Analytical solutions provide accurate approach for wavefield calculations. However, conventional seismic analytical solutions assume simplified boundary conditions and constant layer orientations, which makes them unsuitable for accurately modeling of seismic wave propagation in media with inclined layers. To derive the analytical solutions for the elastic wave equations of inclined layered formations, a natural coordinate system is established. Using coordinate transformation techniques, the boundary conditions and elastic seismic wave equations are transformed into the natural coordinate system. Recursive matrices for seismic wavefields in inclined multi-layered formations are derived in natural coordinate system. The verification results confirm that these derived analytical solutions satisfy both the elastic seismic wave equations and boundary conditions across inclined interfaces. The effects of dipping angles and azimuths on seismic displacements and stresses are studied. The numerical results indicate that seismic wavefields in inclined multi-layered formations exhibit irregular spatial periodicity and complex interference patterns.

Given the potential influence of seismic anisotropy on multichannel seismic data acquired over sedimentary basins, applying an optimal anisotropic time-lapse seismic imaging technique to accurately estimate the injected CO2 plume is imperative. This study conducts acoustic multiparameter assumption full-waveform inversion (FWI) based on the elliptical anisotropy to enhance the accuracy of time-lapse seismic monitoring results at the Sleipner field. The Sleipner project is the pioneering commercial-scale offshore carbon capture and storage (CCS), marking the successful implementation of time-lapse seismic surveys to monitor the injected CO2 plume. To validate the necessity of anisotropic time-lapse FWI at the Sleipner field, we construct an initial anisotropic velocity model using Backus averaging. Subsequently, we compare the accuracy of the velocity structure obtained with isotropic and anisotropic FWI starting from the same initial model. Consequently, we confirm that the elliptical anisotropic time-lapse FWI significantly enhances accuracy, as demonstrated by the improved matching of synthetic data derived from anisotropic FWI to the real data, compared to the isotropic FWI results.

The frequency-dependent amplitude-versus-offset (FAVO) method has great potential for reservoir parameters estimation. However, it is hard work to establish the FAVO inversion model. It is also difficult to solve the inverse problem for FAVO by traditional methods. In this paper, we propose a new workflow to extract the reservoir fluid parameters from the FAVO gathers based on a deep neural network (DNN). The proposed method is applied to predict the tight sandstone gas reservoir properties. Within the framework of this workflow, we generate the synthetic FAVO gathers. First, we establish the petrophysical model using the logging interpretation results. Then, the Backus average, Biot-Gassmann fluid substitution, velocity dispersion equations of the binary medium, and Rüger equation are applied to generate the FAVO reflectivity series. By introducing the DNN-based seismic wavelet estimation method and the optimal basis wavelet transform (OBWT), we can generate different frequency components of the seismic wavelet. These different frequency components are used to convolve the FAVO reflectivity series to obtain FAVO gathers that are used to generate the sample pairs for DNN training. At the same time, the OBWT is used to decompose the real AVO gathers to get the FAVO gathers. Finally, to testify its validity and effectiveness, the proposed workflow is applied to synthetic and field data.

Sedimentary strata formed by orientational vertical fractures are approximately equivalent to transversely isotropic media with a horizontal symmetry axis (HTI). Parameter inversion for the isotropic background and fracture parameters can provide valuable information for predicting fractured reservoirs. Following Bakulin’s modeling theory, we parameterized the HTI medium with the first- and second-order Lamé parameters of the isotropic background, host rock density, fracture density, and fracture azimuth. We calculated the fracture azimuth and separated split shear waves using the Alford rotation. Based on the exact reflection coefficients, we develop a joint P-to-P reflected wave (PP), PS1, and PS2 amplitude variation with angle (AVA) inversion method in the depth domain by using the second-order Levenberg–Marquardt (LM) algorithm to invert the remaining four parameters. Numerical model tests revealed that our method was more accurate compared to the traditional LM method and works for both weak/strong contrasts and anisotropy magnitudes. We used real data from the walkaway vertical seismic profiling (VSP) as an example to propose a set of strategies, thereby improving the practicality of our inversion method. To protect the fracture information contained in the wavefields, we adopted vector-feature-preserving data processing procedures to preprocess the field VSP data and separate PP, PS1, and PS2 reflections. We utilized P-wave first breaks to successfully discriminate and match these three wave modes from the same fractured formation in the depth domain; these were subsequently transformed to AVA gathers with ray tracing. We synthetically incorporated the time delays and layer velocities to build the initial models and to constrain the inversion process.

Seismic traveltime is crucial for the inversion of anisotropy parameters. In the inversion for fractured rock, a typical transversely isotropic medium with a horizontal symmetry axis (HTI), the joint utilization of traveltime of P- and split shear waves can provide more anisotropy information than the utilization of only P-wave traveltime. The computational effort of nonlinear parameter inversion also increases with the involvement of split shear waves. Therefore, based on the series expansion of vertical slowness projection, we derive the linear approximations for the first-break traveltimes of P-, S1-, and S2-waves with respect to fracture weaknesses, which are used to accelerate and stabilize the inversion process. Linear coefficients are used to analyze the sensitivity of the traveltime to fracture weakness and thus the accuracy of the results. To make our proposed approximation more practical, we expand our linear equations to the traveltime difference between the HTI model and its isotropic background model and derive the joint inversion equation for fracture weaknesses in a vertical seismic profile (VSP) survey by jointly using P-, S1-, and S2-waves. Field data application shows that our method is feasible for estimating fracture weaknesses by using walkaround VSP data. The error caused by linear approximation can be reduced by the joint utilization of multiple wave modes.