Estimation of Q and inverse Q filtering for prestack reflected PP-and converted PS-waves

Multi-component seismic exploration technology, combining reflected PP- and converted PS-waves, is an effective tool for solving complicated oil and gas exploration problems. The improvement of converted wave resolution is one of the key problems. The main factor affecting converted wave resolution is the absorption of seismic waves in overlying strata. In order to remove the effect of absorption on converted waves, inverse Q filtering is used to improve the resolution. In this paper, we present a method to estimate the S-wave Q values from prestack converted wave gathers. Furthermore, we extend a stable and effective poststack inverse Q filtering method to prestack data which uses wave field continuation along the ray path to compensate for attenuation in prestack common shot PP- and PS-waves. The results of theoretical modeling prove that the method of estimating the S-wave Q values has high precision. The results from synthetic and real data prove that the stable inverse Q filtering method can effectively improve the resolution of prestack PP- and PS-waves.

Zoeppritz equation-based prestack inversion and its application in fluid identification

Prestack seismic inversion methods adopt approximations of the Zoeppritz equations to describe the relation between reflection coefficients and P-wave velocity, S-wave velocity, and density. However, the error in these approximations increases with increasing angle of incidence and variation of the elastic parameters, which increases the number of inversion solutions and minimizes the inversion accuracy. In this study, we explore a method for solving the reflection coefficients by using the Zoeppritz equations. To increase the accuracy of prestack inversion, the simultaneous inversion of P-wave velocity, S-wave velocity, and density by using prestack large-angle seismic data is proposed based on generalized linear inversion theory. Moreover, we reduce the ill posedness and increase the convergence of prestack inversion by using the regularization constraint damping factor and the conjugate gradient algorithm. The proposed prestack inversion method uses prestack large-angle seismic data to obtain accurate seismic elastic parameters that conform to prestack seismic data and are consistent with logging data from wells.

Study of prestack elastic parameter consistency inversion methods

The three parameters of P-wave velocity, S-wave velocity, and density have remarkable differences in conventional prestack inversion accuracy, so study of the consistency inversion of the ＂three parameters＂ is very important. In this paper, we present a new inversion algorithm and approach based on the in-depth analysis of the causes in their accuracy differences. With this new method, the inversion accuracy of the three parameters is improved synchronously by reasonable approximations and mutual constraint among the parameters. Theoretical model calculations and actual data applications with this method indicate that the three elastic parameters all have high inversion accuracy and maintain consistency, which also coincides with the theoretical model and actual data. This method has good application prospects.

Prestack inversion based on anisotropic Markov random field-maximum posterior probability inversion and its application to identify shale gas sweet spots

Economic shale gas production requires hydraulic fracture stimulation to increase the formation permeability. Hydraulic fracturing strongly depends on geomechanical parameters such as Young＇s modulus and Poisson＇s ratio. Fracture-prone sweet spots can be predicted by prestack inversion, which is an ill-posed problem; thus, regularization is needed to obtain unique and stable solutions. To characterize gas-bearing shale sedimentary bodies, elastic parameter variations are regarded as an anisotropic Markov random field. Bayesian statistics are adopted for transforming prestack inversion to the maximum posterior probability. Two energy functions for the lateral and vertical directions are used to describe the distribution, and the expectation-maximization algorithm is used to estimate the hyperparameters of the prior probability of elastic parameters. Finally, the inversion yields clear geological boundaries, high vertical resolution, and reasonable lateral continuity using the conjugate gradient method to minimize the objective function. Antinoise and imaging ability of the method were tested using synthetic and real data.

Detection of gas hydrate sediments using prestack seismic AVA inversion

Bottom-simulating reflectors (BSRs) in seismic profile always indicate the bottom of gas hydrate stability zone, but is difficult to determine the distribution and features of gas hydrate sediments (GHS). In this study, based on AVA forward modeling and angle-domain common-image gathers we use prestack AVA parameters consistency inversion in predicting gas hydrate sediments in the Shenhu area at northern slope of South China Sea, and obtain the vertical and lateral features and saturation of GHS.

Attenuation compensation in multicomponent Gaussian beam prestack depth migration

Gaussian beam prestack depth migration is an accurate imaging method of subsurface media. Prestack depth migration of multicomponent seismic data improves the accuracy of imaging subsurface complex geological structures. Viscoelastic prestack depth migration is of practical significance because it considers the viscosity of the subsurface media. We use Gaussian beam migration to compensate for the attenuation in multicomponent seismic data. First, we use the Gaussian beam method to simulate the wave propagation in a viscoelastic medium and introduce the complex velocity Q-related and exact viscoelastic Zoeppritz equation. Second, we discuss PP- and PS-wave Gaussian beam prestack depth migration algorithms for common-shot gathers to derive expressions for the attenuation and compensation. The algorithms correct the amplitude attenuation and phase distortion caused by Q, and realize multicomponent Gaussian beam prestack depth migration based on the attenuation compensation and account for the effect of inaccurate Q on migration. Numerical modeling suggests that the imaging resolution of viscoelastic Gaussian beam prestack depth migration is high when the viscosity of the subsurface is considered.

High angle prestack depth migration with absorption compensation

The absorption effect of actual subsurface media can weaken wavefield energy, decrease the dominating frequency, and further lead to reduced resolution. In migration, some actions can be taken to compensate for the absorption effect and enhance the resolution. In this paper, we derive a one-way wave equation with an attenuation term based on the time- space domain high angle one-way wave equation. A complicated geological model is then designed and synthetic shot gathers are simulated with acoustic wave equations without and with an absorbing term. The derived one-way wave equation is applied to the migration of the synthetic gathers without and with attenuation compensation for the simulated shot gathers. Three migration profiles are obtained. The first and second profiles are from the shot gathers without and with attenuation using the migration method without compensation, the third one is from the shot gathers with attenuation using the migration method with compensation. The first and third profiles are almost the same, and the second profile is different from the others below the absorptive layers. The amplitudes of the interfaces below the absorptive layers are weak because of their absorption. This method is also applied to field data. It is concluded from the migration examples that the migration method discussed in this paper is feasible.

Anisotropic converted wave amplitude-preserving prestack time migration by the pseudo-offset method

In this paper, we use the method of pseudo-offset migration （POM） to complete converted wave pre-stack time migration with amplitude-preservation in an anisotropic medium. The method maps the original traces into common conversion scatter point （CCSP） gathers directly by POM, which simplifies the conventional processing procedure for converted waves. The POM gather fold and SNR are high, which is favorable for velocity analysis and especially suitable for seismic data with low SNR. We used equivalent anisotropic theory to compute anisotropic parameters. Based on the scattering wave traveltime equation in a VTI medium, the POM pseudo-offset migration in anisotropic media was deduced. By amplitude-preserving POM gather mapping, velocity analysis, stack processing, and so on, the anisotropic migration results were acquired. The forward modeling computation and actual data processing demonstrate the validity of converted wave pre-stack time migration with amplitude-preservation using the anisotropic POM method.

Effect of inaccurate wavelet phase on prestack waveform inversion

Wavelets are critical to inversion methods. Incorrect phase estimation will affect the objective function and cause convergence to local minima, and thus produce biased or incorrect results. Based on two simple models and ignoring all other factors, we studied the variation of the wavelet phase as a function of frequency and its effect on the prestack waveform inversion. Numerical experiments show that an incorrect phase may result in large deviations from the real solution, even if there is a high similarity between the model and real wavelets. The precision of the inversion slightly improves by using the constant-phase rotation; however, the effect of phase inaccuracy is not eliminated, which limits the precision of prestack inversion.

Amplitude.preserving plane-wave prestack time migration for AVO analysis

To support amplitude variation with offset （AVO） analysis in complex structure areas, we introduce an amplitude-preserving plane-wave prestack time migration approach based on the double-square-root wave equation in media with little lateral velocity variation. In its implementation, a data mapping algorithm is used to obtain offset-plane-wave data sets from the common-midpoint gathers followed by a non-recursive phase-shift solution with amplitude correction to generate common-image gathers in offset-ray-parameter domain and a structural image. Theoretical model tests and a real data example show that our prestack time migration approach is helpful for AVO analysis in complex geological environments.

Bayesian prestack seismic inversion with a self-adaptive Huber-Markov random-field edge protection scheme

Seismic inversion is a highly ill-posed problem, due to many factors such as the limited seismic frequency bandwidth and inappropriate forward modeling. To obtain a unique solution, some smoothing constraints, e.g., the Tikhonov regularization are usually applied. The Tikhonov method can maintain a global smooth solution, but cause a fuzzy structure edge. In this paper we use Huber-Markov random-field edge protection method in the procedure of inverting three parameters, P-velocity, S-velocity and density. The method can avoid blurring the structure edge and resist noise. For the parameter to be inverted, the Huber- Markov random-field constructs a neighborhood system, which further acts as the vertical and lateral constraints. We use a quadratic Huber edge penalty function within the layer to suppress noise and a linear one on the edges to avoid a fuzzy result. The effectiveness of our method is proved by inverting the synthetic data without and with noises. The relationship between the adopted constraints and the inversion results is analyzed as well.

One-way wave equation seismic prestack forward modeling with irregular surfaces

Mathematical geophone （MG） and equal-time stacking （ETS） principles are used to implement seismic prestack forward modeling with irregular surfaces using the oneway acoustic wave-equation. This method receives seismic primary reflections from the subsurface using a set of virtual MGs. The receivers can be located anywhere on an irregular observing surface. Moreover, the ETS method utilizes the one-way acoustic wave equation to easily and quickly image and extrapolate seismic reflection data. The method is illustrated using high single-noise ratio common shot gathers computed by numerical forward modeling of two simple models, one with a flat surface and one with an irregular surface, and a complex normal fault model. A prestack depth migration method for irregular surface topography was used to reoroduce the normal fault model with high accuracy.

Simultaneous prestack inversion of variable-depth streamer seismic data

Variable-depth streamer seismic data are characterized by low and high frequencies and can be used to obtain high-quality and resolution images of complex subsurface structures. Taking advantage of the frequency range in the variable-depth streamer data, we propose the simultaneous inversion of prestack data from variable-offset stack gathers to obtain the P-wave impedance, S-wave impedance, and density. Next, we validate the method by using model and actual variable-depth streamer data from the Huizhou block. The results suggest that the broadband data recorded by variable-depth streamers improve the signal-to-noise ratio and quality of the inversion results and outperform the constant-depth streamer data in delineating the underground stratigraphy.

Beamlet prestack depth migration and illumination： A test based on the Marmousi model

Beamlet sources have strong local and directional character and can easily accomplish local illumination and migration. Besides, they provide better migration results than conventional migration methods. We introduce the basic principles of beamlet prestack depth migration that includes a windowed Fourier transform and frame theory. We explain the Gabor-Daubechies （G-D） frame based on a Gaussian function. Beamlet decomposition provides information on the local space and direction of wavefield. We synthesize the beamlet source and beamlet records in the wavelet domain using both rectangle and Gaussian windows and then extrapolate the synthesized data with a Fourier finite-difference operator. We test the method using the standard Marmousi model. By comparing and analyzing the migration results of single directional beamlet and beamlets with different windows and directions, we demonstrate the validity of the prestack depth migration with Gaussian beamlets method.

Inversion of shear wave interval velocity on prestack converted wave data

Seismic velocity is important to migration of seismic data, interpretation of lithology and lithofacies as well as prediction of reservoir. The information of shear wave velocity is required to reduce the uncertainty for discriminating lithology, identifying fluid type in porous material and calculating gas saturation in reservoir prediction. Based on Zoeppritz equations, a numeral and scanning method was proposed in this paper. Shear wave velocity can be calculated with prestack converted wave data. The effects were demonstrated by inversion of theoretical and real seismic data.

Study of the Sensitive Properties of Marine Gas Hydrate Based on the Prestack Elastic Inversion

Using a bottom simulating reflector(BSR)on a seismic profile to identify marine gas hydrate is a traditional seismic exploration method.However,owing to the abundance differences between the gas hydrate and free gas in different regions,the BSR may be unremarkable on the seismic profile and invisible in certain cases.With the improvement of exploration precision,difficulty arises in meeting the requirements of distinguishing the abundance differences in the gas hydrate based on BSR.Hence,we studied other sensitive attributes to ascertain the existence of gas hydrate and its abundance variations,eventually improving the success rate of drilling and productivity.In this paper,we analyzed the contradiction between the seismic profile data and drilling sampling data from the Blake Ridge.We extracted different attributes and performed multi-parameter constraint analysis based on the prestack elastic wave impedance inversion.Then,we compared the analysis results with the drilling sampling data.Eventually,we determined five sensitive attributes that can better indicate the existence of gas hydrate and its abundance variations.This method overcomes the limitations of recognizing the gas hydrate methods based on BSR or single inversion attribute.Moreover,the conclusions can notably improve the identification accuracy of marine gas hydrate and provide excellent reference significance for the recognition of marine gas hydrate.Notably,the different geological features of reservoirs feature different sensitivities to the prestacking attributes when using the prestack elastic inversion in different areas.

Prestack AVA joint inversion of PP and PS waves using the vectorized reflectivity method

Most current prestack AVA joint inversion methods are based on the exact Zoeppritz equation and its various approximations. However, these equations only reflect the relation between reflection coefficients, incidence angles, and elastic parameters on either side of the interface, which means that wave-propagation effects, such as spherical spreading, attenuation, transmission loss, multiples, and event mismatching of P-and S-waves, are not considered and cannot accurately describe the true propagation characteristics of seismic waves. Conventional AVA inversion methods require that these wave-propagation effects have been fully corrected or attenuated before inversion but these requirements can hardly be satisfied in practice. Using a one-dimensional(1 D) earth model, the reflectivity method can simulate the full wavefield response of seismic waves. Therefore, we propose a nonlinear multicomponent prestack AVA joint inversion method based on the vectorized reflectivity method, which uses a fast nondominated sorting genetic algorithm(NSGA II) to optimize the nonlinear multiobjective function to estimate multiple parameters, such as P-wave velocity, S-wave velocity, and density. This approach is robust because it can simultaneously cope with more than one objective function without introducing weight coefficients. Model tests prove the effectiveness of the proposed inversion method. Based on the inversion results, we find that the nonlinear prestack AVA joint inversion using the reflectivity method yields more accurate inversion results than the inversion by using the exact Zoeppritz equation when the wave-propagation effects of transmission loss and internal multiples are not completely corrected.

Application of Amplitude Ratio Profiles Extracted with Prestack Kirchhoff Integral Migration

The Z component and X component profiles of seismic waves extracted with the prestack Kirchhoff integral migration could approximate to the primary wave （P wave） and converted shear wave （PS wave） profiles under certain conditions. The relative change of their reflection amplitude reflects the formation stress anomaly and subsurface media anisotropy. The principle and method for extracting amplitude ratios were studied and the application of amplitude ratio profiles was also examined when processing and interpreting actual seismic data. The amplitude ratio profile is an effective supplementary means of identifying the stratigraphic boundary and lithology.

Prestack inversion identification of organic reef gas reservoirs of Permian Changxing Formation in Damaoping area, Sichuan Basin, SW China

Organic reef reservoirs in the platform margin of Kaijiang-Liangping trough in Damaoping area, Sichuan Basin are thin in single layer, fast in lateral variation, and have small P-impedance difference from the surrounding rock, it is difficult to identify and predict the reservoirs and fluid properties by conventional post-stack inversion. Through correlation analysis of core test data and logging P-S wave velocity, this work proposed a formula to calculate the shear wave velocity in different porosity ranges, and solved the issue that some wells in the study area have no S-wave data. AVO forward analysis reveals that formation porosity is the main factor affecting the variation of AVO type, the change of water saturation cannot affect the AVO type, but it has an effect on the change range of AVO. Through cross-plotting analysis of elastic parameters, it is found that fluid factor is a parameter sensitive to gas-bearing property of organic reef reservoir in the study area. By comparing results of post-stack impedance inversion, post-stack high frequency attenuation property, pre-stack simultaneous inversion and AVO anomaly analysis of angle gathers, it is found that the gas-bearing prediction of organic reef reservoirs by using fluid factor derived from simultaneous pre-stack inversion had the highest coincidence rate with actual drilling data. At last, according to the characteristics of fluid factor distribution, the favorable gas-bearing area of the organic reef reservoir in Changxing Formation was predicted, and the organic reef trap at the top of Changxing Formation in Block A of Damaoping area was sorted out as the next exploration target.

Calculation method of prestack FAGVO and its applications

Frequency attenuation occurs when seismic waves propagate through the porous reservoirs containing hydrocarbons. Current researches on the seismic frequency attenuation mainly focus on the post-stack domain instead of the prestack domain. Here we propose the frequency attenuation gradient vs. offset （FAGVO） based on the amplitude variation with offset and frequency attenuation integral equations. We derive the FAGVO equation that equals to zero in a full-elastic medium and is negative in a viscoelastic medium. FAGVO is affected by the viscosity of the medium, the coefficients of reflection, the frequency variation, and high-frequency attenuation. FAGVO uses the differences of partially stacked data to decrease the interference caused by subsurface strata affecting the frequency attenuation, highlights the frequency attenuation gradient anomalies in hydrocarbon-bearing reservoir pores, and finally realizes the hydrocarbon fluid identification. The method was verified using a two-dimensional wave equation forward model and was found to be cost effective. Furthermore, the method does not require well information, which can be applied in the stage of seismic exploration, especially, in the exploration of a none-well project.