THE SECTIONAL AUTO-CORRELOGRAM AND THE SECTIONAL RETRO-CORRELOGRAM *

The auto-correlation function of a seismic trace contains information on all the multiple reflection activity present in the trace. The interpretation of this information is facilitated by the arrangement of autocorrelation functions in cross-sectional form, in the manner of a normal record section. This is the concept of the Sectional Auto-Correlogram. Specifically, the Sectional Auto-Correlogram will. Show if the record section does not include significant multiples, thus allowing confident picking of the primary reflections. Show if the record section does include significant multiples, giving their travel times and inclinations (and, under certain circumstances, their reflection coefficients). Indicate by what process the multiples should be treated. Yield an authoritative measure of the success of a multiple-attenuating treatment. Delineate shallow horizons, even those whose primary reflections are too early to be recorded satisfactorily. Give the true travel time of a primary reflector, and the sign of its reflection coefficient. The Sectional Auto-Correlogram allows the study of primary reflectors by consideration of the multiples generated by them, and in this sense may be said to turn multiple reflections to advantage. Thus a primary reflection at a certain time is defined if we find that every reflection on the record is followed by a multiple after this certain time. Alternatively, a primary reflection at a certain time is defined if, after that certain time, we can find a repetition of the entire record. The Sectional Auto-Correlogram also has secondary uses in fault identification, crustal studies and weathering problems.     

地震多次波成像

地震资料含有各种类型多次波,而传统成像方法仅利用地震一次反射波成像,在地震成像前需将多次波去除.然而,多次波携带了丰富的地下结构信息,多次波偏移能够提供除反射波外的额外地下照明.修改传统逆时偏移方法,用包含一次反射波和多次波的原始记录代替震源子波,将SRME方法预测的表面多次波代替一次反射波作为输入数据,可将表面多次波成像.多次波成像的挑战和困难在于大量串扰噪声的产生,针对表面多次波成像中的成像噪声问题,将最小二乘逆时偏移方法与多次波分阶思想结合起来,发展可控阶数的表面多次波反演成像方法,有望初步实现高精度的表面多次波成像.在消除原始记录中的表面多次波后,通过逆散射级数方法预测得到层间多次波,将层间多次波作为逆时偏移方法的输入数据可将其准确归位到地下反射位置.数值实验表明,多次波成像能够有效地为地下提供额外照明,而可控阶表面多次波最小二乘逆时偏移成像方法几乎完全避免成像噪声.     

基于波射线路径偏移压制多次波

波射线路径压制多次波的反射波成像是在偏移过程去除多次波同时仅对反射波成像.通过在共炮道集和共检波点道集分别计算炮点射线的入射角和检波点射线的出射角计算射线的路径.从炮点入射的射线与从检波点出射的射线的交点形成的走时,若等于观测走时,可以判断此条射线是反射波;反之,若不相等,则是多次波.数值实验表明此方法可以有效地去掉由于多次波能量产生的假成像点和压制多次波,因此界面可以正确归位,同时去掉由于多次波引起的假成像位置.     

Subcrustal Low Velocity Layers in Central India and their Implications

A 2-D subcrustal velocity model for the central Indian continental lithosphere has been derived by travel time and relative amplitude modeling of a digitally normalized analog seismic record section of the Hirapur-Mandla DSS profile, using a ray-tracing technique. Some prominent wave groups with apparent velocities slightly higher than the Moho reflection phase (P_MP) are identified on the normalized record sections assembled with a reduction velocity of 6 km s⁻¹. We interpret these phases as the wide-angle reflections from subcrustal lithospheric boundaries. Comparison of synthetic seismograms with the observed record section shows that the observed phases cannot be explained either by multiples or by the P-to-S converted phase (P_MS) from the Moho. Subcrustal velocity models either with a velocity increase or with a single low velocity layer (LVL) also do not provide a satisfactory fit. We infer that a subcrustal velocity model with two alternate LVLs (velocity 7.2 km s⁻¹), separated by a 6-km thick high velocity layer (velocity 8.1 km s⁻¹), can satisfy both the observed travel times and amplitudes. The prominent reflection phases are modeled at depths of 49, 51, 57 and 60 km. It is inferred that the subcrustal lithosphere in the central Indian region has a lamellar structure with varying structural and mechanical properties. The alternating LVLs, occurring at relatively shallow depths below Moho, may be associated with the zones of weakness and lower viscosity suggesting continued mobility, with a possible thermal source in the upper mantle. This explains the source of observed high heat flow values in the central Indian region.     

Migration of multiples from the South China Sea

The South China Sea where water depth is up to 5000 m is the most promising oil and gas exploration area in China in the future.The seismic data acquired in the South China Sea contain various types of multiples that need to be removed before imaging can be developed.However,compared with the conventional reflection migration,multiples carry more information of the underground structure that helps provide better subsurface imaging.This paper presents a method to modify the conventional reverse time migration so that multiple reflections can migrate to their correct locations in the subsurface.This approach replaces the numerical impulsive source with the recorded data including primaries and multiples on the surface,and replaces the recorded primary reflection data with multiples.In the reverse time migration process,multiples recorded on the surface are extrapolated backward in time to each depth level,while primaries and multiples recorded on the surface are extrapolated forward in time to the same depth levels.By matching the difference between the primary and multiple images using an objective function,this algorithm improves the primary resultant image.Synthetic tests on Sigsbee2 B show that the proposed method can obtain a greater range and better underground illumination.Images of deep water in the South China Sea are obtained using multiples and their matching with primaries.They demonstrate that multiples can make up for the reflection illumination and the migration of multiples is an important research direction in the future.     

SLOPE DATA WATER-BOTTOM MULTIPLE ATTENUATION1

Methods for predicting and attenuating water-bottom multiples by wavefield extrapolation have been discussed by several investigators. Because these prediction methods operate on shot records, boundary conditions must be specified for every shot record. The approach presented operates in the common-offset plane; a model of expected water-bottom multiples is generated from the observed surface wavefield using a finite-difference wave-equation migration algorithm with an offset term. An accurate water-depth profile is required, but there is no restriction on the shape of the water bottom other than a dip limit of approximately 18–20°. In generating a multiple model, the water-bottom primary and each water-bottom multiple reflection of the observed surface wavefield are extrapolated to a higher order. Thus, the extrapolated water-bottom primary of the model is lined up with a water-bottom multiple in the data and each multiple in the model is lined up with a higher-order (or later) multiple in the data. Prestack multiple attenuation is achieved, for one offset at a time, by first adapting the model of expected multiples to the observed data and then subtracting the predicted multiple energy. An error-constrained adaptation algorithm is proposed in order to control instabilities. No assumptions are made about primary reflections and no subwater-bottom velocities are required. Computational efficiency of modelling and adaptation can be improved by applying this method only to near and intermediate offsets as the stacking process usually provides sufficient multiple attenuation at far offsets. A field data example demonstrates the potential of the proposed method for improving the primary-to-multiple ratio in prestack and post-stack data.     

ACOUSTIC MODELING OF THE SEAFLOOR*

Data from routine seismic surveys contain considerable information about the geo-acoustic properties of the seafloor. Waves are reflected at a wide range of angles of incidence from near-vertical reflections (higher multiples) to supercritical reflections (primary and lower multiples). The reflection coefficient is approximately constant for small angles of incidence (< 10°) but varies greatly for larger angles of incidence. Near-vertical reflections are used to determine the seafloor density. The P-velocity in the seafloor is determined in advance from the critical distance using the amplitude variation of the primary as well as the multiples. The V_p/V_S ratio is determined by modeling the amplitude variation with the angle of incidence. The primary reflection from the seafloor and the first three multiples are included in the modeling. Seismic data obtained with both conventional and superlong airgun arrays have been modeled. Data collected from the Barents Sea show that even if the P-velocity is the same at different sites, the V_p/V_s ratio, density and Poisson's ratio vary significantly. The most extreme example shows that for a P-velocity of 2.80 km/s the V_p/V_s ratio varies between 1.9 and 6.0. The corresponding densities vary from 2.36 g/cm³ to 1.80 g/cm³ and the Poisson's ratio varies from 0.31 to 0.49. The acoustic modeling offers a method of assessing the mean geotechnical or mechanical properties of larger volumes of marine sediments in terms of incompressibility, shear modulus and Poisson's ratio.     

波路径偏移压制层间多次波的理论与应用

消除层间多次波是地震勘探资料处理研究领域的难题,尤其对于实际资料的处理,到目前为止还很难找到一种完全有效的方法. 本文给出了仅对一次波成像既波路径偏移方法压制层间多次波方法,在共炮道集和共检波点道集分别计算炮点射线的入射角和检波点射线的出射角,由此计算的角度作为射线追踪的初始角度,计算地震波射线的传播路径. 结合由程函方程计算的走时表,判断偏移范围是反射波还是多次波. 在前期偏移过程压制多次波的理论研究基础上,本文主要研究波路径偏移消除多次波的应用部分. 为了进一步说明效果的有效性,计算了在单炮和共成像点道集压制层间多次波,给出了实际资料的压制多次波的偏移结果.     

Estimating primaries by sparse inversion of the 3D curvelet transform and the L1-norm constraint

In this paper, we built upon the estimating primaries by sparse inversion (EPSI) method. We use the 3D curvelet transform and modify the EPSI method to the sparse inversion of the biconvex optimization and L1-norm regularization, and use alternating optimization to directly estimate the primary reflection coefficients and source wavelet. The 3D curvelet transform is used as a sparseness constraint when inverting the primary reflection coefficients, which results in avoiding the prediction subtraction process in the surface-related multiples elimination (SRME) method. The proposed method not only reduces the damage to the effective waves but also improves the elimination of multiples. It is also a wave equationbased method for elimination of surface multiple reflections, which effectively removes surface multiples under complex submarine conditions.     

IS IT POSSIBLE TO INCREASE THE RESOLUTION IN SEISMIC EXPLORATION FOR COAL BY USING HIGH FREQUENCY SIGNALS?*

In seismic exploration for coal data resolution is a fundamental problem. Modeling helps to understand those details of the geology that can be interpreted from the seismic image. For single seam exploration, the vertical resolution of a seismic section is defined by the bandwidth of the signals. If there are several seams, each seam acts as a high-pass filter for reflections and as a low-pass filter for transmitted waves. Synthetic seismograms show that reflections from deep seams have a low frequency content. Within a layered sequence of coal seams, many multiples are generated which disturb later primary reflections. The ratio of primaries to multiples depends on the frequency content of the seismic data and on the number of overlying seams. The multiple problem is more severe with high frequencies. Primary reflections from deep coal seams within a sequence can be detected only if low-frequency signals are used. However, the use of low-frequency signals reduces the resolution of the deeper data.     

Source wavelet correction for practical Marchenko imaging: A sub-salt field-data example from the Gulf of Mexico

Imaging a target zone below a salt body can be challenging because large velocity contrasts in the overburden between the salt and surrounding sediments generate internal multiples, which interfere with primary reflections from the target level in the imaging process. This can lead to an erroneous interpretation of reflections in the sub-salt area if multiples are misinterpreted as primaries. The Marchenko redatuming method may enable imaging of the sub-salt target area where the effect of the multiply-scattering overburden is removed. This is achieved by creating a redatumed reflection response where virtual sources and receivers are located below the overburden using a macromodel of the velocity field and the surface reflection data. The accuracy of the redatumed data and the associated internal multiple removal, however, depends on the accurate knowledge of the source wavelet of the acquired reflection data. For the first time, we propose a method which can accurately and reliably correct the amplitudes of the reflection response in field data as required by the Marchenko method. Our method operates by iteratively and automatically updating the source function so as to cancel the most artefact energy in the focusing functions, which are also generated by the Marchenko method. We demonstrate the method on a synthetic dataset and successfully apply it to a field dataset acquired in a deep-water salt environment in the Gulf of Mexico. After the successful source wavelet estimation for the field dataset, we create sub-salt target-oriented images with Marchenko redatumed data. Marchenko images using the proposed source wavelet estimation show clear improvements, such as increased continuity of reflectors, compared to surface-based images and to conventional Marchenko images computed without the inverted source wavelet. Our improvements are corroborated by evidence in the literature and our own synthetic results.     

A NEW METHOD OF CANCELLING MULTIPLE REFLECTIONS: “SOUSTON”*

Cancelling of multiple reflections by CDP stacking is generally incomplete. When the order of coverage is low, an improvement may be obtained by the use of special filters (e.g. Schneider et al: Geophysics 1965; D'Hoeraene: Geophysics 1966). But when the order of coverage is high, the efficiency of these filters is less obvious. On the other hand, the higher the order of coverage, the higher the efficiency in the solution presented. Schematically, our method includes three steps: Firstly: Searching for the multiple reflections. For this purpose Move Out corrections corresponding to the multiples are applied to each individual record, then CDP stacking is carried out. Secondly: Cleaning up of the individual records. “Decorrections” are firstly applied, then multiples are subtracted. For this, subtraction is weighed versus the energy of the multiples, that is to say versus the correlation between the original record and the pure multiple reflections. Thirdly: Normal processing with the cleaned records which have been obtained. The different steps of this method are illustrated with the help of theoretical examples. Its efficiency improvement in regard to normal CDP stacking is then demonstrated by means of true examples.     

Sub-B″ layering in the Southern Caribbean: The Aruba Gap and Venezuela Basin

Multichannel seismic data in the Aruba Gap region near JOIDES/DSDP Site 153 verify the presence of a deep sub-B″ reflection. One multichannel seismic line trends NE-SW on and along the edge of Beata Ridge and passes within 1 km of Site 153, and another line runs N-S across the entire Aruba Gap with the drill site 4 km east from its northern end. Closely spaced velocity analyses indicate the presence of deep primary reflection events and enable calculation of interval velocities between the A″-B″ marker horizons. Deconvolved, true amplitude, normal incidence profiles sharply delineate the A″-B″ marker horizons and indicate the presence of the sub-B″ reflection event. On the NE-SW line, this deep reflector is best described as a “diffuse” discontinuous zone, relatively horizontal, lying about 0.8 seconds of two-way travel time below the B″ reflector, with an interval velocity of approximately 5.0 km/s between Horizon B″ and this reflection. The N-S line is more complex since the sub-B′' reflection event is masked by a strong internal multiple from the A″-B″ interval. In the central and western Venezuela Basin, deep primary reflections beneath Horizon B″ are also observed on the northern and western sides of what appears to be a major fault zone. This fault zone separates the smooth B″ and sub-B″ reflectors on the northern and western sides of this fault zone from what appears to be typical oceanic basement. The widespread presence of sub-B″ reflections yielding high interval velocities for the section between these events and Horizon B″ suggest that this material is probably igneous in origin.     

Migration methods for imaging different-order multiples

Multiples contain valuable information about the subsurface, and if properly migrated can provide a wider illumination of the subsurface compared to imaging with VSP primary reflections. In this paper we review three different methods for migrating multiples. The first method is model-based, and it is more sensitive to velocity errors than primary migration; the second method uses a semi-natural Green's function for migrating multiples, where part of the traveltimes are computed from the velocity model, and part of the traveltimes (i.e., natural traveltimes) are picked from the data to construct the imaging condition for multiples; the third method uses cross-correlation of traces. The last two methods are preferred in the sense that they are significantly less sensitive to velocity errors and statics because they use “natural data” to construct part of the migration imaging conditions. Compared with the interferometric (i.e., crosscorrelation) imaging method the semi-natural Green's function method is more computationally efficient and is sometimes less prone to migration artifacts. Numerical tests with 2-D and 3-D VSP data show that a wider subsurface coverage, higher-fold and more balanced illumination of the subsurface can be achieved with multiple migration compared with migration of primary reflections only. However, there can be strong interference from multiples with different orders or primaries when multiples of high order are migrated. One possible solution is to filter primaries and different orders of multiples before migration, and another possible solution is least squares migration of all events. A limitation of multiple migration is encountered for subsalt imaging. Here, the multiples must pass through the salt body more than twice, which amplifies the distortion of the image.     

LONG PERIOD SEA-FLOOR MULTIPLES AND THEIR SUPPRESSION*

Multiple sea-floor reflections in deep water often are not effectively suppressed by either CDP stacking nor standard predictive deconvolution methods. These methods fail because the reflection coefficient varies markedly with angle of incidence and also because of the variation of arrival time with offset and because of dip. For a reasonablly flat sea-floor, multiples of various orders and the primary sea-floor reflection which have all been reflected at nearly the same angle lie along a straight line through the origin in time-offset space. This line is called the “radial direction.” The multiples which lie along this line show a systematic relationship because they all experience the same water-bottom reflection effect. In other words, multiples behave in a stationary manner along the radial directions on multi-trace seismic records. A technique of multi-channel predictive deconvolution, called “Radial Multiple Suppression,” utilizes this aspect to design Wiener operators for the prediciton and suppression of water bottom multiples. The effectiveness of the technique is demonstrated by the study of field records, autocorrelations, velocity analyses, and stacked sections before and after Radial Multiple Suppression processing.     

MULTIPLE REFLECTIONS AND HEAD WAVES IN THE GULF OF SUEZ*

Inferior reflection quality in the Gulf of Suez at the target depth interval is attributable in part to surficial multiple reflections. An excellent example of the latter is observed on a typical seismic line in the northern portion of the Gulf. An increase in prominence of the multiple reflections appears associated with decreasing depth to a dipping highvelocity layer. Inversion of a second-order polynomial time-distance function, fitted to the observed refraction onset time-distance values, gives the velocity-depth function for sediments between the water bottom and a high-velocity layer. Velocities thus determined increase non-linearly with depth from a value near water velocity at the water bottom. Depths to the high-velocity layer are obtained from the associated head-wave linear time-distance function and by ray tracing in the overlying sediments. As the high-velocity layer approaches the water bottom from sub-water depths exceeding 0.6 km to a depth of 56 m, intensity of the multiple reflections increases to the extent of completely dominating individual records to a time of at least 3 s. The estimated plane-wave normal-incident reflection coefficient at the top of the high-velocity layer increases with decreasing depth to this layer, approaching 0.5 at the shallowest depth. This strong reflection coefficient further substantiates the existence of multiple reflections between the high-velocity layer and water layer. However, existence of water-layer multiples cannot be ruled out. The estimated water-bottom reflection coefficient is approximately 0.3, a substantial value. Multiple reflections of considerably less intensity are apparent where the high-velocity layer is deepest, and it is likely that such are waterlayer multiple reflections. Unfortunately, water-layer multiple reflections and multiple reflections between the water surface and high-velocity layer cannot be separated by their coincidence with time-distance (normal moveout) curves, the configuration of each visibly matching the curves equally well.     

A procedure to reduce side lobes of reflection wavelets: A contribution to low frequency information

Side lobes of the wavelets arise from the lack of low frequency content in a reflection wavelet. They tend to increase the time span of an individual reflection event and interfere with the other primary reflections or side lobes. Furthermore, their trace-by-trace consistency may produce pseudo-reflections and may cause misinterpretations of the side lobes as weak reflections.A procedure in order to improve the low frequency content of the seismic traces by suppressing the side lobe amplitudes based on the complex trace envelope is proposed. Using the average energies of the seismic trace and its envelope, the polarity table of the trace is obtained and used to correct the phase of the envelope. The resultant trace is termed “side lobe reduced (SLR) trace”. The method can be applied to the stack or migrated seismic data by a trace-by-trace basis. The only required parameter of the method is the moving average operator length which is used to calculate average energies of the input traces. In general, shorter operator lengths yield better results when the dominant frequency of the input increases.Results from synthetics and real seismic data sets show that the procedure improves the low frequency components of the input trace and side lobes in the output SLR trace are significantly suppressed. The method may be considered as a seismic amplitude attribute, which aids the interpreter to obtain the true seismic signature of the geological formations by removing the side lobes of the wavelet and restoring the low frequency components if the lower frequencies of deeper reflections are of primary concern.     

HORIZONTAL STACKING AND MULTICHANNEL FILTERING APPLIED TO COMMON DEPTH POINT SEISMIC DATA*

The common depth point method of shooting in oil exploration provides a series of seismic traces which yield information about the substrata layers at one location. After normal moveout and static corrections have been applied, the traces are combined by horizontal stacking, or linear multichannel filtering, into a single record in which the primary reflections have been enhanced relative to the multiple reflections and random noise. The criterion used in optimum horizontal stacking is to maximize the signal to noise power ratio, where signal refers to the primary reflection sequence and noise includes the multiple reflections. It is shown when this criterion is equivalent to minimizing the mean square difference between the desired signal (primary reflection sequence) and the weighted horizontally stacked traces. If the seismic traces are combined by multichannel linear filtering, the primary reflection sequence will have undergone some phase and frequency distortion on the resulting record. The signal to noise power ratio then becomes less meaningful a criterion for designing the optimum linear multichannel filter, and the mean square criterion is adopted. In general, however, since more a priori information about the seismic traces is required to design the optimum linear multichannel filter than required for the optimum set of weights of the horizontal stacking process, the former will be an improvement over the latter. It becomes evident that optimum horizontal stacking is a restricted form of linear multichannel filtering.     

HORIZONTAL STACKING AND MULTICHANNEL FILTERING APPLIED TO COMMON DEPTH POINT SEISMIC DATA*

The common depth point method of shooting in oil exploration provides a series of seismic traces which yield information about the substrata layers at one location. After normal moveout and static corrections have been applied, the traces are combined by horizontal stacking, or linear multichannel filtering, into a single record in which the primary reflections have been enhanced relative to the multiple reflections and random noise. The criterion used in optimum horizontal stacking is to maximize the signal to noise power ratio, where signal refers to the primary reflection sequence and noise includes the multiple reflections. It is shown when this criterion is equivalent to minimizing the mean square difference between the desired signal (primary reflection sequence) and the weighted horizontally stacked traces. If the seismic traces are combined by multichannel linear filtering, the primary reflection sequence will have undergone some phase and frequency distortion on the resulting record. The signal to noise power ratio then becomes less meaningful a criterion for designing the optimum linear multichannel filter, and the mean square criterion is adopted. In general, however, since more a priori information about the seismic traces is required to design the optimum linear multichannel filter than required for the optimum set of weights of the horizontal stacking process, the former will be an improvement over the latter. It becomes evident that optimum horizontal stacking is a restricted form of linear multichannel filtering.