Precise modeling of the attenuation parameter Q is important to confirm the robust and diagnostic attenuation characteristics of seismic waveforms in oil and gas reservoirs. For this purpose, the nearly constant Q viscoacoustic wave equation is beneficial. Compared with attenuation models such as standard linear solid (SLS), the wave equation corresponding to the nearly constant Q model contains an explicit Q, which is conducive to inversion and can provide a more effective parameterization. This parameterization facilitates the initial suppression of parameter crosstalk in multiparameter inversion. We derive the adjoint equation containing auxiliary variables, compare the sensitive kernels of different parameterizations, and explain the superiority of the constructed parameterization. The truncated Gauss-Newton (GN-TRN) method is introduced to suppress parameter crosstalk further. The GN-TRN method updates the model parameters by calculating the Hessian vector product and iteratively solving the approximation of the Newton gradient directions. The test results of the theoretical model and field data verify the effectiveness and stability of the inversion method.

Although full waveform inversion (FWI) is widely recognized as one of the state-of-the-art techniques in geophysical exploration, there remain several aspects of FWI that require further improvements, specifically in resolution and modeling efficiency. To address this, we introduce an inverse scattering approach to frequency-domain seismic FWI by utilizing a regularized objective function. Different from traditional adjoint methods, the scattering theory allows us to derive the sensitivity kernel explicitly through two Greens’ functions and transforms the nonlinear inverse scattering problem into a series of linear inverse scattering problems, thereby facilitating the calculation of the gradient and Hessian. To mitigate the computational cost when calculating the background and actual wavefields, the fast Fourier transform (FFT) combined with the Krylov subspace method is used to solve the Lippmann-Schwinger (L-S) integral equation (IE) iteratively. Additionally, we incorporate minimum support (MS) stabilizing functional as an extra model misfit term alongside the traditional data misfit function, for a better recovery of the shape structure within the model. Furthermore, the inversion framework is enhanced by integrating an improved limited memory Broyden-Fletcher–Goldfarb-Shanno algorithm, with the regularized Hessian serving as a preconditioner. To demonstrate the efficacy of our method, numerical tests on Marmousi and BP models are presented to validate the performance and robustness of the proposed approach.

Seismic exploration is an important tool for the detection of road diseases. However, since engineering seismic exploration usually deals with near-surface problems, its detection is complex and difficult. Time-frequency analysis is an important seismic attribute extraction method, which can provide hidden information that is difficult to obtain from seismic profiles, which can effectively help to identify subsurface structures and various types of disease. The S-transform is an important linear time-frequency analysis method, but the window function is fixed during its time-frequency feature extraction, resulting in a shift of the spectrum to higher frequencies, which reduces the accuracy of the time-frequency analysis. The unscaled S-transform, which removes the linear frequency term in the window function, overcomes the above problem to some extent, but affects the temporal resolution of the spectrum in the low-frequency region. To this end, we propose a modified frequency-domain unscaled S-transform method (MFUST) to perform the time-frequency decomposition of seismic signals, and the proposed method adds additional parameters to its window function, which ensures the time-frequency accuracy while realizing the improvement of the spectrum in terms of temporal resolution through the adjustment of the parameters. The effectiveness of the proposed method is verified using synthetic numerical experiments and a real data test.

The seismoelectric effect, characterized by the coupling of seismic and electromagnetic (EM) waves in fluid-saturated porous media, offers a promising avenue for subsurface exploration and earthquake seismology. However, the complexity of the Earth’s subsurface, particularly the presence of anisotropic velocity and attenuation, poses challenges for accurate modeling and interpretation. Here, we introduce a novel approach to model seismoelectric wave propagation in viscoelastic anisotropic porous media by incorporating the nearly constant Q model into the seismoelectric wave equations. Using a series of 2-D and 3-D models, we analyze the influence of both velocity and attenuation anisotropy on the propagation of seismoelectric waves. Our results show that both velocity and attenuation anisotropies contribute to the attenuation of the seismoelectric wavefield. Spatial changes in the elastic and electrical parameters of the subsurface media generate interface response of EM waves, although these are weaker compared to coseismic electric fields. Our extended seismoelectric models provide a robust description of wave propagation in poro-viscoelastic anisotropic media, which can allow for enhancing the current understanding of the Earth’s interior.

Seismic inversion is one of the effective techniques to obtain elastic parameters for reservoir characterization. Deep learning is widely used in seismic inversion and has yielded many satisfactory results. The performance of the existing deep learning-based seismic inversion methods mainly depends on the network structure and a large number of effective training datasets. However, due to the limitation of expensive acquisition costs, it is difficult to obtain enough effective training datasets for network training in seismic surveys. To this end, we develop a double-dual network structure that incorporates both physics and model information to alleviate the dependence of deep learning methods on training data and even enables unsupervised learning and inversion. One of the dual networks is responsible for using the physical information to constrain the inversion results and ensure the physical validity of the predictions. The other dual network is responsible for using the priori information from the model domain to constrain the inversion results and improve the stability of the predictions. Ultimately, the two dual networks are coupled by a loss function to realize labeled/unlabeled network training and inversion applications. We then implement the method in a synthetic model as well as field data. The results are compared with traditional data-driven seismic inversion method and physics-guided data-driven seismic inversion method, and it is shown that the proposed method outperforms these two methods.

The Earth is often characterized by viscoelastic rocks, porous sediments and anisotropic structures. Poro-elasticity with Biot’s theory is considered fundamental to describe the interaction between the deformation of the elastic porous solid and the flow of fluid in the porous structure. The quality factor (Q) in the theory of viscoelasticity relates seismic wave attenuation and dispersion to physical properties of the Earth’s interior, e. g. temperature, stress and composition. However, the constantQwave equation in its time-domain differential form remains difficult to solve when describing the attenuation in an explicitly specifiedQparameter. Here, we introduce the first-and second-order nearly constantQmodels capable of describing the attenuation of the solid skeleton, thereby extending the Biot and Biot-squirt (BISQ) models to poro-viscoelastic media. The bulk and shear moduli of the solid frame are represented by the modified relaxation function. By presenting examples with finite-difference time-domain (FDTD) numerical modeling for seismic wavefields in anisotropic, viscoelastic porous media including transversely isotropic media with a vertical symmetry axis (VTI) and orthorhombic meida, we demonstrate that the extended Biot and BISQ models provide good descriptions of the wave propagation in poro-viscoelastic anisotropic media and can thus help better understand the Earth’s interior.

Considering the viscoelastic anisotropy and electrical depression characteristics of the complex geological media, we introduce the generalized standard linear solid (GSLS) model to describe the relaxation effect of the solid skeleton and the Cole-Cole model to describe the frequency dependence of electric conductivity. The seismoelectric model of the poro-viscoelastic anisotropic medium was constructed, and the corresponding wave and diffusion equations in the time domain were derived. We then analyze the characteristics of seismoelectric wavefields in viscoelastic transverse isotropic (TI) media with a homogenous model, a two-layer model and a layered-model with depression. Results show that the TI anisotropy, viscosity of fluid, tilt angle all have significant effects on the propagation of seismoelectric waves in the homogenous model. The strong attenuation of seismoelectric waves in the two-layer model shows the validity of the relaxed skeleton and frequency dependent conductivity used in our approach, which could also effectively capture the reflection and transmission phenomena in the seismic and associated EM fields in the layered model with depression.