Borehole study of compressional and shear attenuation of basalt flows penetrated by the Brugdan and William wells on the Faroes shelf

We investigated the seismic attenuation of compressional (P‐) and converted shear (S‐) waves through stacked basalt flows using short‐offset vertical seismic profile (VSP) recordings from the Brugdan (6104/21–1) and William (6005/13–1A) wells in the Faroe‐Shetland Trough. The seismic quality factors (Q) were evaluated with the classical spectral ratio method and a root‐mean‐square time‐domain amplitude technique. We found the latter method showed more robust results when analysing signals within the basalt sequence. For the Brugdan well we calculated effective Q estimates of 22–26 and 13–17 for P‐ and S‐waves, respectively, and 25–33 for P‐waves in the William well. An effective Q_S/Q_P ratio of 0.50–0.77 was found from a depth interval in the basalt flow sequence where we expect fully saturated rocks. P‐wave quality factor estimates are consistent with results from other VSP experiments in the North Atlantic Margin, while the S‐wave quality factor is one of the first estimates from a stacked basalt formation using VSP data. Synthetic modelling demonstrates that seismic attenuation for P‐ and S‐waves in the stacked basalt flow sequence is mainly caused by one‐dimensional scattering, while intrinsic absorption is small.     

Estimating permeability from field measurements of seismic attenuation in fractured chalk

Broadband (100–4000 Hz) cross‐hole seismic data have been acquired at a borehole test site where extensive hydrological investigations have previously been performed, including in situ estimates of permeability. The rock type is homogeneous chalk and fractures and bedding planes have been identified from well logs. High values of seismic attenuation, Q= 22 ≤ 27 ≤ 33, were observed over a 10 m depth interval where fracture permeability values of 20–50 darcy had been recorded. An attempt has been made to separate the attenuation due to scattering and intrinsic mechanisms. The estimated values of intrinsic attenuation, Q= 31 ≤ 43 ≤ 71, have been reproduced using a number of current theories of seismic‐wave propagation and fluid‐flow‐induced seismic attenuation in cracked and fractured media. A model that considers wavelength‐scale pressure gradients is the preferred attenuation mechanism. Model parameters were obtained from the hydro‐geological and seismic data. However, we conclude that it is not possible to use seismic Q to measure rock permeability remotely, principally because of the inherent uncertainties arising from model parameterisations.     

Seismicity and codaQ values in the eastern Pyrenees: First results from the La Cerdanya seismic network

Seismicity in the La Cerdanya region of the eastern Pyrenees has been accurately mapped for the first time using data from a local seismic network. The majority of earthquakes lies on or near the La Cerdanya fault or secondary faults to the south. Coda magnitudes determined for these earthquakes, using magnitude relations from other regions, range between –0.5 and 2.2. These are, however, presumed to be underdetermined values sinceQ values appear to be very low in the La Cerdanya region. CodaQ values at a frequency of 1.5 Hz range between 17 and 120, the lowest values being obtained for the most seismically active regions. CodaQ values also increase with increasing distance, a result which indicates decreasing seismic attenuation with increasing depth in the crust.     

Tomographic joint inversion of first arrivals in a real case fromSaudi Arabia

A joint inversion of both first and refracted arrivals is applied on a seismic line, acquired onshore, in order to obtain a well‐resolved velocity field for the computation of static corrections. The use of different arrivals in the inversion involves exploiting the information derived from the different raypaths associated with each wave type, thus enhancing the reliability of the inversion. The data was gathered by Saudi Aramco in an area of the Arabian Peninsula characterized by strong lateral variations, both in topography and shallow velocity, and where therefore a well‐defined near‐surface velocity field is important. In addition to velocity, the depth distribution of the quality factor Q is computed from the tomographic inversion of the seismic‐signal frequency shift. Thus, the Q‐factor field is used to perform an inverse Q‐data filtering and improve the resolution of the final stacked section.     

Multiwell study of seismic attenuation at the CO2CRC Otway project geosequestration site: Comparison of amplitude decay,centroid frequency shift and 1D waveform inversion methods

At the CO2CRC Otway geosequestration site, the abundance of borehole seismic and logging data provides a unique opportunity to compare techniques of Q (measure of attenuation) estimation and validate their reliability. Specifically, we test conventional time-domain amplitude decay and spectral-domain centroid frequency shift methods versus the 1D waveform inversion constrained by well logs on a set of zero-offset vertical seismic profiles. The amplitude decay and centroid frequency shift methods of Q estimation assume that a seismic pulse propagates in a homogeneous medium and ignore the interference of the propagating wave with short-period multiples. The waveform inversion explicitly models multiple scattering and interference on a stack of thin layers using high-resolution data from sonic and density logs. This allows for stable Q estimation in small depth windows (in this study, 150 m), and separation of the frequency-dependent layer-induced scattering from intrinsic absorption. Besides, the inversion takes into account band-limited nature of seismic data, and thus, it is less dependent on the operating frequency bandwidth than on the other methods. However, all considered methods of Q estimation are unreliable in the intervals where subsurface significantly deviates from 1D geometry. At the Otway site, the attenuation estimates are distorted by sub-vertical faults close to the boreholes. Analysis of repeated vertical seismic profiles reveals that 15 kt injection of the CO₂-rich fluid into a thin saline aquifer at 1.5 km depth does not induce detectable absorption of P-waves at generated frequencies 5–150 Hz, most likely because the CO₂ plume in the monitoring well is thin, <15 m. At the Otway research site, strong attenuation Q ≈ 30–50 is observed only in shaly formations (Skull Creek Mudstone, Belfast Mudstone). Layer-induced scattering attenuation is negligible except for a few intervals, namely 500–650 m from the surface, and near the injection interval, at around 1400–1550 m, where Q_scat ≈ 50–65.     

大同地震窗P波频散衰减的异常变化特征

通过测量介质品质因子来开展大同窗附近测震台站记录P波衰减频散特征的研究,并分析大同窗近场区和外围区震例前后的变化。对山自皂台记录的2001年以来大同窗地震序列的研究结果表明,近场区3次和外围区6次地震前,介质品质因子显示超出1倍均方差的高值变化特征,震后逐渐恢复到背景起伏状态;与大同窗传统的频次指标相比,介质品质因子的映震效果更好;阳原台的结果表明,仅近场区1次和外围区2次地震前,介质品质因子显示超出1倍均方差的高值变化特征,且有虚报、漏报。所处地质构造位置不同、传播路径介质差异可能是引起上述两个台站附近介质品质因子的地震对应效果明显不同的原因。     

Anisotropic P-wave attenuation measured from a multi-azimuth surface seismic reflection survey

A system of aligned vertical fractures produces azimuthal variations in stacking velocity and amplitude variation with offset, characteristics often reported in seismic reflection data for hydrocarbon exploration. Studies of associated attenuation anisotropy have been mostly theoretical, laboratory or vertical seismic profiling based. We used an 11 common‐midpoint‐long portion of each of four marine surface‐seismic reflection profiles, intersecting each other at 45° within circa 100 m of a common location, to measure the azimuthal variation of effective attenuation, Q⁻¹_eff and stacking velocity, in a shallow interval, about 100 m thick, in which consistently orientated vertical fracturing was expected due to an underlying salt diapirism. We found qualitative and quantitative consistency between the azimuthal variation in the attenuation and stacking velocity, and published amplitude variation with offset results. The 135° azimuth line showed the least apparent attenuation (1000 Q⁻¹_eff= 16 ± 7) and the fastest stacking velocity, hence we infer it to be closest to the fracture trend: the orthogonal 45° line showed the most apparent attenuation (1000Q⁻¹_eff= 52 ± 15) and slowest stacking velocity. The variation of Q⁻¹_eff with azimuth φ is well fitted by 1000Q⁻¹_eff = 34 − 18cos[2(φ+40°)] giving a fracture direction of 140 ± 23° (±1SD, derived from ‘bootstrapping’ fits to all 11⁴ combinations of individual common‐midpoint/azimuth measurements), compared to 134 ± 47° from published amplitude variation with offset data. The effects of short‐window spectral estimation and choices of spectral ratio bandwidth and offset ranges used in attenuation analysis, individually give uncertainties of up to ±13° in fracture direction. This magnitude of azimuthal variation can be produced by credible crack geometries (e.g., dry cracks, radius 6.5 m, aspect ratio 3 × 10⁻⁵, crack density 0.2) but we do not claim these to be the actual properties of the interval studied, because of the lack of well control (and its consequences for the choice of theoretical model and host rock physical properties) and the small number of azimuths available here.     

Source/receiver array directivity effects on marine seismic attenuation measurements

Attenuation of seismic waves, quantified by the seismic quality factor Q, holds important information for seismic interpretation, due to its sensitivity to rock and fluid properties. A recently published study of Q, based on surface seismic reflection data, used a modified spectral ratio approach (QVO), but both source and receiver responses were treated as isotropic, based on simple raypath arguments. Here, this assumption has been tested by computing apparent attenuation generated by frequency-dependent directivity of typical marine source and receiver arrays and acquisition geometries. Synthetic wavelet spectra were computed for reflected rays, summed over the first Fresnel zone, from the base of a single interval, 50–3000 m thick and velocity 2000 m/s, overlying a 2200 m/s half-space, and for offsets of 71–2071 m. The source and receiver geometry were those of an actual survey. The modelled spectra are clearly affected by directivity, most strongly because of surface ghosts. In general, the strong high-frequency component, produced by the array design, leads to apparently negative attenuation in individual reflection events, though this is dependent on offset and target depth. For shallow targets (less than 400–500 ms two-way traveltime (TWT) depth), apparent Q-values as extreme as ?50 to ?100 were obtained. For deeper target depths, the directivity effect is far smaller. The implications of the model study were tested on real data. QVO was applied to 20 true-spectrum-processed CMPs, in a shallow (405–730 ms TWT) and a deeper (1000–1300 ms TWT) interval, firstly using a measured far-field source signature (effectively isotropic), and secondly using computed directivity effects instead. Mean interval Q^?1-values for the deeper interval, 0.029 ± 0.011 and 0.027 ± 0.018 for conventional and directional processing, respectively, suggested no directivity influence on attenuation estimation. For the shallow interval (despite poor spectral signal-to-noise ratios and hence scattered attenuation estimates), directional processing removed directivity-generated irregularities from the spectral ratios, resulting in an improvement from Q^?1_int = ?0.036 ± 0.130 to a realistic Q^?1_int = 0.012 ± 0.030: different at 94% confidence level. Equivalent Q-values are: for the deeper interval, 35 and 37 for conventional and directional processing, respectively, and ?28 and 86 for the shallow interval. These results support the conclusions of the model studies, i.e. that source/receiver directivity has a negligible effect except for shallow targets (e.g. TWT depth ≤ 500 ms) imaged with conventional acquisition geometry. In such cases directivity corrections to spectra are strongly recommended.     

不同参数对地震干涉实现VSP向SWP波场重构的影响

地震干涉是近几年勘探地球物理领域研究的一个热点方向,它是波场重构的有力工具.然而,地震干涉往往引入虚假同相轴,影响波场重构的质量.为进一步分析虚假同相轴产生的原因并改善波场重构的质量,本文基于稳相分析,详细探讨子波主频、激发炮数、检波器埋深、检波器间距和地层倾角五个因素对波场重构的影响.模型结果表明,震检排列方式和地层倾角等因素通过改变有限震检范围内稳相点的位置来影响波场重构的质量.将垂直地震剖面VSP中的下行直达波与下行反射波进行地震干涉处理,可有效重构来自高陡反射面的下行反射波,将传统的VSP转化为单井地震剖面SWP.直接利用重构SWP波场进行成像,不仅扩大传统VSP的成像范围,而且避免常规勘探面临的静校正和近地表速度建模问题,为高陡构造成像提供一种新方法.     

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

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

A laboratory study of seismic velocity and attenuation anisotropy in near-surface sedimentary rocks

The laboratory ultrasonic pulse‐echo method was used to collect accurate P‐ and S‐wave velocity (±0.3%) and attenuation (±10%) data at differential pressures of 5–50 MPa on water‐saturated core samples of sandstone, limestone and siltstone that were cut parallel and perpendicular to the vertical borehole axis. The results, when expressed in terms of the P‐ and S‐wave velocity and attenuation anisotropy parameters for weakly transversely isotropic media (ɛ, γ, ɛ_Q, γ_Q) show complex variations with pressure and lithology. In general, attenuation anisotropy is stronger and more sensitive to pressure changes than velocity anisotropy, regardless of lithology. Anisotropy is greatest (over 20% for velocity, over 70% for attenuation) in rocks with visible clay/organic matter laminations in hand specimens. Pressure sensitivities are attributed to the opening of microcracks with decreasing pressure. Changes in magnitude of velocity and attenuation anisotropy with effective pressure show similar trends, although they can show different signs (positive or negative values of ɛ, ɛ_Q, γ, γ_Q). We conclude that attenuation anisotropy in particular could prove useful to seismic monitoring of reservoir pressure changes if frequency‐dependent effects can be quantified and modelled.     

Joint viscoacoustic waveform inversion with the separated upgoing and downgoing wavefields in zero-offset vertical seismic profile data

The attenuation of seismic waves propagating in reservoirs can be obtained accurately from the data analysis of vertical seismic profile in terms of the quality-factor Q. The common methods usually use the downgoing wavefields in vertical seismic profile data. However, the downgoing wavefields consist of more than 90% energy of the spectrum of the vertical seismic profile data, making it difficult to estimate the viscoacoustic parameters accurately. Thus, a joint viscoacoustic waveform inversion of velocity and quality-factor is proposed based on the multi-objective functions and analysis of the difference between the results inverted from the separated upgoing and downgoing wavefields. A simple separating step is accomplished by the reflectivity method to obtain the individual wavefields in vertical seismic profile data, and then a joint inversion is carried out to make full use of the information of the individual wavefields and improve the convergence of viscoacoustic full-waveform inversion. The sensitivity analysis of the different wavefields to the velocity and quality-factor shows that the upgoing and downgoing wavefields contribute differently to the viscoacoustic parameters. A numerical example validates our method can improve the accuracy of viscoacoustic parameters compared with the direct inversion using full wavefield and the separate inversion using upgoing or downgoing wavefield. The application on real field data indicates our method can recover a reliable viscoacoustic model, which helps reservoir appraisal.     

Empirical model for estimating Fourier amplitude spectra of ground acceleration in Taiwan region

A collection of ground‐motion recordings (1070 acceleration records) of moderate (5.1⩽M_L⩽6.5) earthquakes obtained during the execution of the Taiwan Strong Motion Instrumentation Program (TSMIP) since 1991 was used to study source scaling model and attenuation relations for a wide range of earthquake magnitudes and distances and to verify the models developed recently for the Taiwan region. The results of the analysis reveal that the acceleration spectra of the most significant part of the records, starting from S‐wave arrival, can be modelled accurately using the Brune's ω‐squared source model with magnitude‐dependent stress parameter Δσ, that should be determined using the recently proposed regional relationships between magnitude (M_L) and seismic moment (M₀) and between M₀ and Δσ. The anelastic attenuation Q of spectral amplitudes with distance may be described as Q=225 ƒ^1.1 both for deep (depth more than 35 km) and shallow earthquakes. The source scaling and attenuation models allow a satisfactory prediction of the peak ground acceleration for magnitudes 5.1⩽M⩽6.5 and distances up to about 200 km in the Taiwan region, and may be useful for seismic hazard assessment. Copyright © 2000 John Wiley & Sons, Ltd.     

Sensitivity of time-lapse seismic to reservoir stress path

The change in reservoir pore pressure due to the production of hydrocarbons leads to anisotropic changes in the stress field acting on the reservoir. Reservoir stress path is defined as the ratio of the change in effective horizontal stress to the change in effective vertical stress from the initial reservoir conditions, and strongly influences the depletion‐induced compaction behaviour of the reservoir. Seismic velocities in sandstones vary with stress due to the presence of stress‐sensitive regions within the rock, such as grain boundaries, microcracks, fractures, etc. Since the response of any microcracks and grain boundaries to a change in stress depends on their orientation relative to the principal stress axes, elastic‐wave velocities are sensitive to reservoir stress path. The vertical P‐ and S‐wave velocities, the small‐offset P‐ and SV‐wave normal‐moveout (NMO) velocities, and the P‐wave amplitude‐versus‐offset (AVO) are sensitive to different combinations of vertical and horizontal stress. The relationships between these quantities and the change in stress can be calibrated using a repeat seismic, sonic log, checkshot or vertical seismic profile (VSP) at the location of a well at which the change in reservoir pressure has been measured. Alternatively, the variation of velocity with azimuth and distance from the borehole, obtained by dipole radial profiling, can be used. Having calibrated these relationships, the theory allows the reservoir stress path to be monitored using time‐lapse seismic by combining changes in the vertical P‐wave impedance, changes in the P‐wave NMO and AVO behaviour, and changes in the S‐wave impedance.     

An attenuation model for distant earthquakes

Large magnitude earthquakes generated at source–site distances exceeding 100km are typified by low‐frequency (long‐period) seismic waves. Such induced ground shaking can be disproportionately destructive due to its high displacement, and possibly high velocity, shaking characteristics. Distant earthquakes represent a potentially significant safety hazard in certain low and moderate seismic regions where seismic activity is governed by major distant sources as opposed to nearby (regional) background sources. Examples are parts of the Indian sub‐continent, Eastern China and Indo‐China. The majority of ground motion attenuation relationships currently available for applications in active seismic regions may not be suitable for handling long‐distance attenuation, since the significance of distant earthquakes is mainly confined to certain low to moderate seismicity regions. Thus, the effects of distant earthquakes are often not accurately represented by conventional empirical models which were typically developed from curve‐fitting earthquake strong‐motion data from active seismic regions. Numerous well‐known existing attenuation relationships are evaluated in this paper, to highlight their limitations in long‐distance applications. In contrast, basic seismological parameters such as the Quality factor (Q‐factor) could provide a far more accurate representation for the distant attenuation behaviour of a region, but such information is seldom used by engineers in any direct manner. The aim of this paper is to develop a set of relationships that provide a convenient link between the seismological Q‐factor (amongst other factors) and response spectrum attenuation. The use of Q as an input parameter to the proposed model enables valuable local seismological information to be incorporated directly into response spectrum predictions. The application of this new modelling approach is demonstrated by examples based on the Chi‐Chi earthquake (Taiwan and South China), Gujarat earthquake (Northwest India), Nisqually earthquake (region surrounding Seattle) and Sumatran‐fault earthquake (recorded in Singapore). Field recordings have been obtained from these events for comparison with the proposed model. The accuracy of the stochastic simulations and the regression analysis have been confirmed by comparisons between the model calculations and the actual field observations. It is emphasized that obtaining representative estimates for Q for input into the model is equally important.Thus, this paper forms part of the long‐term objective of the authors to develop more effective communications across the engineering and seismological disciplines. Copyright © 2003 John Wiley & Sons, Ltd.     

An efficient and self‐adaptive approach for Q value optimization

The time‐invariant gain‐limit‐constrained inverse Q‐filter can control the numerical instability of the inverse Q‐filter, but it often suppresses the high frequencies at later times and reduces the seismic resolution. To improve the seismic resolution and obtain high‐quality seismic data, we propose a self‐adaptive approach to optimize the Q value for the inverse Q‐filter amplitude compensation. The optimized Q value is self‐adaptive to the cutoff frequency of the effective frequency band for the seismic data, the gain limit of the inverse Q‐filter amplitude compensation, the inverse Q‐filter amplitude compensation function, and the medium quality factor. In the processing of the inverse Q‐filter amplitude compensation, the optimized Q value, corresponding gain limit, and amplitude compensation function are used simultaneously; then, the energy in the effective frequency band for the seismic data can be recovered, and the seismic resolution can be enhanced at all times. Furthermore, the small gain limit or time‐variant bandpass filter after the inverse Q‐filter amplitude compensation is considered to control the signal‐to‐noise ratio, and the time‐variant bandpass filter is based on the cutoff frequency of the effective frequency band for the seismic data. Synthetic and real data examples demonstrate that the self‐adaptive approach for Q value optimization is efficient, and the inverse Q‐filter amplitude compensation with the optimized Q value produces high‐resolution and low‐noise seismic data.     

sPL,一个近距离确定震源深度的震相

实际地震波形观测表明,对于大陆结构相对简单的地壳中的地震而言,有一震相出现在P 波和S波之间.一般在30~50 km附近发育得较好,其能量主要集中在径向分量,而垂向分量的振幅相对径向要小,切向分量上的振幅很弱,且波形以低频为主,通常没有P波尖锐.在利用FK方法计算合成地震图的基础上,发现该震相是由S波入射到自由地表形成水平传播的P波(文献称为surface P wave,自由地表P波)或者包括S波入射到地表后形成的多次P波或其散射震相.由于该震相是由S波和P波之间耦合而形成,本文将其定义为sPL(s coupled into P) 震相.理论波形研究表明,sPL相对直达P波的到时差对震中距离不敏感,而随着震源深度的增加几乎呈线性增加,因此可以很好的约束震源深度.本文以2005年江西九江地震为例,证实了sPL确定震源深度的可行性和可靠性.在观测到sPL震相的情况下,离震源50 km以内的一个三分量地震台站的波形就可以帮助获得可靠的震源深度,而不需要精确的震中距离.由于sPL震相出现距离较近,对于较小(三级以上)的地震也可以应用,因此在稀疏台网布局情形下sPL对于确定中小地震深度应该具有很好的应用意义.     

Burying receivers for improved time‐lapse seismic repeatability: CO2CRC Otway field experiment

4D seismic is widely used to remotely monitor fluid movement in subsurface reservoirs. This technique is especially effective offshore where high survey repeatability can be achieved. It comes as no surprise that the first 4D seismic that successfully monitored the CO₂ sequestration process was recorded offshore in the Sleipner field, North Sea. In the case of land projects, poor repeatability of the land seismic data due to low S/N ratio often obscures the time‐lapse seismic signal. Hence for a successful on shore monitoring program improving seismic repeatability is essential. Stage 2 of the CO2CRC Otway project involves an injection of a small amount (around 15,000 tonnes) of CO₂/CH₄ gas mixture into a saline aquifer at a depth of approximately 1.5 km. Previous studies at this site showed that seismic repeatability is relatively low due to variations in weather conditions, near surface geology and farming activities. In order to improve time‐lapse seismic monitoring capabilities, a permanent receiver array can be utilised to improve signal to noise ratio and hence repeatability. A small‐scale trial of such an array was conducted at the Otway site in June 2012. A set of 25 geophones was installed in 3 m deep boreholes in parallel to the same number of surface geophones. In addition, four geophones were placed into boreholes of 1–12 m depth. In order to assess the gain in the signal‐to‐noise ratio and repeatability, both active and passive seismic surveys were carried out. The surveys were conducted in relatively poor weather conditions, with rain, strong wind and thunderstorms. With such an amplified background noise level, we found that the noise level for buried geophones is on average 20 dB lower compared to the surface geophones. The levels of repeatability for borehole geophones estimated around direct wave, reflected wave and ground roll are twice as high as for the surface geophones. Both borehole and surface geophones produce the best repeatability in the 30–90 Hz frequency range. The influence of burying depth on S/N ratio and repeatability shows that significant improvement in repeatability can be reached at a depth of 3 m. The level of repeatability remains relatively constant between 3 and 12 m depths.     

Dynamic pile-soil-pile interaction. Part II: Lateral and seismic response

A simplified three-step procedure is proposed for estimating the dynamic interaction between two vertical piles, subjected either to lateral pile-head loading or to vertically-propagating seismic S-waves. The starting point is the determination of the deflection profile of a solitary pile using any of the established methods available. Physically-motivated approximations are then introduced for the wave field radiating from an oscillating pile and for the effect of this field on an adjacent pile. The procedure is applied in this paper to a flexible pile embedded in a homogeneous stratum. To obtain analytical closed-form results for both pile-head and seismic-type loading pile-soil and soil-pile interaction are accounted for through a single dynamic Winkler model, with realistic frequency-dependent ‘springs’ and ‘dashpots’. Final- and intermediate-step results of the procedure compare favourably with those obtained using rigorous formulations for several pile group configurations. It is shown that, for a homogeneous stratum, pile-to-pile interaction effects are far more significant under head loading than under seismic excitation.     

Strategies for stable attenuation compensation in reverse‐time migration

Attenuation in seismic wave propagation is a common cause for poor illumination of subsurface structures. Attempts to compensate for amplitude loss in seismic images by amplifying the wavefield may boost high‐frequency components, such as noise, and create undesirable imaging artefacts. In this paper, rather than amplifying the wavefield directly, we develop a stable compensation operator using stable division. The operator relies on a constant‐Q wave equation with decoupled fractional Laplacians and compensates for the full attenuation phenomena by performing wave extrapolation twice. This leads to two new imaging conditions to compensate for attenuation in reverse‐time migration. A time‐dependent imaging condition is derived by applying Q‐compensation in the frequency domain, whereas a time‐independent imaging condition is formed in the image space by calculating image normalisation weights. We demonstrate the feasibility and robustness of the proposed methods using three synthetic examples. We found that the proposed methods are capable of properly compensating for attenuation without amplifying high‐frequency noise in the data.