Linearized waveform inversion for vertical transversely isotropic elastic media:Methodology and multi-parameter crosstalk analysis

Seismic migration and inversion are closely related techniques to portray subsurface images and identify hydrocarbon reservoirs.Seismic migration aims at obtaining structural images of subsurface geologic discontinuities.More specifically,seismic migration estimates the reflectivity function(stacked average reflectivity or pre-stack angle-dependent reflectivity)from seismic reflection data.On the other hand,seismic inversion quantitatively estimates the intrinsic rock properties of subsurface formulations.Such seismic inversion methods are applicable to detect hydrocarbon reservoirs that may exhibit lateral variations in the inverted parameters.Although there exist many differences,pre-stack seismic migration is similar with the first iteration of the general linearized seismic inversion.Usually,seismic migration and inversion techniques assume an acoustic or isotropic elastic medium.Unconventional reservoirs such as shale and tight sand formation have notable anisotropic property.We present a linearized waveform inversion(LWI)scheme for weakly anisotropic elastic media with vertical transversely isotropic(VTI)symmetry.It is based on two-way anisotropic elastic wave equation and simultaneously inverts for the localized perturbations(ΔVp_(0)/Vp_(0)/Vs_(0)/Vs_(0)/,Δ∈,Δδ)from the long-wavelength reference model.Our proposed VTI-elastic LWI is an iterative method that requires a forward and an adjoint operator acting on vectors in each iteration.We derive the forward Born approximation operator by perturbation theory and adjoint operator via adjoint-state method.The inversion has improved the quality of the images and reduces the multi-parameter crosstalk comparing with the adjoint-based images.We have observed that the multi-parameter crosstalk problem is more prominent in the inversion images for Thomsen anisotropy parameters.Especially,the Thomsen parameter is the most difficult to resolve.We also analyze the multi-parameter crosstalk using scattering radiation patterns.The linearized waveform inversion for VTI-elastic media presented in this article provides quantitative information of the rock properties that has the potential to help identify hydrocarbon reservoirs.

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.

Gas sand distribution prediction by prestack elastic inversion based on rock physics modeling and analysis

Seismic inversion is one of the most widely used technologies for reservoir prediction. Many good results have been obtained but sometimes it fails to differentiate the lithologies and identify the fluids. However, seismic prestack elastic inversion based on rock physics modeling and analysis introduced in this paper is a significant method that can help seismic inversion and interpretation reach a new quantitative （or semi-quantitative） level from traditional qualitative interpretation. By doing rock physics modeling and forward perturbation analysis, we can quantitatively analyze the essential relationships between rock properties and seismic responses and try to find the sensitive elastic properties to the lithology, porosity, fluid type, and reservoir saturation. Finally, standard rock physics templates （RPT） can be built for specific reservoirs to guide seismic inversion interpretation results for reservoir characterization and fluids identification purpose. The gas sand distribution results of the case study in this paper proves that this method has unparalleled advantages over traditional post-stack methods, by which we can perform reservoir characterization and seismic data interpretation more quantitatively and efficiently.

Elastic envelope inversion using multicomponent seismic data with filtered-out low frequencies

The absence of low-frequency information in seismic data is one of the most difficult problems in elastic full waveform inversion. Without low-frequency data, it is difficult to recover the long-wavelength components of subsurface models and the inversion converges to local minima. To solve this problem, the elastic envelope inversion method is introduced. Based on the elastic envelope operator that is capable of retrieving low- frequency signals hidden in multicomponent data, the proposed method uses the envelope of multicomponent seismic signals to construct a misfit function and then recover the long- wavelength components of the subsurface model. Numerical tests verify that the elastic envelope method reduces the inversion nonlinearity and provides better starting models for the subsequent conventional elastic full waveform inversion and elastic depth migration, even when low frequencies are missing in multicomponent data and the starting model is far from the true model. Numerical tests also suggest that the proposed method is more effective in reconstructing the long-wavelength components of the S-wave velocity model. The inversion of synthetic data based on the Marmousi-2 model shows that the resolution of conventional elastic full waveform inversion improves after using the starting model obtained using the elastic envelope method. Finally, the limitations of the elastic envelope inversion method are discussed.

An illustrated guide to:Parsimonious multi-scale full-waveform inversion

Having been a seemingly unreachable ideal for decades,3-D full-waveform inversion applied to massive seismic datasets has become reality in recent years.Often achieving unprecedented resolution,it has provided new insight into the structure of the Earth,from the upper few metres of soil to the entire globe.Motivated by these successes,the technology is now being translated to medical ultrasound and non-destructive testing.Despite remarkable progress,the computational cost of fullwaveform inversion continues to be a major concern.It limits the amount of data that can be exploited,and it largely inhibits quantitative and comprehensive uncertainty analyses.These notes complement a presentation on recent developments in full-waveform inversion that are intended to reduce computational cost and assimilate more data,thereby improving tomographic resolution.The suite of strategies includes flexible and user-friendly spectral-element simulations,the design of wavefieldadapted meshes that harness prior information on wavefield geometry,dynamic mini-batch optimisation that naturally takes advantage of data redundancies,and collaborative multi-scale updating to jointly constrain crustal and mantle structure.

Time-Lapse Full-Waveform Inversion Using Cross-Correlation-Based Dynamic Time Warping

Offshore carbon capture, utilization, and storage(OCCUS) is regarded as a crucial technology for mitigating greenhouse gas emissions.Quantitative monitoring maps of sealed carbon dioxide are necessary in a comprehensive OCCUS project. A potential high-resolution method for the aforementioned purpose lies in the full-waveform inversion(FWI) of time-lapse seismic data. However, practical applications of FWI are severely restricted by the well-known cycle-skipping problem. A new time-lapse FWI method using cross-correlation-based dynamic time warping(CDTW) is proposed to detect changes in the subsurface property due to carbon dioxide(CO_(2)) injection and address the aforementioned issue. The proposed method, namely CDTW, which combines the advantages of cross-correlation and dynamic time warping, is employed in the automatic estimation of the discrepancy between the seismic signals simulated using the baseline/initial model and those acquired. The proposed FWI method can then back-project the estimated discrepancy to the subsurface space domain, thereby facilitating retrieval of the induced subsurface property change by taking the difference between the inverted baseline and monitor models. Numerical results on pairs of signals prove that CDTW can obtain reliable shifts under amplitude modulation and noise contamination conditions. The performance of CDTW substantially outperforms that of the conventional dynamic time warping method. The proposed time-lapse fullwaveform inversion(FWI) method is applied to the Frio-2 CO_(2) storage model. The baseline and monitor models are inverted from the corresponding time-lapse seismic data. The changes in velocity due to CO_(2) injection are reconstructed by the difference between the baseline and the monitor models.

Cauchy prior distribution-based AVO elastic parameter estimation via weakly nonlinear waveform inversion

Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.

Lamé parameters inversion based on elastic impedance and its application

The Connolly （1999） elastic impedance （EI） equation is a function of P-wave velocity, S-wave velocity, density, and incidence angle. Conventional inversion methods based on this equation can only extract P-velocity, S-velocity, and density data directly and the elastic impedance at different incidence angles are not at the same scale, which makes comparison difficult. We propose a new elastic impedance equation based on the Gray et al. （1999） Zoeppritz approximation using Lamé parameters to address the conventional inversion method＇s deficiencies. This equation has been normalized to unify the elastic impedance dimensions at different angles and used for inversion. Lamé parameters can be extracted directly from the elastic impedance data obtained from inversion using the linear relation between Lamé parameters and elastic impedance. The application example shows that the elastic parameters extracted using this new method are more stable and correct and can recover the reservoir information very well. The new method is an improvement on the conventional method based on Connolly＇s equation.

Application of joint elastic impedance inversion in the GD Oilfield

For the complicated reservoir description of the GD oilfield, P-wave and S-wave elastic impedance inversion was carried out using pre-stack seismic data to accurately identify the lithology of the reservoir. The joint inversion was performed using three or more partial stacks to overcome the singularity of post-stack seismic inversion that can not satisfy the requirements of complex reservoir description and to avoid the instability of the inversion result caused by low signal-noise ratio in the pre-stack gather. The basic theory of prestack elastic impedance inversion is briefly described in this paper and, using real data of the GD oilfield, the key steps of angle gather wavelet extraction, horizon calibration, S-wave velocity prediction, and elastic parameter extraction were analyzed and studied. The comprehensive interpretation of multiple elastic parameters determined from log analysis is a key to improving the effect ofprestack seismic inversion.

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.

Effective elastic thickness of the lithosphere from joint inversion in western China and its implications

The western China lies in the convergence zone between Eurasian and Indian plates.It is an ideal place to study the lithosphere dynamics and tectonic evolutions on the continental Earth.The lithospheric strength is a key factor in controlling the lithosphere dynamics and deformations.The effective elastic thickness(T_(e))of the lithosphere can be used to address the lithospheric strength.Previous researchers only used one of the admittance or coherence methods to investigate the T_(e) in the western China.Moreover,most of them ignored the internal loads of the lithosphere during the T_(e) calculation,which can produce large biases in the T_(e) estimations.To provide more reliable T_(e) estimations,we used a new joint inversion method that integrated both admittance and coherence techniques to compute the T_(e) in this study,with the WGM2012 gravity data,the ETOPO1 topographic data,and the Moho depths from the CRUST1.0 model.The internal loads are considered and investigated using the load ratio(F).Our results show that the joint inversion method can yield reliable T_(e) and F values.Based on the analysis of T_(e) and F distributions,we suggest(1)the northern Tibetan Plateau could be the front edge of the plate collision of Eurasian and Indian plates;(2)the southern and part of central Tibetan Plateau have a strong lithospheric mantle related to the rigid underthrusting Indian plate;(3)the southeastern Tibetan Plateau may be experiencing the delamination of lithosphere and upwelling of asthenosphere.

Complex spherical-wave elastic inversion using amplitude and phase reflection information

Unlike the real-valued plane wave reflection coefficient(PRC)at the pre-critical incident angles,the frequency-and depth-dependent spherical-wave reflection coefficient(SRC)is more accurate and always a complex value,which contains more reflection amplitude and phase information.In near field,the imaginary part of complex SRC(phase)cannot be ignored,but it is rarely considered in seismic inversion.To promote the practical application of spherical-wave seismic inversion,a novel spherical-wave inversion strategy is implemented.The complex-valued spherical-wave synthetic seismograms can be obtained by using a simple harmonic superposition model.It is assumed that geophone can only record the real part of complex-valued seismogram.The imaginary part can be further obtained by the Hilbert transform operator.We also propose the concept of complex spherical-wave elastic impedance(EI)and the complex spherical-wave EI equation.Finally,a novel complex spherical-wave EI inversion approach is proposed,which can fully use the reflection information of amplitude,phase,and frequency.With the inverted complex spherical-wave EI,the velocities and density can be further extracted.Synthetic data and field data examples show that the elastic parameters can be reasonably estimated,which illustrate the potential of our spherical-wave inversion approach in practical applications.

Fluids discrimination by ray-path elastic impedance inversion: A successful case from Sulige tight gas field

Existing seismic prediction methods struggle to effectively discriminate between fluids in tight gas reservoirs,such as those in the Sulige gas field in the Ordos Basin,where porosity and permeability are extremely low and the relationship between gas and water is complicated.In this paper,we have proposed a comprehensive seismic fluid identification method that combines ray-path elastic impedance(REI)inversion with fluid substitution for tight reservoirs.This approach is grounded in geophysical theory,forward modeling,and real data applications.We used geophysics experiments in tight gas reservoirs to determine that Brie's model is better suited to calculate the elastic parameters of mixed fluids than the conventional Wood’s model.This yielded a more reasonable and accurate fluid substitution model for tight gas reservoirs.We developed a forward model and carried out inversion of REI.which reduced the non-uniqueness problem that has plagued elastic impedance inversion in the angle domain.Our well logging forward model in the ray-path domain with different fluid saturations based on a fluid substitution model proved that REI identifies fluids more accurately when the ray parameters are large.The distribution of gas saturation can be distinguished from the crossplot of REI(p=0.10)and porosity.The inverted ray-path elastic impedance profile was further used to predict the porosity and gas saturation profile.Our new method achieved good results in the application of 2D seismic data in the western Sulige gas field.

Seismic fluid identification using a nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo method

Elastic impedance inversion with high efficiency and high stability has become one of the main directions of seismic pre-stack inversion. The nonlinear elastic impedance inversion method based on a fast Markov chain Monte Carlo （MCMC） method is proposed in this paper, combining conventional MCMC method based on global optimization with a preconditioned conjugate gradient （PCG） algorithm based on local optimization, so this method does not depend strongly on the initial model. It converges to the global optimum quickly and efficiently on the condition that effi- ciency and stability of inversion are both taken into consid- eration at the same time. The test data verify the feasibility and robustness of the method, and based on this method, we extract the effective pore-fluid bulk modulus, which is applied to reservoir fluid identification and detection, and consequently, a better result has been achieved.

THE MULTI-PARAMETER INVERSION OF ELASTIC WAVE IN HALF-SPACE

The multi-parameter inverse scattering problem of elastic waveequation with single fre- quency is investigated within Bornapproximation. By use of a wideband measuring scheme in which bothtransmitters and receivers scan over the half-space surface, theformula of the scattering field of elastic wave is derived. Fourtypes of mode conversion of elastic wave(P→P, P→S, S→P, S→S)areseparated from the scattering field. These components containsufficient information for usto recon- struct the configuration ofthe density and Lame parameters of the medium.

Inversion for negative dislocation on elastic block boundaries in the northeastern margin of Qinghai-Xizang block and prediction for strong earthquake location

On the basis of the velocity field results of horizontal crustal movement obtained from GPS measurements during the periods of 1993-1999, 1999-2001 and 2001-2003 in the northeastern margin of Qinghai-Xizang block, and by the inversion of negative dislocation model for the elastic block boundaries, we provide in this paper a qualitative analysis and quantitative description for the difference of motion and deformation between the tectonic blocks and their boundary faults, time-space distribution of tectonic strain field, and locations with highly accumulated strain energy and correlative intensity. Furthermore, taking the regional tectonics and block strain into full consideration, we investigate the common features of background precursors relating to location prediction for M greater than or equal 6 earthquakes.

Elastic direct envelope inversion based on wave mode decomposition for multi-parameter reconstruction of strong-scattering media

The parameter reconstruction of strong-scattering media is a challenge for conventional full waveform inversion(FWI).Direct envelope inversion(DEI)is an effective method for large-scale and strongscattering structures imaging without the need of low-frequency seismic data.However,the current DEI methods are all based on the acoustic approximation.Whereas,in real cases,seismic records are the combined effects of the subsurface multi-parameters.Therefore,the study of DEI in elastic media is necessary for the accurate inversion of strong-scattering structures,such as salt domes.In this paper,we propose an elastic direct envelope inversion(EDEI)method based on wave mode decomposition.We define the objective function of EDEI using multi-component seismic data and derive its gradient formulation.To reduce the coupling effects of multi-parameters,we introduce the wave mode decomposition method into the gradient calculation of EDEI.The update of Vp is primarily the contributions of decomposed P-waves.Two approaches on Vs gradient calculation are proposed,i.e.using the petrophysical relation and wave mode decomposition method.Finally,we test the proposed method on a layered salt model and the SEG/EAGE salt model.The results show that the proposed EDEI method can reconstruct reliable large-scale Vp and Vs models of strong-scattering salt structures.The successive elastic FWI can obtain high-precision inversion results of the strong-scattering salt model.The proposed method also has a good anti-noise performance in the moderate noise level.

Robust elastic impedance inversion using L1-norm misfit function and constraint regularization

The classical elastic impedance （EI） inversion method, however, is based on the L2-norm misfit function and considerably sensitive to outliers, assuming the noise of the seismic data to be the Guassian-distribution. So we have developed a more robust elastic impedance inversion based on the Ll-norm misfit function, and the noise is assumed to be non-Gaussian. Meanwhile, some regularization methods including the sparse constraint regularization and elastic impedance point constraint regularization are incorporated to improve the ill-posed characteristics of the seismic inversion problem. Firstly, we create the Ll-norm misfit objective function of pre-stack inversion problem based on the Bayesian scheme within the sparse constraint regularization and elastic impedance point constraint regularization. And then, we obtain more robust elastic impedances of different angles which are less sensitive to outliers in seismic data by using the IRLS strategy. Finally, we extract the P-wave and S-wave velocity and density by using the more stable parameter extraction method. Tests on synthetic data show that the P-wave and S-wave velocity and density parameters are still estimated reasonable with moderate noise. A test on the real data set shows that compared to the results of the classical elastic impedance inversion method, the estimated results using the proposed method can get better lateral continuity and more distinct show of the gas, verifying the feasibility and stability of the method.

Elastic Full Waveform Inversion Based on the Trust Region Strategy

In this paper, we investigate the elastic wave full-waveform inversion (FWI) based on the trust region method. The FWI is an optimization problem of minimizing the misfit between the observed data and simulated data. Usually, the line search method is used to update the model parameters iteratively. The line search method generates a search direction first and then finds a suitable step length along the direction. In the trust region method, it defines a trial step length within a certain neighborhood of the current iterate point and then solves a trust region subproblem. The theoretical methods for the trust region FWI with the Newton type method are described. The algorithms for the truncated Newton method with the line search strategy and for the Gauss-Newton method with the trust region strategy are presented. Numerical computations of FWI for the Marmousi model by the L-BFGS method, the Gauss-Newton method and the truncated Newton method are completed. The comparisons between the line search strategy and the trust region strategy are given and show that the trust region method is more efficient than the line search method and both the Gauss-Newton and truncated Newton methods are more accurate than the L-BFGS method.

Reflection full-waveform inversion using a modified phase misfit function

Reflection full-waveform inversion （RFWI） updates the low- and high- wavenumber components, and yields more accurate initial models compared with conventional full-waveform inversion （FWI）. However, there is strong nonlinearity in conventional RFWI because of the lack of low-frequency data and the complexity of the amplitude. The separation of phase and amplitude information makes RFWI more linear. Traditional phase-calculation methods face severe phase wrapping. To solve this problem, we propose a modified phase-calculation method that uses the phase-envelope data to obtain the pseudo phase information. Then, we establish a pseudophase-information-based objective function for RFWI, with the corresponding source and gradient terms. Numerical tests verify that the proposed calculation method using the phase-envelope data guarantees the stability and accuracy of the phase information and the convergence of the objective function. The application on a portion of the Sigsbee2A model and comparison with inversion results of the improved RFWI and conventional FWI methods verify that the pseudophase-based RFWI produces a highly accurate and efficient velocity model. Moreover, the proposed method is robust to noise and high frequency.