In seismic exploration, establishing a reliable parameter model (such as velocity, density, impedance) is crucial for seismic migration imaging and reservoir characterization. The interpolation of well data to obtain a complete spatial model is an important aspect of parameter modeling. However, in practical applications, well data are often sparse and irregularly distributed, which complicates the accurate construction of subsurface parameter models. The Kriging method is an effective interpolation method based on discrete well data, but its theoretical assumptions do not meet the practical requirements in seismic exploration, resulting in low modeling accuracy. This article introduces seismic facies information into the Kriging method and proposes a novel parameter modeling method named the facies-constrained Kriging (FC-Kriging) method. The FC-Kriging method modifies the Euclidean distance metric used in Kriging so that the distance between two points depends not only on their spatial coordinates but also on their associated facies categories. The proposed method is a multi-information fusion method that integrates facies information based on well data, enabling good interpolation results even with a limited number of wells. The parameter modeling results based on the FC-Kriging method are more consistent with geological logic, exhibiting clearer boundary features and higher resolution. Furthermore, the FC-Kriging method does not introduce additional computational complexity, making it convenient to implement in a 3D situation. The FC-Kriging method is applied to the 2D Sigsbee model, the 3D Standford V reservoir model and F3 block field data. The results demonstrate its accuracy and effectiveness.

Picking the reflection horizon is an important step in velocity inversion and seismic interpretation. Manual picking is time-consuming and no longer suitable for current large-scale seismic data processing. Automatic algorithms using different seismic attributes such as instantaneous phase or dip attributes have been proposed. However, the computed attributes are usually inaccurate near discontinuities. The waveforms in the horizontal direction often change dramatically, which makes it difficult to track a horizon using the similarity of attributes. In this paper, we propose a novel method for automatic horizon picking using multiple seismic attributes and the Markov decision process (MDP). For the design of the MDP model, the decision time and state are defined as the horizontal and vertical spatial position on a seismic image, respectively. The reward function is defined in multi-dimensional feature attribute space. Multiple attributes can highlight different aspects of a seismic image and therefore overcome the limitations of the single-attribute MDP through the cross-constraint of multiple attributes. The optimal decision is made by searching the largest state value function in the reward function space. By considering cumulative reward, the lateral continuity of a seismic image can be effectively considered, and the impacts of abnormal waveform changes or bad traces in local areas for automatic horizon picking can be effectively avoided. An effective implementation scheme is designed for picking multiple reflection horizons. The proposed method has been successfully tested on both synthetic and field data.

High-resolution and high-fidelity seismic inversion imaging is one of the core issues of lithologic reservoir exploration. As a linearization subproblem of full-waveform inversion, least-squares migration (LSM) can obtain inversion results with more reliable amplitude, better resolution, and fewer artifacts that can be solved in either the data domain or image domain. For data-domain LSM, the calculation of the data-domain iteration can be very computationally intensive. In practical situations, the convexity of the cost function of LSM could be poor, resulting in slow or even nonconvergence iteration, so the ideal inversion imaging results cannot be reached. The image-domain LSM (ID-LSM) follows the logic of image deblurring, which realizes the effects of LSM in another way. The key problem of ID-LSM is to calculate a reliable Hessian matrix that can be effectively replaced by a set of point-spread functions (PSFs). Affected by the unknown source wavelet, the accuracy of the background velocity, and the accuracy of the forward/migration operator, the calculation results of the Hessian/PSF cannot be accurate. We first illustrate the impact of incorrect Hessian/PSF on ID-LSM through numerical experiments. To eliminate the influence of the inaccuracy of PSF, we develop the ID-LSM problem as a high-dimensional image deconvolution problem. An alternate update strategy of PSF and imaging results is given under the framework of the expectation-maximization algorithm by additionally introducing prior information about PSF and the inversion result. Numerical examples of synthetic data and field data verify that our method significantly improves image quality.

Introducing a high-precision deep-depth velocity model is essential for accurately imaging seismic data in complex areas such as deepwater and deep depth in oil and gas exploration. Conventional methods, such as reflection full-waveform inversion (RFWI), face challenges, notably the cycle-skipping issue, especially when the initial velocity model is far away from the true model. To address this, we develop a novel wave equation traveltime inversion (WETI) using the characteristic reflection wavefield (CRW) to update the low-wavenumber components of the velocity model. The CRWs are primary reflections in seismic data that contribute significantly to velocity model updates. We implement a multistep approach, including migration, characteristic reflector structure (CRS) picking, and demigration to extract the CRW. This extraction, constrained by CRS, ensures accurate matching between the observed and the simulated CRWs, even with an inaccurate initial velocity model, thus enabling an accurate traveltime shift estimation during inversion. Unlike conventional methods that use all reflection data simultaneously, CRW-WETI strategically selects fewer CRWs, enhancing inversion convexity and avoiding local minima from the cycle-skipping problem. This selective inversion begins with a limited number of CRWs to ensure stability and progressively incorporates more as the WETI process advances, eventually transitioning into conventional RFWI. Moreover, with the CRS constraint, CRW can be selected based on the target region. The target-oriented velocity inversion can also be implemented easily to update a local anomalous velocity model. Numerical examples of synthetic and field data demonstrate the effectiveness and validity of our method.