The ensemble Kalman inversion (EKI) for the solution of Bayesian inverse problems type , with being an unknown parameter, a given datum, and measurement noise, is powerful tool usually derived from sequential Monte Carlo point view. It describes dynamics particles whose initial empirical measure sampled prior, evolving over artificial time toward approximate problem, emulating posterior, corres...

The minimum number of NOT gates in a Boolean circuit computing a Boolean function f is called the inversion complexity of f . In 1958, Markov determined the inversion complexity of every Boolean function and particularly proved that ⌈log 2 (n+ 1)⌉ NOT gates are sufficient to compute any Boolean function on n variables. In this paper, we consider circuits computing non-deterministically and dete...

in exploration seismology, estimation of elastic parameters of rocks using seismic amplitudes is considered as inverse problems. nowadays, model-based and more generally optimization-based algorithms are of the most common methods of seismic inversion. these algorithms which are known as deterministic methods, are suffering from two main problems; first, vertical resolution of outputs is very l...

We analyze reduced basis acceleration of recently proposed deterministic Bayesian inversion algorithms for partial differential equations with uncertain distributed parameter, for observation data subject to additive, Gaussian observation noise. Specifically, Bayesian inversion of affine-parametric, linear operator families on possibly high-dimensional parameter spaces. We consider “high-fideli...

[1] Time-lapse geophysical measurements are widely used to monitor the movement of water and solutes through the subsurface. Yet commonly used deterministic least squares inversions typically suffer from relatively poor mass recovery, spread overestimation, and limited ability to appropriately estimate nonlinear model uncertainty. We describe herein a novel inversion methodology designed to rec...

The conventional approach in reservoir characterization uses an extrapolation of petrophysical properties calculated from well logs determining the entire field volume. This technique fails to acknowledge/ factor heterogeneity a reservoir, and consequently leads errors capacity quantification. research work employs deterministic seismic inversion each sand. First, sand was identified intervals ...

An overview of the geophysical tomography interpretation method is presented. Two approaches are reviewed, (1) deterministic tomography inversion, developed for rock elasticity investigations, and (2) probability tomography imaging, developed in the domain of potential field methods. The theoretical basis of both approaches is initially outlined, then selected laboratory and field applications ...

Present-day high quality 3D acquisition can give us lower frequencies and longer offsets with which to invert. However, the computational costs involved in handling this data explosion are tremendous. Therefore, recent developments in full-waveform inversion have been geared towards reducing the computational costs involved. A key aspect of several approaches that have been proposed is a dramat...

Deterministic waveform inversion in the p ? domain permits estimation of the long-wavelength p-wave background velocity, the short-wavelength elastic parameter uctuations, and the energy source for a marine data set from the Gulf of Mexico. The forward map is a convolutional model for p-wave primaries-only seismograms of viscoelastic, layered media. Two types of inversion (output least squares ...

Abstract We consider the reconstruction of moving sources using partial measured data. A two-step deterministic-statistical approach is proposed. In first step, an approximate direct sampling method developed to obtain locations at different times. Such information coded in priors, which critical for success Bayesian second step. The well-posedness posterior measure analyzed sense Hellinger dis...