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.

Attenuation compensation method based on inversion

Attenuation compensation,which corrects the attenuation and dispersion of seismic waves,is one of the effective methods for improving seismic data resolution.In general,the attenuation compensation is achieved by an inverse Q-filter based on wave field continuation.In this paper,using the Futterman attenuation model,a method to compute synthetic seismogram is derived for an attenuation medium.Based on the synthetic method,the attenuation compensation problem is reduced to an inversion problem of the Fredholm integral equation and can be achieved by inversion.The Tikhonov regularization is used to improve inversion stability.The processing results of numerical simulation and real data show the effectiveness of the method.

Time-reverse location of microseismic sources in viscoelastic orthotropic anisotropic medium based on attenuation compensation

Time reversal is a key component of time-reverse migration and source location using wavefield extrapolation.The implementation of time reversal depends on the time symmetry of wave equations in acoustic and elastic media.This symmetry in time is no longer valid in attenuative medium.Not only the velocity is anisotropic in shale oil and gas reservoirs,but also the attenuation is usually anisotropic,which can be characterized by viscoelastic orthotropic media.In this paper,the fractional order viscoelastic anisotropic wave equation is used to decouple the energy dissipation and the velocity dispersion.By changing the sign of the dissipation term during backpropagation,the anisotropic attenuation is compensated and the time symmetry is restored.The attenuation compensation time-reverse location algorithm can eff ectively locate the source in viscoelastic orthotropic media.Compared to cases without attenuation compensation or using isotropic attenuation compensation,this method can remove location error caused by anisotropic attenuation and improve the imaging eff ect of the source.This paper verifi es the eff ectiveness of the method through theoretical analysis and model testing.

Inversion-based attenuation compensation with dip constraint

Instability is an inherent problem with the attenuation compensation methods and has been partially relieved by using the inverse scheme.However,the conventional inversion-based attenuation compensation approaches ignore the important prior information of the seismic dip.Thus,the compensated result appears to be distorted spatial continuity and has a low signal-to-noise ratio(S/N).To alleviate this issue,we have incorporated the seismic dip information into the inversion framework and have developed a dip-constrained attenuation compensation(DCAC)algorithm.The seismic dip information,calculated from the poststack seismic data,is the key to construct a dip constraint term.Benefiting from the introduction of the seismic dip constraint,the DCAC approach maintains the numerical stability and preserves the spatial continuity of the compensated result.Synthetic and field data examples demonstrate that the proposed method can not only improve seismic resolution,but also protect the continuity of seismic data.

Seismic attenuation compensation with spectral-shaping regularization

Because of the viscoelasticity of the subsurface medium,seismic waves will inherently attenuate during propagation,which lowers the resolution of the acquired seismic records.Inverse-Q filtering,as a typical approach to compensating for seismic attenuation,can efficiently recover high-resolution seismic data from attenuation.Whereas most efforts are focused on compensating for highfrequency energy and improving the stability of amplitude compensation by inverse-Q filtering,low-frequency leakage may occur as the high-frequency component is boosted.In this article,we propose a compensation scheme that promotes the preservation of lowfrequency energy in the seismic data.We constructed an adaptive shaping operator based on spectral-shaping regularization by tailoring the frequency spectra of the seismic data.We then performed inverse-Q filtering in an inversion scheme.This data-driven shaping operator can regularize and balance the spectral-energy distribution for the compensated records and can maintain the low-frequency ratio by constraining the overcompensation for high-frequency energy.Synthetic tests and applications on prestack common-reflectionpoint gathers indicated that the proposed method can preserve the relative energy of low-frequency components while fulfilling stable high-frequency compensation.

Attenuation-compensated reverse time migration of GPR data constrained by resistivity

The high-frequency electromagnetic waves of ground-penetrating radar(GPR)attenuate severely when propagated in an underground attenuating medium owing to the influence of resistivity,which remarkably decreases the resolution of reverse time migration(RTM).As an effective high-resolution imaging method,attenuation-compensated RTM(ACRTM)can eff ectively compensate for the energy loss caused by the attenuation related to media absorption under the influence of resistivity.Therefore,constructing an accurate resistivity-media model to compensate for the attenuation of electromagnetic wave energy is crucial for realizing the ACRTM imaging of GPR data.This study proposes a resistivity-constrained ACRTM imaging method for the imaging of GPR data by adding high-density resistivity detection along the GPR survey line and combining it with its resistivity inversion profile.The proposed method uses the inversion result of apparent resistivity data as the GPR RTM-resistivity model for imposing resistivity constraints.Moreover,the hybrid method involving image minimum entropy and RTM is used to estimate the medium velocity at the diff raction position,and combined with the distribution characteristics of the reflection in the GPR profile,a highly accurate velocity model is built to improve the imaging resolution of the ACRTM.The accuracy and eff ectiveness of the proposed method are verified using the ACRTM test of the GPR simulated data of a typical attenuating media model.On this basis,the GPR and apparent resistivity data were observed on a field survey line,and use the GPR resistivity-constrained ACRTM method to image the observed data.A comparison of the proposed method with the conventional ACRTM method shows that the proposed method has better imaging depth,stronger energy,and higher resolution,and the obtained results are more conducive for subsequent data analysis and interpretation.

Prestack nonstationary deconvolution based on variable-step sampling in the radial trace domain

The conventional nonstationary convolutional model assumes that the seismic signal is recorded at normal incidence. Raw shot gathers are far from this assumption because of the effects of offsets. Because of such problems, we propose a novel prestack nonstationary deconvolution approach. We introduce the radial trace （RT） transform to the nonstationary deconvolution, we estimate the nonstationary deconvolution factor with hyperbolic smoothing based on variable-step sampling （VSS） in the RT domain, and we obtain the high-resolution prestack nonstationary deconvolution data. The RT transform maps the shot record from the offset and traveltime coordinates to those of apparent velocity and traveltime. The ray paths of the traces in the RT better satisfy the assumptions of the convolutional model. The proposed method combines the advantages of stationary deconvolution and inverse Q filtering, without prior information for Q. The nonstationary deconvolution in the RT domain is more suitable than that in the space-time （XT） domain for prestack data because it is the generalized extension of normal incidence. Tests with synthetic and real data demonstrate that the proposed method is more effective in compensating for large-offset and deep data.