long-wave equivalent averaging formulae for the effective elastic properties of a stack of thin layers, which gives the same traveltime delays as the low-frequency limit of the scattering dispersion. We consider the application of these averaging formulae over a frequency-dependent window with the hope of extending their use to frequencies higher than those allowed by the original validity conditions. However, comparison of the time delay due to window-averaging with the scattering dispersion predicted by the O'Doherty-Anstey formula reveals that it is not possible to specify a form of window that will fit the dispersion across the spectrum for arbitrary log statistics. A window with a width proportional to the wavelength squared matches the behaviour at the low-frequency end of the dispersive range for most logs, and allows an almost exact match of the drift across the entire spectrum for exponential correlation functions. We examine a real log, taken from a hole in nearly plane-layered geology, which displays strong quasi-cyclical variations on one scale as well as more random, smaller-scale fluctuations. The details of its drift behaviour are studied using simple models of the gross features. The form of window which gave a good theoretical fit to the dispersion for an exponential log correlation function can only fit the computed drift at high or low frequencies, confirming that there are at least two significant scale-lengths of fluctuation. A better overall fit is obtained for a window whose width is proportional to the wavelength. The calculated scattering drift is significantly less than that observed from a vertical seismic profile, but the difference cannot be wholly ascribed to absorption. This is because the source frequency of the sonic tool is not appropriate for its resolution (receiver spacing) so that the scattering drift from sonic to seismic frequencies cannot be fully estimated from the layer model derived from the log.     

Deriving effects of pressure depletion on elastic framework moduli from sonic logs

We have developed a method to determine the effect of pore pressure depletion on elastic framework moduli, by utilizing sonic logs from wells drilled at different locations through a reservoir at varying depletion stages. This is done by first inverting the sonic logs for elastic framework bulk and shear moduli, thus carefully removing pressure dependent fluid effects. By crossplotting these elastic framework moduli against an increase in net stress (which is directly related to depletion), we derive the stress sensitivity of the elastic framework moduli. We found that the observed stress sensitivity was consistent with time-lapse seismic results and that the sensitivity derived from the sonic logs was much smaller than predicted by hydrostatic measurements on core samples. This method is applicable to depletion scenarios in mature fields and can be used both for modelling and inverting time-lapse seismic data for effects of pore pressure depletion on seismic data.     

Scaling behavior and the effects of heterogeneity on shallow seismic imaging of mineral deposits: A case study from Brunswick No. 6 mining area,Canada

We have studied the scaling behavior of compressional-wave velocity and density logs from an exploration borehole that extends down to about 700 m depth in the Brunswick No. 6 mining area, Bathurst Mining Camp, Canada. Using statistical methods, vertical and horizontal scale lengths of heterogeneity were estimated. Vertical scale length estimates from the velocity, density and calculated acoustic impedance are 14 m, 33 m, and about 20 m, respectively. Although the estimated scale length for the acoustic impedance implies a weak scattering environment, elastic finite difference modeling of seismic wave propagation in 2D heterogeneous media demonstrates that even this weak scattering medium can mask seismic signals from small, but yet economically feasible, massive sulfide deposits. Further analysis of the synthetic seismic data suggests that in the presence of heterogeneity, lenticular-shaped targets may only exhibit incomplete diffraction signals whereby the down-dip tails of these diffractions are mainly visible on the stacked sections. Therefore, identification of orebody generated diffractions is much easier on the unmigrated stacked sections than on migrated stacked sections. The numerical seismic modeling in 2D heterogeneous media indicates that in the presence of large horizontal, but small vertical scale lengths (structural anisotropy), identification of massive sulfide deposits is possible, but their delineation at depth requires detailed velocity modeling and processing algorithms which can handle the anisotropy.     

ON VERTICAL SEISMIC PROFILE PROCESSING*

From the wealth of information which can be deduced from VSP, the information most directly comparable to well logs is considered: P-wave and S-wave interval velocity, acoustic impedance, and the velocity ratio γ=V_s/V_p. This information not only allows better interpretation of surface seismic sections but also improves processing. For these results to be usable a number of precautions must be taken during acquisition and processing; the sampling in depth should be chosen in such a way that aliasing phenomena do not unnecessarily limit the spectra during the separation of upwards and downwards travelling waves. True amplitudes should be respected and checked by recording of signatures, and the interference of upwards and downwards travelling waves should be taken into account for the picking of first arrivals. The different steps in processing and the combination of results in the interpretation of surface seismic results are described with actual records.     

Test of rock physics models for prediction of seismic velocities in shallow unconsolidated sands: a well log data case‡

This paper tests the ability of various rock physics models to predict seismic velocities in shallow unconsolidated sands by comparing the estimates to P and S sonic logs collected in a shallow sand layer and ultrasonic laboratory data of an unconsolidated sand sample. The model fits are also evaluated with respect to the conventional model for unconsolidated sand. Our main approach is to use Hertz‐Mindlin and Walton contact theories, assuming different weight fractions of smooth and rough contact behaviours, to predict the elastic properties of the high porosity point. Using either the Hertz‐Mindlin or Walton theories with rough contact behaviour to define the high porosity endpoint gives an over‐prediction of the velocities. The P‐velocity is overpredicted by a factor of ～1.5 and the S‐velocity by a factor of ～1.8 for highly porous gas‐sand. The degree of misprediction decreases with increasing water saturation and porosity.Using the Hertz‐Mindlin theory with smooth contact behaviour or weighted Walton models gives a better fit to the data, although the data are best described using the Walton smooth model. To predict the properties at the lower porosities, the choice of bounding model attached to the Walton Smooth model controls the degree of fit to the data, where the Reuss bound best captures the porosity variations of dry and wet sands in this case since they are caused by depositional differences. The empirical models based on lab experiments on unconsolidated sand also fit the velocity data measured by sonic logs in situ, which gives improved confidence in using lab‐derived results.     

MIGRATION OF SEISMIC INTERFACES*

Most interpretation work is still based on stacked and not on migrated sections. In the case of heavy faulting and considerable velocity contrasts between formations, migration of interpreted interfaces poses a problem. In more detail, the problem may be specified as follows: — a given interpretation of a number of interfaces along with a given heterogeneous velocity field may not always have a plausible solution in the form of migrated interfaces in depth; — fault planes, salt boundaries, etc., are, in most cases, not directly interpretable in a section and are plotted by intuition using interface terminations as a guide; — the velocity field in fault zones is, in most cases, hard to determine. The interpreter may arrive at a plausible solution by repeating the migration process with various possible interpretations and various velocity assumptions. The subject of this paper is an algorithm based on ray-theory which allows one: — to handle faults and velocity variations at faults properly; — to perform migration in steps, working a particular geological unit at a time and proceeding to the next unit once the foregoing one has been properly migrated; — to display ray-paths, where necessary, for investigation of interface distortions, e.g., below fault areas. The algorithm is designed and implemented for application in an interactive environment. Inspection of intermediate and final results, investigation of interface distortions and modifications are performed on a graphics screen. Thus, various possible interpretations and velocity assumptions may be investigated within a short time. Interfaces interpreted on migrated sections may be over-migrated because of neglection of the influence of refraction in most section migration programs. This over-migration may also be corrected using the above algorithm in the “image ray” mode.     

CHOOSING THE AVERAGING INTERVAL WHEN CALCULATING PRIMARY REFLECTION COEFFICIENTS FROM WELL LOGS1

Most seismic data is processed using a sample interval of 4 ms two-way time (twt). The study of the statistical properties of primary reflection coefficients showed that the power spectrum of primaries can change noticeably when the logs are averaged over blocks of 0.5, 1 and 2 ms twt (block-averaging). What is a suitable block-averaging interval for producing broadband synthetics, and in particular how should the power spectrum of primaries be constructed when it is to be used to correct 4 ms sampled deconvolved seismic data for the effects of coloured primary reflectivity? In this paper we show that for a typical sonic log, a block-averaging interval of 1 ms twt should satisfy some important requirements. Firstly, it is demonstrated that if the reflection coefficients in an interval are not too large the effect of all the reflection impulses can be represented by another much sparser set at intervals of Δt twt, The coefficient amplitudes are given by the differences in the logarithmic acoustic impedances, thus justifying block-averaging. However, a condition for this to hold up to the aliasing (Nyquist) frequency is that Δt takes a maximum value of about 1 ms twt. Secondly, an event on a log should be represented in the seismic data. For this the acoustic impedance contrast must have sufficient lateral extent or continuity. By making some tentative suggestions on the relation between continuity and bed-thickness, a bed-thickness requirement of 0.15 m or more is obtained. Combining this requirement with the maximum number of beds allowable in an interval in order that multiple reflections do not contribute significantly to the reflections in the interval, again suggests a value of about 1 ms for the block-averaging interval. With this in mind an experiment was performed on three sonic logs. The logs were block-averaged at 1 ms, and primary reflection coefficients calculated. These primaries were then anti-alias filtered and resampled to get a series of primaries at 4 ms, followed by ARMA spectrum fitting. The same logs were also block-averaged at 4 ms directly and primaries computed, followed by ARMA spectrum fitting. In all three cases the first approach gave the ARM A model spectrum with greatest dynamic range, which strongly suggests that direct 4 ms block-averaging introduces significant aliased energy into low frequencies of the primaries spectrum. The conclusion is that routine computation of broadband synthetics (primaries only or primaries plus multiples) should be carried out using a block-averaging interval of 1 ms twt, followed by anti-alias filtering and thinning to the desired final sample interval. In theory it would be advantageous to go to even finer intervals-say 0.5 ms-but in practice at this level the averaging of slowness imposed by the somic logging tool appears to attenuate high-wave number fluctuations, i.e. it interferes with the‘real’data. The 1ms choice is thus a reasonable compromise which will help minimize non-trivial aliasing effects and should give better matches to the seismic data.     

岩石声学参数的实验测量及研究

通过对天然岩芯及人工岩芯的测量，研究２４０ｋＨｚ-１．ＳＭＨｚ频段内的声频散、温度对岩石声速的影响、岩石含水饱和度对岩石声速和声衰减的影响，给出岩石中声衰减与声波频率间关系的最佳拟合，并讨论了裂缝对岩石中声波传播的影响。     

Seismic velocities in complex media

Knowledge of seismic velocities in natural rock formations is needed for several purposes: converting travel-time to reflector depth, efficiently performing data processing such as common-midpoint (cmp) stacking and reflector migration, and finally studying lithofacies. When dip and faulting conditions are mild, all these goals can be reached without too much difficulty.Complex structures can be defined from a geophysicist's standpoint as being those which make it difficult or even impossible to conduct conventional processing operations, such as cmp stacking and post-stack migration. The principal reason for the difficulties encountered lies in the presence of lateral velocity variations strong enough to preclude the use of any processing procedure which would require hyperbolic time- distance curves on cmp trace gathers. This does not necessarily mean the presence of steep dips, but rather intense faulting that puts blocks of very different velocities in contact.Medium velocity can be estimated by using the redundancy of possible migration results. These results must be coherent from shotpoint to shotpoint or from one offset to another. If the velocity-model is unsatisfactory, it can be modified in order to give better coherence to migrated events. Travel-time tomography is another method for obtaining velocity-distributions, but for a successful application it assumes that reflected events can be picked and timed. Because tomography is an inverse method, it lends itself very easily to the introduction of outside information or of a priori constraints.Velocity investigation in complex regions is still in its infancy. Attempting to derive detailed and accurate information for lithofacies studies must be put aside for the time being, all efforts being concentrated obtaining the velocity needed to improve reflector imaging and positioning. Much progress is still necessary before 3-D, P and S velocity surveys can be conducted in all regions with complex geological structures.     

Linearized elastic parameter sections1

Contrasts in elastic parameters can be estimated directly from seismic data using offset-dependent information in the PP reflection coefficient. A linear approximation to the PP reflection coefficient including three coefficients is fitted to the data, and relative contrasts in various elastic parameters are obtained from linear combinations of the estimated coefficients. Linearized elastic parameter sections for the contrasts in P-wave impedance, P-wave velocity, density, plane-wave modulus, and the change in bulk modulus and shear modulus normalized with the plane-wave modulus are estimated. If the average P- to S-wave velocity ratio is known, linearized parameter sections including the contrast in the average P- to S-wave velocity ratio and a fluid factor section can be computed. Applied to synthetic data, visual comparison of the estimated and true elastic parameter sections agree qualitatively, and the results are confirmed by an analysis of the standard deviation of the estimated parameters. The parameter sections obtained by inversion of a shallow seismic anomaly in the Barents Sea are promising, but the reliability is uncertain because neither well data nor regional trends are available.     

Wavelet power spectrum analysis of heterogeneities from sonic velocity logs

The continuous wavelet transform (CWT) is used to evaluate local variations in the power-law exponents of sonic log data. The resulting wavelet spectrum can be compared with the corresponding global estimates obtained by conventional Fourier transform methods. In Fourier analysis, the fundamental tool used to characterize a fluctuating velocity distribution is the power spectrum. It represents the energy contained in each wavenumber and thus provides information regarding the importance of each scale of heterogeneity. However, important spatial information regarding the location of events becomes implicit in the phase angle of the Fourier transform. In this paper, it is shown how the square of the amplitude of the wavelet transform is related to the Fourier spectrum and how spatial information can be expressed in an explicit manner. Using the conservation of energy, it is shown that the average wavelet power spectrum over the total depth range is equal to the global power spectrum. A Gaussian wavelet is chosen to realize the wavelet transform. Two synthetic sonic logs with exponential and von Karman correlation functions are used to demonstrate the potential of the suggested analysis. Furthermore, the wavelet transform is applied to the KTB (Continental Deep Drilling Program) sonic log data. The wide range of applications of the CWT shows that this transform is a natural tool for characterizing the structural properties of underground heterogeneities. It offers the possibility of separating the multiscale components of heterogeneities.     

谐振Q理论井震匹配法及品质因子反演

储层勘测中地震波速度一般低于声波测井速度,撇开观测系统与人为因素造成的误差,岩石本征的黏弹性是造成这一现象的重要原因.本文在井、震匹配问题中引入了黏弹性岩石的杨氏谐振品质因子(Q)模型,对储层岩石进行了井震匹配与Q反演.文章阐述了如何通过谐振Q模型合理的校正声波速度,从而实现井震匹配.在波形匹配的基础上,进行地层品质因子的反演,合理的计算出目的层位的品质因子值.     

井间高分辨率纵横波层析成像研究井间油藏

采用视速度-偏振井间波场分离法分离得到纵波和横波波场,使用跨孔地震走时层析成像级联方法计算井间纵波和横波速度结构以及泊松比空间分布.综合纵横波速度、泊松比和测井参数,分析两井间岩性和储层特性.数值模型试验表明该方法垂直分辨率达到主频波长的1/4,并能准确分辨倾斜断层和垂直断层.处理相同纵波资料结果表明本文方法分辨率远远高于以往的井间走时层析成像方法,比井间声波层析成像分辨率更高.使用该方法处理垦71区井间资料,得到同台同源纵波和横波速度结构和泊松比分布.泊松比的低/高变化与测井参数指示的砂/泥岩层基本吻合.根据泊松比分布,参考岩石地震物理学测试数据,可以区分井间介质中的泥岩层、砂岩层,以及砂岩层中的饱水和饱油区,确定储层的连通性,圈定井间的剩余油藏.     

基于倾角-偏移距域道集的绕射波成像

地震绕射波是地下非连续性地质体的地震响应,绕射波成像对地下断层、尖灭和小尺度绕射体的识别具有重要的意义.在倾角域共成像点道集中,反射波同相轴表现为一条下凸曲线,能量主要集中在菲涅耳带内,绕射波能量则比较发散.由于倾角域菲涅耳带随偏移距变化而存在差异,因此本文提出一种在倾角-偏移距域道集中精确估计菲涅耳带的方法,在各偏移距的倾角域共成像点道集中实现菲涅耳带的精确切除,从而压制反射波.在倾角-偏移距域道集中还可以分别实现绕射波增强,绕射波同相轴相位校正,因此能量弱的绕射波可以清晰地成像.在倾角域共成像点道集中,反射波同相轴的最低点对应于菲涅耳带估计所用的倾角,因此本文提出一种在倾角域共成像点道集中直接自动拾取倾角场的方法.理论与实际资料试算验证了本文绕射波成像方法的有效性.     

TIME MIGRATION—SOME RAY THEORETICAL ASPECTS*

Using an elementary theory of migration one can consider a reflecting horizon as a continuum of scattering centres for seismic waves. Reflections arising at interfaces can thus be looked upon as the sum of energy scattered by interface points. The energy from one point is distributed among signals upon its reflection time surface. This surface is usually well approximated by a hyperboloid in the vicinity of its apex. Migration aims at focusing the scattered energy of each depth point into an image point upon the reflection time surface. To ensure a complete migration the image must be vertical above the depth point. This is difficult to achieve for subsurface interfaces which fall below laterally in-homogeneous velocity media. Migration is hence frequently performed for these interfaces as well by the Kirchhoff summation method which systematically sums signals into the apex of the approximation hyperboloid even though the Kirchhoff integral is in this case not strictly valid. For a multilayered subsurface isovelocity layer model with interfaces of a generally curved nature this can only provide a complete migration for the uppermost interface. Still there are various advantages gained by having a process which sums signals consistently into the minimum of the reflection time surface. The position of the time surface minimum is the place where a ray from the depth point emerges vertically to the surface. The Kirchhoff migration, if applied to media with laterally inhomogeneous velocity, must necessarily be followed by a further time-to-depth migration if the true depth structure is to be recovered. Primary normal reflections and their respective migrated reflections have a complementary relationship to each other. Normal reflections relate to rays normal to the reflector and migrated reflections relate to rays normal to the free surface. Ray modeling is performed to indicate a new approach for simulating seismic reflections. Commonly occuring situations are investigated from which lessons can be learned which are of immediate value for those concerned with interpreting time migrated reflections. The concept of the ‘image ray’ is introduced.     

Azimuthal anisotropy analysis of walkaround vertical seismic profiling vertical seismic profiling: a case study from Saudi Arabia

Understanding fracture orientations is important for optimal field development of fractured reservoirs because fractures can act as conduits for fluid flow. This is especially true for unconventional reservoirs (e.g., tight gas sands and shale gas). Using walkaround Vertical Seismic Profiling (VSP) technology presents a unique opportunity to identify seismic azimuthal anisotropy for use in mapping potential fracture zones and their orientation around a borehole. Saudi Aramco recently completed the acquisition, processing and analysis of a walkaround VSP survey through an unconventional tight gas sand reservoir to help characterize fractures. In this paper, we present the results of the seismic azimuthal anisotropy analysis using seismic traveltime, shear‐wave splitting and amplitude attenuation. The azimuthal anisotropy results are compared to the fracture orientations derived from dipole sonic and image logs. The image log interpretation suggests that an orthorhombic fracture system is present. VSP data show that the P‐wave traveltime anisotropy direction is NE to SW. This is consistent with the cemented fractures from the image log interpretation. The seismic amplitude attenuation anisotropy direction is NW to SE. This is consistent with one of the two orientations obtained using transverse to radial amplitude ratio analysis, with the dipole sonic and with open fracture directions interpreted from image log data.     

CALCULATION OF VELOCITY FROM SEISMIC REFLECTION AMPLITUDE *

It is not possible to determine accurate geological velocities from seismic velocity analysis for thin layers or complex structural features, especially under an unconformity. Instead, we can approach the problem of interval velocity with seismic amplitudes analysis and compute the reflection coefficient along the unconformity surface. An error estimation has been made on a model to test the possibility of such a method and to choose the best parameters to be used. The method has been applied on an actual case: the computed interval velocities show good correlation with the values obtained by a sonic log.