S-wave Quality Factor Research Articles

Complex spherical-wave seismic inversion in anelastic media for the P-wave minimum quality factor

Attenuation always exists when seismic waves propagate in underground anelastic media, especially in hydrocarbon-bearing reservoirs. Quality factor Q or attenuation factor 1/ Q can be used to quantify the seismic wave attenuation and has become an important hydrocarbon indicator. The relationship between the plane-wave reflection coefficient ([Formula: see text]) in anelastic media and P- and S-wave quality factors has been widely used in the plane-wave seismic inversion to estimate the quality factors. The [Formula: see text] provides an adequate approximation for the deeper subsurface. However, for the shallow subsurface and anelastic wavefields excited by point sources, the [Formula: see text] is inaccurate and its meaning involves some fundamental difficulties. In view of this, a Q-dependent P-P spherical-wave reflection coefficient ([Formula: see text]) in anelastic media is used here. Considering that having too many parameters to be inverted will lead to unstable and inaccurate inversion results, we further derive an approximate anelastic [Formula: see text] and anelastic spherical-wave impedance ([Formula: see text]), which are frequency dependent and are the functions of P- and S-wave velocities, density, and P-wave minimum quality factor ([Formula: see text]). Finally, a complex spherical-wave seismic inversion approach in anelastic media for the P-wave minimum quality factor is developed. Using the Bayesian inversion approach and complex convolution model, we first estimate the multilayer [Formula: see text] from the complex seismic traces with different frequencies and incidence angles. Based on the inverted angle- and frequency-dependent [Formula: see text], the P- and S-wave velocities, density, and P-wave minimum quality factor are further estimated using a nonlinear inversion tool. Synthetic examples verify the feasibility and robustness of the complex spherical-wave seismic inversion approach in anelastic media. In the shallow subsurface, the spherical-wave inversion is superior to plane-wave inversion. A field example further demonstrates the accuracy and great potential of our approach in hydrocarbon-bearing reservoir prediction.

Dispersion of Scholte wave under horizontally layered viscoelastic seabed

SUMMARY Dispersion inversion of Scholte wave is an effective method for constructing the shear wave velocity models of seabed sediments, but it is usually conducted based on the elastic layered medium theory, which ignores the viscoelasticity of sediments. In this work, we use the transitive matrix method to establish the dispersion equation for Scholte wave under horizontally layered viscoelastic seabed. This equation integrates the kinematic property of seismic wave in a viscoelastic media and the fluid–solid coupling mechanism. The phase velocity and attenuation coefficient dispersion curves of Scholte wave are presented by the real and imaginary parts of the complex-valued roots of the dispersion equation at different frequencies solved by Muller iteration algorithm, respectively. We perform numerical comparisons and analyses on the dispersion curves of Scholte waves for three typical seabed models under both elastic and viscoelastic conditions. Results demonstrate that the seabed viscoelasticity could greatly affect the propagation and dispersion characteristics of Scholte wave. Moreover, the dispersion curves of Scholte wave are sensitive to the variations in S-wave velocity and quality factor of seabed sediments.

Average QP and QS estimation in marine sediments using a dense receiver array

A new spectral ratio method has been used to compute average P- and S-wave quality factors, [Formula: see text] and [Formula: see text], for the sedimentary sequence below the “V”-shaped Oseberg permanent reservoir monitoring (PRM) system. Quality factors are important for a more accurate characterization of the subsurface and to obtain additional information on the physical processes within the earth, such as fluid content and partial melt. However, few methods compute the average Q-value in sediments for P and S waves in a region, which can be used as a constraint for attenuation models in more sophisticated inversion techniques such as full-waveform inversion or attenuation tomography. To address this, a spectral ratio method using two receiving stations, one installed on sediment and one installed on bedrock, has been developed. This has resulted in quality factor estimations ranging from approximately 64 to 137 for P waves and 29 to 123 for S waves using a subset of the 172 ocean-bottom nodes in the Oseberg PRM system and a seismometer in Bergen, Norway. The [Formula: see text] values are more scattered and hence more uncertain than the [Formula: see text] values due to the P-wave signal being close to the background noise level. In the study area, local earthquakes of magnitude as low as [Formula: see text] 2.4 can be used to obtain [Formula: see text] values and earthquakes of magnitude lower than 2.1 to find [Formula: see text] values, with the possibility of using lower magnitude events if the epicentral distances to the receivers are similar and smaller. Using this method, the average quality factor in sediment packages, for a variety of regions, can be estimated using appropriate raypath configurations connecting source and receiver.

Adjoint Q tomography with central-frequency measurements in viscoelastic medium

SUMMARY Accurate Q (quality factor) structures can provide important constraints for characterizing subsurface hydrocarbon/water resources in exploration geophysics and interpreting tectonic evolution of the Earth in earthquake seismology. Attenuation effects on seismic amplitudes and phases can be included in forward and inverse modellings by invoking a generalized standard linear solid rheology. Compared to traditional ray-based methods, full-waveform-based adjoint tomography approach, which is based on numerical solutions of the visco-elastodynamic wave equation, has the potential to provide more accurate Q models. However, applications of adjoint Q tomography are impeded by the computational complexity of Q sensitivity kernels and by strong velocity-Q trade-offs. In this study, following the adjoint-state method, we show that the Q (P- and S-wave quality factors QP and QS) sensitivity kernels can be constructed efficiently with adjoint memory strain variables. A novel central-frequency difference misfit function is designed to reduce the trade-off artefacts for adjoint Q tomography. Compared to traditional waveform-difference misfit function, this new central-frequency approach is less sensitive to velocity variations, and thus is expected to produce fewer trade-off uncertainties. The multiparameter Hessian-vector products are calculated to quantify the resolving abilities of different misfit functions. Comparative synthetic inversion examples are provided to verify the advantages of this strategy for adjoint QP and QS tomography. We end with a 3D viscoelastic inversion example designed to simulate a distributed acoustic sensing/vertical seismic profile survey for monitoring of CO2 sequestration.

Frequency-dependent AVO inversion applied to physically based models for seismic attenuation

SUMMARYSeismic inversion of amplitude versus offset (AVO) data in viscoelastic media can potentially provide high-resolution subsurface models of seismic velocities and attenuation from offset/angle seismic gathers. P- and S-wave quality factors (Q), whose inverse represent a measure of attenuation, depend on reservoir rock and pore fluid properties, in particular, saturation, permeability, porosity, fluid viscosity and lithology; however, these quality factors are rarely taken into account in seismic AVO inversion. For this reason, in this work, we aim to integrate quality factors derived from physically based models in AVO inversion by proposing a gradient descent optimization-based inversion technique to predict the unknown model properties (P- and S-wave velocities, the related quality factors and density). The proposed inversion minimizes the non-linear least-squares misfit with the observed data. The optimal solution is iteratively obtained by optimizing the data misfit using a second-order limited-memory quasi-Newton technique. The forward model is performed in the frequency–frequency-angle domain based on a convolution of broad-band signals and a linearized viscoelastic frequency-dependent AVO (FAVO) equation. The optimization includes the adjoint-state-based gradients with the Lagrangian formulation to improve the efficiency of the non-linear seismic FAVO inversion process. The inversion is tested on synthetic seismic data, in 1-D and 2-D, with and without noise. The sensitivity for seismic quality factors is evaluated using various rock physics models for seismic attenuation and quality factors. The results demonstrate that the proposed inversion method reliably retrieves the unknown elastic and an-elastic properties with good convergence and accuracy. The stability of the inverse solution especially seismic quality factors estimation relies on the noise level of the seismic data. We further investigate the uncertainty of the solution as a function of the variability of the initial models.

Feasibility study on calculating the Q value of shallow media by using a dense seismic array and a large-volume airgun source

The feasibility of using a dense seismic array with an airgun source to study the quality factors of shallow media is verified. Data were obtained from 37 stations in the dense seismic array located in Binchuan, Yunnan Province, China, and the amplitude–distance attenuation method and the coda normalization method were applied to calculate the S-wave quality factors in the area. The amplitude–distance attenuation method yielded {Q}_{s}^{-1}=0.0260 pm 0.0103, and the frequency-dependent {Q}_{s}^{-1} calculated by the coda normalization method can be expressed by the power law {Q}_{s}^{-1}(f)cong 0.0554{f}^{-0.5643}. The consistency between the results of these two methods shows that a dense seismic array with an airgun source can be used to study the attenuation characteristics of shallow media. The amplitudes at some points deviate substantially from the fitted curve and thus have a certain influence on the fitting results; hence, we must select high-precision data for the calculation. Given the topography, we speculate that the anomalous stations located on the edge of the Binchuan Basin and in the western hilly area are due to the edge effect of the basin and the weak attenuation of the hilly area and that the anomalous station located in the northern Binchuan depocenter is attributable to local site factors. Compared with the {Q}_{s}^{-1} estimated by previous studies, the {Q}_{s}^{-1} in the Binchuan area is found to lie between those of the hard soil and sedimentary rock and is similar to the {Q}_{s}^{-1} in the North China Basin, corresponding to the shallow velocity structure in this area.Graphical

Viscoelastic Wave Propagation Simulation Using New Spatial Variable-Order Fractional Laplacians

ABSTRACTTime-domain constant-Q (CQ) viscoelastic wave equations have been derived to efficiently model Q, but are known to break down in accuracy in describing CQ attenuation at low Q. In view of this, a new time-domain viscoelastic wave equation for modeling wave propagation in anelastic medium is evaluated based on Kjartansson’s CQ model to improve the accuracy in describing CQ attenuation at low Q. We use an approximate frequency-domain viscoelastic wave equation to replace the accurate frequency-domain viscoelastic wave equation. Then, a new time-domain wave equation is derived by converting the approximate viscoelastic wave equation from the frequency domain to the time domain. The newly derived viscoelastic wave equation consists of several Laplacian differential operators with variable fractional order. We use an arbitrary-order Taylor series expansion (TSE) to approximate the derived mixed domain fractional Laplacian operators, and realize the decoupling of the wavenumber and fractional order. Then, the proposed viscoelastic wave equation can be solved directly using the staggered-grid pseudospectral method (SGPSM). We evaluate the precision of the new viscoelastic wave equation by comparing the numerical solutions with the analytical solutions in homogeneous medium. Theoretical curve analysis and numerical results indicate that the proposed fractional viscoelastic wave equation has higher precision in describing CQ attenuation than that of the traditional fractional viscoelastic wave equation, especially for cases that P-wave quality factor QP is less than 10, and S-wave quality factor QS is less than 8. Furthermore, we use two numerical examples to verify the effectiveness of the TSE SGPSM in heterogeneous media. The discussion shows that the advantage of using our fractional viscoelastic wave equation over the traditional fractional viscoelastic wave equation is the higher precision in describing CQ attenuation at different frequency.

Seismic Envelopes of Coda Decay for Q-coda Attenuation Studies of the Gargano Promontory (Southern Italy) and Surrounding Regions

Here, we describe the dataset of seismic envelopes used to study the S-wave Q-coda attenuation quality factor Qc of the Gargano Promontory (Southern Italy). With this dataset, we investigated the crustal seismic attenuation by the Qc parameter. We collected this dataset starting from two different earthquake catalogues: the first regarding the period from April 2013 to July 2014; the second regarding the period from July 2015 to August 2018. Visual inspection of the envelopes was carried out on recordings filtered with a Butterworth two-poles filter with central frequency fc = 6 Hz. The obtained seismic envelopes of coda decay can be linearly fitted in a bilogarithmic diagram in order to obtain a series of single source-receiver measures of Qc for each seismogram component at different frequency fc. The analysis of the trend Qc(fc) gives important insights into the heterogeneity and the anelasticity of the sampled Earth medium.

Rock Anelasticity, Pore Geometry and the Biot–Gardner Effect

The anelastic properties of porous rocks depend on the pore characteristics, specifically, the pore aspect ratio and the pore fraction (related to the soft porosity). At high frequencies, there is no fluid pressure communication throughout the pore space and the rock becomes stiffer than at low frequencies, where the pore pressure is fully equilibrated. The models considered here include explicit pore geometry information in determining the poroelastic parameters. They are extensions of the EIAS (equivalent inclusion-average stress) and CPEM (cracks and pores effective medium) models to the whole frequency range, based on the Zener model. Knowing the degree of stiffness dispersion between the low- and high-frequency limits, we fit experimental data in the whole frequency range and obtain the average crack aspect ratio and soft porosity as a function of effective pressure. Then, we compute the dispersion and quality factor of the bulk, shear and Young moduli, and the P- and S-wave seismic velocities and quality factors as a function of frequency. However, when measuring axial or volumetric motions along a cylindrical sample, there is fluid flow at the ends of the sample in the experiments considered here. This generates dispersion and attenuation due to axial flow of the pore fluid, which does not occur for a plane wave in unbounded media. This phenomenon is called “drained/undrained transition" Pimienta et al. (J Geophys Res Solid Earth; https://doi.org/10.1002/2017JB014645 , 2017). Actually, it is an axial version of the Biot–Gardner (BG) effect, and implies an “artificial" (mesoscopic) attenuation peak (and dispersion) due to the generation of slow (diffusion) Biot modes at the cylinder boundary, inducing a global flow at the scale of the sample. The classical BG effect is due to fluid flow along the radial direction, on the basis of open-pore conditions at the sides of the sample. In this case, the sides are sealed. To use the EIAS and CPEM models, the BG effect has to be removed to obtain the intrinsic Q of the rock. The models are applied here for measurements on sandstone. The axial BG effect is more evident if the intrinsic attenuation is weak or absent. An example is Lavoux limestone, which has a bimodal porosity distribution, with an equal proportion of intragranular microporosity and intergranular macroporosity (round pores). In this case, the attenuation and dispersion are related to the BG effect, since no squirt flow is detected due to the absence of cracks. We verified that the bulk and Young moduli obtained from the axial and hydrostatic oscillations are consistent with each other, and that the theoretical description of the axial BG effect shows some discrepancies with the data.

Spatial variability studies of attenuation characteristics of Qα and Qβ in Kumaon and Garhwal region of NW Himalaya

The present work explores the attenuation characteristics of Garhwal and Kumaon regions of northwest Himalaya, India. A comparative study of P- and S-wave quality factors (Qα and Qβ) is used to appreciate the different attenuation characteristics of these two regions. The strong motion data of 105 local earthquakes recorded in Garhwal and Kumaon region are considered for the analysis. The coda normalization method is implemented to compute Qα and Qβ at each recording site of form Q(f) = Qofn. The regional relationship obtained by using site-specific quality factor relations is Qα(f) = (55 ± 3)f(0.90±0.06), Qβ(f) = (74 ± 5)f(0.87±0.08) for Garhwal region and Qα(f) = (34 ± 1)f(0.94±0.03), Qβ(f) = (58 ± 2)f(0.90±0.02) for Kumaon region, which clearly suggest the existence of spatial variation of attenuation properties in these two regions. The Kumaon region has low Qα and Qβ as compared to Garhwal, which means Kumaon region has high rate of attenuation than Garhwal region, as Q is inversely proportional to the attenuation. Hence, based on obtained attenuation properties it is proposed that Garhwal region has high seismic hazard potential zone as compared to its adjacent Kumaon region. The high value of Qβ/Qα (˃ 1) obtained in the present work indicates the presence of fluid or partially saturated rocks in the earth crust for both Garhwal and Kumaon regions. The variable value of ratio (Qβ/Qα) obtained for Garhwal and Kumaon region specifies the different fluid saturations or fluid types existing for both the regions, and it may be the possible reason of distinct attenuation properties of these two regions.

Estimation of geometrical spreading, quality factor and kappa in the zagros region

We have investigated the attenuation characteristics of the S-wave of 129 earthquakes recorded by 180 accelerometers in the Zagros region of Iran. A total number of 1641 Fourier amplitude spectra were used for a step by step estimation of the high-frequency attenuation, geometrical spreading parameters and the frequency dependence of S-wave quality factor. Two different criteria for isolating the S-wave window were examined in order to assess the effect of window selection on the estimated parameters. For the horizontal and vertical zero-distance, kappa values of 0.043 and 0.033 were obtained, respectively. The S-wave window selection method does not affect the estimated kappa values. We used Bayesian approach to estimate the tri-linear geometrical spreading parameters. The hinge positions of the tri-linear model (63 ± 5 and 124 ± 18 km) and the geometrical spreading coefficient (−0.8) for distances smaller than 63 km were found to be independent of frequency and window type. Both spreading coefficients for distances beyond the first hinge are highly frequency dependent, while at distances beyond 124 km, the coefficients at all frequencies are sensitive to the window type. The frequency-independent spreading coefficients were estimated by simultaneous inversion of all frequencies, and the absolute value of the coefficients at longer distances were found to be larger for longer S-wave windows. The average of the coefficients over both windows for the second and third hinges are −0.17 and −0.55, respectively. The S-wave quality factor is influenced by window type only at frequencies larger than 5 Hz. The frequency dependence of the quality factor at lower frequencies was determined as 141f0.84.

Amplitude anisotropy of shear-wave splitting and fluid detection in thin-layer reservoir

Thin interbeds are typical reservoirs in eastern China. Thin layers and fractures bring huge challenge to fluid identification in anisotropic reservoir. This study focuses on thin-fractured reservoirs and amplitude attributes of shear-wave splitting, and consequently predicted fluid type in fractured reservoir based on the response of fast and slow S-waves to fluids. 3D HTI viscoelastic equation was employed to analyze amplitudes of split S-waves through fluid-filled and fractured media, including oil- and water-saturated synthetic models. Similar to velocity anisotropy, amplitude anisotropy was proposed to avoid the calculation of S-wave quality factor. Amplitude ratio and substation derived from amplitude anisotropy were used to identify fluid type. Example from the Luojia area of Shengli oilfield was used to demonstrate the effectiveness of the inversion method. Results show that amplitude ratio and amplitude subtraction are useful to distinguish fluids, while the former works better than the latter.

Estimation of the quality factor based on the microseismicity recordings from Northern Poland

We use the peak frequency method to estimate effective P- and S-wave quality factors (QP and QS) based on the recorded waveforms of microseismic events. We analyze downhole datasets recorded during the hydraulic stimulation of the two unconventional gas reservoirs located in the northern part of Poland. The effective attenuation is lower in the deeper reservoir consistent with higher compaction. In both cases, we observe high QS values relative to QP which is consistent with attenuation coefficients of saturated reservoirs.

Amplitude-based misfit functions in viscoelastic full-waveform inversion applied to walk-away vertical seismic profile data

Viscoelastic full-waveform inversion is applied to walk-away vertical seismic profile data acquired at a producing heavy-oil field in Western Canada for the determination of subsurface velocity models (P-wave velocity [Formula: see text] and S-wave velocity [Formula: see text]) and attenuation models (P-wave quality factor [Formula: see text] and S-wave quality factor [Formula: see text]). To mitigate strong velocity-attenuation trade-offs, a two-stage approach is adopted. In Stage I, [Formula: see text] and [Formula: see text] models are first inverted using a standard waveform-difference (WD) misfit function. Following this, in Stage II, different amplitude-based misfit functions are used to estimate the [Formula: see text] and [Formula: see text] models. Compared to the traditional WD misfit function, the amplitude-based misfit functions exhibit stronger sensitivity to attenuation anomalies and appear to be able to invert [Formula: see text] and [Formula: see text] models more reliably in the presence of velocity errors. Overall, the root-mean-square amplitude-ratio and spectral amplitude-ratio misfit functions outperform other misfit function choices. In the final outputs of our inversion, significant drops in the [Formula: see text] to [Formula: see text] ratio (~1.6) and Poisson’s ratio (~0.23) are apparent within the Clearwater Formation (depth ~0.45–0.50 km) of the Mannville Group in the Western Canada Sedimentary Basin. Strong [Formula: see text] (~20) and [Formula: see text] (~15) anomalies are also evident in this zone. These observations provide information to help identify the target attenuative reservoir saturated with heavy-oil resources.

Non-parametric spectral modelling of source parameters, path attenuation and site effects from broad-band waveforms of the Alborz earthquakes (2005–2017)

SUMMARYS-wave spectral amplitudes from 312 crustal earthquakes recorded at the Iranian National Broadband Seismic Network in the Alborz region between 2005 and 2017 are analysed in order to evaluate earthquake source parameters, path attenuation and site amplification functions using the non-parametric generalized inversion technique (GIT). We exploit a total number of 1117 seismograms with ML 3–5.6 in the frequency range 0.3–20 Hz. The evaluated non-parametric attenuation functions decay uniformly with distance for the entire frequency range and the estimated S-wave quality factor shows low Q values with relatively strong frequency dependence. We assume the omega-square source model to retrieve earthquake source parameters from the inverted source spectra. The obtained stress drops range from 0.02 to 16 MPa with a mean value of 1.1 MPa. Stress drop and radiated energy show fairly self-similar scaling with seismic moment over the available magnitude range; however, the magnitude range of this study is too narrow to draw a definite conclusion on source scaling characteristics. The obtained moment magnitude Mw and the local magnitude ML are linearly correlated and approximately equivalent in the range of Mw 3–4. For larger events, Mw generally underestimates ML by about 0.1–0.5 magnitude units. The estimated site amplification functions for horizontal component (GIT H) are nearly flat with no obvious pre-dominant frequency peaks for most stations, as expected for the sites of permanent broad-band seismic stations located on rock, though a few stations show amplification peaks from 1 to 8 Hz, with a maximum amplification of about a factor of 7 with respect to the reference site. The evaluated site responses for the vertical components present remarkable amplification or deamplification, leading to differences of the H/V amplitude levels in comparison with the GIT H amplification curves. The results of this study provide a valuable basis for predicting appropriate ground motions in a context of seismic hazard assessment.

KFUPM Ghawar digital viscoelastic seismic model

Ghawar is the largest and most prolific oil field in the world. Yet, no digital geological models or synthetic seismic data of this important field are publicly available for testing algorithms to image, analyze, and understand its complex and interesting attributes. We construct a 2D viscoelastic model of the Ghawar field and calculate a corresponding multi-component synthetic seismic data set. The P-wave velocities and densities of the entire stratigraphic column from pre-Cambrian basement to present-day sediments were compiled from public sources. The S-wave velocities were calculated from the P-wave velocities using empirical VS–VP relations established from well logs. An empirical formula was also used to estimate the P-wave and S-wave quality factors from the P-wave and S-wave velocities, respectively. Vertical and horizontal components of viscoelastic seismic shot records were generated using a finite-difference algorithm accurate to the 4th order in space and 2nd order in time. We share the models and seismic data sets publicly hoping that this will motivate interested researchers to test their research ideas, which in turn will help advance the leading edge in hydrocarbon exploration seismology. Finally, we encourage researchers, who will use the models and data sets, to contribute to the geoscience community by sharing their results publicly as well.

Significance and behaviour of the homogeneous and inhomogeneous components of linearized viscoelastic reflection coefficients

In a recent paper, seismic amplitude-variation-with-offset (AVO) equations describing P-to-P and P-to-S reflections from boundaries separating low-loss viscoelastic media, taking into account variations in the attenuation angle, have been derived. We find that opportunities now present themselves to use these equations to expose a range of relationships between measured amplitudes and subsurface elastic and anelastic properties. This has significant applicability in the quantitative interpretation of seismic data in, for instance, reservoir characterization. To facilitate the analysis, we decompose the equations into three parts: elastic, homogeneous and inhomogeneous. We show that, for PP modes, the elastic part is sensitive to changes across a reflecting boundary in density and P- and S-wave velocities; the homogeneous part is sensitive to changes in density, S-wave velocity and the P- and S-wave quality factors; and the inhomogeneous part is sensitive to changes in density, and P-and S-wave velocities. The latter term is seen to vanish when the attenuation angle vanishes. For PP modes, elastic and homogeneous terms are linear with respect to , where is the P-wave incidence angle; however, the inhomogeneous term is similarly linear only if normalized by dividing by tan θ P. For PS modes, the elastic part is sensitive to changes in density and S-wave velocity; the homogeneous part is sensitive to changes in density, S-wave velocity and the S-wave quality factor; and the inhomogeneous part is sensitive to changes in density and S-wave velocity. This term also vanishes for the zero attenuation angle, i.e. in the homogenous limit. For PS modes, the inhomogeneous terms are linear with respect to ; however the elastic and homogeneous terms are first and third order in . A further and key result of this expansion of the wave types allowable in AVO analysis is that, for inhomogeneous PS scattering, the viscoelastic AVO equations predict a non-zero reflectivity at normal incidence. This is a significant deviation from common models of converted wave amplitude analysis.

Compensating Q effects in viscoelastic media by adjoint-based least-squares reverse time migration

Low values of P- and S-wave quality factors [Formula: see text] and [Formula: see text] result in strong intrinsic seismic attenuation in seismic modeling and imaging. We use a linearized waveform inversion approach, by generalizing least-squares reverse time migration (LSRTM) for viscoelastic media ([Formula: see text]-LSRTM), to compensate for the attenuation loss for P- and S-images. We use the first-order particle velocity, stress, and memory variable equations, with explicit [Formula: see text] in the formulations, based on the generalized standard linear solid, as the forward-modeling operator. The linearized two-way viscoelastic modeling operator is obtained with modulus perturbations introduced for the relaxed P- and S-moduli. The viscoelastic adjoint operator and the P- and S-imaging conditions for modulus perturbations are derived using the adjoint-state method and an augmented Lagrangian functional. [Formula: see text]-LSRTM solves the viscoelastic linearized modeling operator for generating synthetic data, and the adjoint operator is used for back propagating the data residual. With the correct background velocity model, and with the inclusion of [Formula: see text] in the modeling and imaging, [Formula: see text]-LSRTM is capable of iteratively updating the P- and S-modulus perturbations, and compensating the attenuation loss caused by [Formula: see text] and [Formula: see text], in the direction of minimizing the data residual between the observed and predicted data. Compared with elastic LSRTM results, the P- and S-modulus perturbation images from [Formula: see text]-LSRTM have stronger (closer to the true modulus perturbation), and more continuous, amplitudes for the structures in and beneath low-[Formula: see text] zones. The residuals in the image space obtained using the correctly parameterized [Formula: see text]-LSRTM are much smaller than those obtained using the incorrectly parameterized elastic LSRTM. However, the data residuals from [Formula: see text]-LSRTM and elastic LSRTM are similar because elastic Born modeling with a weak reflector in the image produces similar reflection amplitudes with viscoelastic Born modeling with a strong reflector.

Modeling of Source Parameters and Moment Tensors of Local Earthquakes Occurring in the Eastern Indian Shield

ABSTRACT Earthquake source parameters and crustal Q are being estimated simultaneously through the inversion of S-wave displacement spectra from three-component recordings of ten local cratonic intraplate earthquakes from 3-6 broadband stations in the eastern Indian shield, wherein, an iterative Levenberg-Marquardt inversion technique is used. The estimated seismic moment (Mo) and source radii (r) vary from 7.4 x 1012 to 7.1 x 1014 N-m and 144.2 to 211.3 m, respectively, while estimated stress drops (Δσ) and multiplicative factor (Emo) values range from 0.11 to 4.13 MPa and 1.33 to 2.16, respectively. The corner frequencies range from 6.23 to 8.62 Hz while moment magnitudes vary from 2.44 to 3.57. The radiated seismic energy and apparent stresses range from 8.3 x 106 to 2.0 x 1010 Joules and 0.06 to 0.94 MPa, respectively, wherein the estimated corner frequencies and seismic moment satisfy the relation Mo ∞ fc−(3+ε) for ε = 12.7. Thus, the source scaling of these events clearly deviates from the self-similarity i.e. f−3. Estimated Zuniga parameters reveal that all selected events satisfy the partial stress drop model, which is in good agreement with the global observations. Our estimated crustal S-wave quality factors vary from 1091 to 4926 with an average of 3006, suggesting a less heterogeneous crustal structure underlying the study region. We also perform moment tensor inversion of five selected local events using ISOLA software, which reveals that the dominant deformation mode for the eastern Indian shield is left-lateral strike slip motion with minor normal dip-slip component on an almost vertical plane. This observation suggests that neotectonic vertical movements might have played a key role in generating these earthquakes. Our modeling also depicts that the seismically mildly active Singhbhum shear zone and Eastern Ghats mobile belt are characterized by the left-lateral strike motion while two events in the Chotanagpur half graben belt suggest a normal dip-slip motion along a south dipping plane. A north-south orientation of P-axis is found to be dominant in the area, which is consistent with the prevailing north–south compression over the Indian plate.

Attenuation from microseismic datasets by the peak frequency method benchmarked with the spectral ratio method

Recently proposed peak-frequency method is used to estimate the P- and S-wave quality factors from microseismic events. We use a downhole monitoring dataset of 10 high signal-to-noise ratio microseismic events to calculate P- and S-wave effective attenuation of a carbonate reservoir. We benchmark these results with the spectral ratio method and obtain mutually consistent results. Additionally we develop and test two techniques of peak frequency determination. We show that the peak frequency method can be successfully used in the estimation of the quality factor and it provides precise measurements of attenuation.