A nonlinear method for multiparameter inversion of pre‐stack seismic data based on anisotropic Markov random field

Abstract

Multiparameter inversion for pre‐stack seismic data plays a significant role in quantitative estimation of subsurface petrophysical properties. However, it remains a complicated problem due to the non‐unique results and unstable nature of the processing; the pre‐stack seismic inversion problem is ill‐posed and band‐limited. Combining the full Zoeppritz equation and additional assumptions with edge‐preserving regularisation can help to alleviate these problems. To achieve this, we developed an inversion method by constructing a new objective function that includes edge‐preserving regularisation and soft constraints based on anisotropic Markov random fields and is intended especially for layered formations. We applied a fast simulated annealing algorithm to solve the nonlinear optimisation problem. The method directly obtains reflectivity RPP values using the full Zoeppritz equation instead of its approximations and effectively controls the stability of the multiparameter inversion by assuming a sectionally constant S‐ and P‐wave velocity ratio and using the generalised Gardner equation. We substituted the inverted parameters, i.e., the P‐wave velocity, the fitting deviation of S‐wave velocity, and the density were inverted instead of the P‐wave velocity, the S‐wave velocity, and the density, and the generalised Gardner equation was applied as a constraint. Test results on two‐dimensional synthetic data indicated that our substitution obtained improved results for multiparameter inversion. The inverted results could be improved by utilising high‐order anisotropic Markov random field neighbourhoods at early stages and low‐order anisotropic Markov random field neighbourhoods in the later stages. Moreover, for layered formations, using a large horizontal weighting coefficient can preserve the lateral continuity of layers, and using a small vertical weighting coefficient allows for large longitudinal gradients of the interlayers. The inverted results of the field data revealed more detailed information about the layers and matched the logging curves at the wells acceptably over most parts of the curves.

Reservoir Lithology Determination by Hidden Markov Random Fields Based on a Gaussian Mixture Model

“…With only the Markov matrix used, the distribution of lithologies is preferential in the horizontal direction ( Fig. 11), since the transition has been governed by the left and right neighbors, demonstrated as larger values, that provides information on the lateral continuity or is under the consideration of layered formations (Appendix A) [29]. However, these matrices have to be modified in order to simulate transitions in a given reservoir which will be discussed in the real case study in the following.…”

High‐resolution reservoir stochastic modelling based on optimized estimation of vertical autocorrelation

“…In the field of oil and gas exploration, seismic inversion is one of the most important and commonly used methods for modelling reservoir elastic properties and evaluating reservoir heterogeneity (Tsvankin et al., 2010). However, owing to the band limitation of seismic data (Williamson & Worthington, 1993), whether it is pre‐stack inversion (Zhang et al., 2017), post‐stack inversion (Ali et al., 2018) or full‐wave inversion (Davy et al., 2021; Virieux & Operto, 2009), the high‐frequency components of elastic property model are missed. Therefore, seismic inversion cannot meet the high‐resolution requirements for evaluating reservoir heterogeneity.…”

The switching control method for the nonlinear response of seismic surface based on the local T-S model

“…With the development of China's national economy and the progress of science and technology, high-strength and light-weight building materials are widely used in building structures (Altukhov et al, 2018), the stiffness and damping of the structures are constantly reduced, and the building structures are more sensitive to seismic excitation. In order to reduce the seismic response of the building structure, in addition to studying the seismic design structure of the bearing system of the building structure itself (Zhang et al, 2017), some energy dissipation devices are set on the structure to increase the structural damping and consume the seismic energy through the nonlinear deformation of the energy dissipation materials, so as to reduce the seismic response of the main structure and effectively suppress the structural vibration (Zhang et al, 2016). Among these energy dissipation devices, the viscoelastic damper is the most concerned one (Ding et al, 2016), because it has the following advantages compared with other energy dissipation devices: as long as the structure starts to vibrate under minor interference, it can consume energy immediately (Zhang et al, 2018).…”