Prestack seismic stochastic inversion based on statistical characteristic parameters

In the conventional stochastic inversion method,the spatial structure information of underground strata is usually characterized by variograms.However,effectively characterizing the heterogeneity of complex strata is difficult.In this paper,multiple parameters are used to fully explore the underground formation information in the known seismic reflection and well log data.The spatial structure characteristics of complex underground reservoirs are described more comprehensively using multiple statistical characteristic parameters.We propose a prestack seismic stochastic inversion method based on prior information on statistical characteristic parameters.According to the random medium theory,this method obtains several statistical characteristic parameters from known seismic and logging data,constructs a prior information model that meets the spatial structure characteristics of the underground strata,and integrates multiparameter constraints into the likelihood function to construct the objective function.The very fast quantum annealing algorithm is used to optimize and update the objective function to obtain the fi nal inversion result.The model test shows that compared with the traditional prior information model construction method,the prior information model based on multiple parameters in this paper contains more detailed stratigraphic information,which can better describe complex underground reservoirs.A real data analysis shows that the stochastic inversion method proposed in this paper can effectively predict the geophysical characteristics of complex underground reservoirs and has a high resolution.

Stochastic seismic inversion and Bayesian facies classification applied to porosity modeling and igneous rock identification

We apply stochastic seismic inversion and Bayesian facies classification for porosity modeling and igneous rock identification in the presalt interval of the Santos Basin. This integration of seismic and well-derived information enhances reservoir characterization. Stochastic inversion and Bayesian classification are powerful tools because they permit addressing the uncertainties in the model. We used the ES-MDA algorithm to achieve the realizations equivalent to the percentiles P10, P50, and P90 of acoustic impedance, a novel method for acoustic inversion in presalt. The facies were divided into five: reservoir 1,reservoir 2, tight carbonates, clayey rocks, and igneous rocks. To deal with the overlaps in acoustic impedance values of facies, we included geological information using a priori probability, indicating that structural highs are reservoir-dominated. To illustrate our approach, we conducted porosity modeling using facies-related rock-physics models for rock-physics inversion in an area with a well drilled in a coquina bank and evaluated the thickness and extension of an igneous intrusion near the carbonate-salt interface. The modeled porosity and the classified seismic facies are in good agreement with the ones observed in the wells. Notably, the coquinas bank presents an improvement in the porosity towards the top. The a priori probability model was crucial for limiting the clayey rocks to the structural lows. In Well B, the hit rate of the igneous rock in the three scenarios is higher than 60%, showing an excellent thickness-prediction capability.

Key parameter optimization and analysis of stochastic seismic inversion

Stochastic seismic inversion is the combination of geostatistics and seismic inversion technology which integrates information from seismic records, well logs, and geostatistics into a posterior probability density function （PDF） of subsurface models. The Markov chain Monte Carlo （MCMC） method is used to sample the posterior PDF and the subsurface model characteristics can be inferred by analyzing a set of the posterior PDF samples. In this paper, we first introduce the stochastic seismic inversion theory, discuss and analyze the four key parameters： seismic data signal-to-noise ratio （S/N）, variogram, the posterior PDF sample number, and well density, and propose the optimum selection of these parameters. The analysis results show that seismic data S/N adjusts the compromise between the influence of the seismic data and geostatistics on the inversion results, the variogram controls the smoothness of the inversion results, the posterior PDF sample number determines the reliability of the statistical characteristics derived from the samples, and well density influences the inversion uncertainty. Finally, the comparison between the stochastic seismic inversion and the deterministic model based seismic inversion indicates that the stochastic seismic inversion can provide more reliable information of the subsurface character.

Inverse stochastic resonance in modular neural network with synaptic plasticity

This work explores the inverse stochastic resonance(ISR) induced by bounded noise and the multiple inverse stochastic resonance induced by time delay by constructing a modular neural network, where the modified Oja’s synaptic learning rule is employed to characterize synaptic plasticity in this network. Meanwhile, the effects of synaptic plasticity on the ISR dynamics are investigated. Through numerical simulations, it is found that the mean firing rate curve under the influence of bounded noise has an inverted bell-like shape, which implies the appearance of ISR. Moreover, synaptic plasticity with smaller learning rate strengthens this ISR phenomenon, while synaptic plasticity with larger learning rate weakens or even destroys it. On the other hand, the mean firing rate curve under the influence of time delay is found to exhibit a decaying oscillatory process, which represents the emergence of multiple ISR. However, the multiple ISR phenomenon gradually weakens until it disappears with increasing noise amplitude. On the same time, synaptic plasticity with smaller learning rate also weakens this multiple ISR phenomenon, while synaptic plasticity with larger learning rate strengthens it. Furthermore, we find that changes of synaptic learning rate can induce the emergence of ISR phenomenon. We hope these obtained results would provide new insights into the study of ISR in neuroscience.

Detailed reservoir inversion addressing geological problems in reservoir development

In the Ken 71 development block, fluvial facies of the Neogene Guantao Formation and delta facies of the Paleogene Dongying Formation are the main pay beds. It is a multiple oil and water system which is complicated by faults. Characteristics of the block include a dense well network, thin reservoirs, complicated horizontal relationships, and small velocity difference between reservoir and non-reservoir. Therefore, it is difficult to conduct detailed reservoir description for subsequent development project adjustment. We demonstrate a stochastic seismic inversion which aims at detailed reservoir description. It is a technology which utilizes multiple wells, seismic data, and geological calibration and integrates with 3D structural interpretation results to build a 3D multi-fault detailed and constrained geological model. On this basis, we adopted stochastic seismic inversion to conduct a multi-stratum parameters inversion such as impedance and lithology. As a result, thin interbedded strata in the block were well resolved and the results demonstrated the importance of detailed reservoir inversion for oilfield development.

Output Feedback for Stochastic Nonlinear Systems with Unmeasurable Inverse Dynamics

This paper considers a concrete stochastic nonlinear system with stochastic unmeasurable inverse dynamics. Motivated by the concept of integral input-to-state stability （iISS） in deterministic systems and stochastic input-to-state stability （SISS） in stochastic systems, a concept of stochastic integral input-to-state stability （SiISS） using Lyapunov functions is first introduced. A constructive strategy is proposed to design a dynamic output feedback control law, which drives the state to the origin almost surely while keeping all other closed-loop signals almost surely bounded. At last, a simulation is given to verify the effectiveness of the control law.

Inhibitory effect induced by fractional Gaussian noise in neuronal system

We discover a phenomenon of inhibition effect induced by fractional Gaussian noise in a neuronal system. Firstly,essential properties of fractional Brownian motion(fBm) and generation of fractional Gaussian noise(fGn) are presented,and representative sample paths of fBm and corresponding spectral density of fGn are discussed at different Hurst indexes.Next, we consider the effect of fGn on neuronal firing, and observe that neuronal firing decreases first and then increases with increasing noise intensity and Hurst index of fGn by studying the time series evolution. To further quantify the inhibitory effect of fGn, by introducing the average discharge rate, we investigate the effects of noise and external current on neuronal firing, and find the occurrence of inhibitory effect about noise intensity and Hurst index of f Gn at a certain level of current. Moreover, the inhibition effect is not easy to occur when the noise intensity and Hurst index are too large or too small. In view of opposite action mechanism compared with stochastic resonance, this suppression phenomenon is called inverse stochastic resonance(ISR). Finally, the inhibitory effect induced by fGn is further verified based on the inter-spike intervals(ISIs) in the neuronal system. Our work lays a solid foundation for future study of non-Gaussian-type noise on neuronal systems.

Effects of potassium channel blockage on inverse stochastic resonance in Hodgkin-Huxley neural systems

Inverse stochastic resonance(ISR)is a phenomenon in which the firing activity of a neuron is inhibited at a certain noise level.In this paper,the effects of potassium channel blockage on ISR in single Hodgkin-Huxley neurons and in small-world networks were investigated.For the single neuron,the ion channel noise-induced ISR phenomenon can occur only in a certain small range of potassium channel blockage ratio.Bifurcation analysis showed that this small range is the bistable region regulated by the external bias current.For small-world networks,the effect of non-homogeneous network blockage on ISR was investigated.The network blockage ratio was used to represent the proportion of potassium-channel-blocked neurons to total network neurons.It is found that an increase in network blockage ratio at small coupling strengths results in shorter ISR duration.When the coupling strength is increased,the ISR is more significant in the case of a large network blockage ratio.The ISR phenomenon is determined by the network blockage ratio,the coupling strength,and the ion channel noise.Our results will provide new perspectives on the observation of ISR in neuroscience experiments.

Adaptive Bayesian Inference for Discontinuous Inverse Problems,Application to Hyperbolic Conservation Laws

Various works from the literature aimed at accelerating Bayesian inference in inverse problems.Stochastic spectral methods have been recently proposed as surrogate approximations of the forward uncertainty propagation model over the support of the prior distribution.These representations are efficient because they allow affordable simulation of a large number of samples from the posterior distribution.Unfortunately,they do not perform well when the forward model exhibits strong nonlinear behavior with respect to its input.In this work,we first relate the fast(exponential)L2-convergence of the forward approximation to the fast(exponential)convergence(in terms of Kullback-Leibler divergence)of the approximate posterior.In particular,we prove that in case the prior distribution is uniform,the posterior is at least twice as fast as the convergence rate of the forward model in those norms.The Bayesian inference strategy is developed in the framework of a stochastic spectral projection method.The predicted convergence rates are then demonstrated for simple nonlinear inverse problems of varying smoothness.We then propose an efficient numerical approach for the Bayesian solution of inverse problems presenting strongly nonlinear or discontinuous system responses.This comes with the improvement of the forward model that is adaptively approximated by an iterative generalized Polynomial Chaos-based representation.The numerical approximations and predicted convergence rates of the former approach are compared to the new iterative numerical method for nonlinear time-dependent test cases of varying dimension and complexity,which are relevant regarding our hydrodynamics motivations and therefore regarding hyperbolic conservation laws and the apparition of discontinuities in finite time.