# A New Stochastic Process of Prestack Inversion for Rock Property Estimation
###### Abstract  
In order to enrich the current prestack stochastic inversion theory, we propose a prestack stochastic inversion method based on adaptive particle swarm optimization combined with Markov chain Monte Carlo (MCMC). The MCMC could provide a stochastic optimization approach, and, with the APSO, have a better performance in global optimization methods. This method uses logging data to define a preprocessed model space. It also uses Bayesian statistics and Markov chains with a state transition matrix to update and evolve each generation population in the data domain, then adaptive particle swarm optimization is used to find the global optimal value in the finite model space. The method overcomes the problem of over-fitting deterministic inversion and improves the efficiency of stochastic inversion. Meanwhile, the fusion of multiple sources of information can reduce the non-uniqueness of solutions and improve the inversion accuracy. We derive the APSO algorithm in detail, give the specific workflow of prestack stochastic inversion, and verify the validity of the inversion theory through the inversion test of two-dimensional prestack data in real areas. p _applied_  
15 September 2021  
[PERSON] and [PERSON] also applied VFSA to AVO inversion with conditionalized model-space, not only to speed convergence, but also to retrieve blocky solutions [13]. [PERSON] and [PERSON] used pseudo-wells and generated synthetic traces to match seismic data via stochastic inversion [14]. Many kinds of stochastic inversion employ Bayesian theory with seismic measurements and well-log information to construct likelihood function and estimate posterior information. [PERSON] et al. used a rock-physics model to allow prior information into a Bayesian likelihood function and then applied it into a probabilistic seismic inversion, improving reservoir characterization [15]. Markov Chain Monte Carlo (MCMC) is widely applied in the Bayesian inversion theorem. The advantage of MCMC is that it provides a stochastic optimization approach. The MCMC algorithm has the capacity to estimate impedance perturbation using a random search strategy ([PERSON] et al., 2015) [16]. However, the simulation of traditional MCMC is ineffective ([PERSON] and [PERSON], 1995) [17]. Particle swarm optimization (PSO) is simulated from the bird's behavior and has a better performance than some other global optimization methods. Among those, adaptive particle swarm optimization (APSO) has been developed in recent decades, and can be applied in inversion issues. We propose using Adaptive Particle Swarm Optimization (APSO), a more efficient optimization tool compared to the traditional PSO, to accelerate MCMC simulation by randomly generating many particles in a swarm ([PERSON] et al., 2009) [18], where every particle contains rock property parameters obtained from well-log data analysis and interpretation. The migration algorithm we use is based on kinematic ray tracing via image ray calculation [19; 20]. As a result, the model perturbation can be correctly positioned in the time or depth domain. Recently, [PERSON] et al. proposed the Prestack Bayesian statistical inversion constrained by reflection features [21], and [PERSON] et al. proposed the simultaneous inversion for S-wave velocity and density from the SV-SV wave [22]. This study proposes using adaptive particle swarm optimization, an improved nonlinear optimization method that has been proven to be more cost-efficient than conventional particle swarm optimization [23]. Additionally, this method can provide the position of global minimums in a finite model space aligning with the best solution of impedance inversion. It overcomes problems of deterministic inversion, which are over-fitting and demand for a good initial model. It combines the low-frequency component of well-log data and the middle-frequency component of seismic data. The method we present solves the problem of ill-posed and non-solution with good properties of noise resistance.