1D elastic full‐waveform inversion and uncertainty estimation by means of a hybrid genetic algorithm–Gibbs sampler approach

Near Surface Geophysics

Tognarelli

Mazzotti

2016

We estimate the elastic properties of marine sediments beneath the seabed by means of high‐resolution velocity analysis and one‐dimensional elastic full‐waveform inversion performed on two‐dimensional broad‐band seismic data of a well‐site survey. A high‐resolution velocity function is employed to exploit the broad frequency band of the data and to derive the P‐wave velocity field with a high degree of accuracy. To derive a complete elastic characterisation in terms of P‐wave and S‐wave velocities (Vp, Vs) and density of the subsurface, and to increase the resolution of the Vp estimates, we apply a one‐dimensional elastic full‐waveform inversion in which the outcomes derived from the velocity analysis are used as a priori information to define the Vp search range. The one‐dimensional inversion is done using genetic algorithm as the optimisation method. It is performed by considering two misfit functions: the first uses the entire waveform to compute the misfit between modelled and observed seismograms, and the second considers the envelope of the seismograms, thus relaxing the requirement of an exact estimation of the wavelet phase. The full‐waveform inversion and the high‐resolution velocity analysis yield comparable Vp profiles, but the full‐waveform inversion reconstruction is much more detailed. Regarding the full‐waveform inversion results, the final depth models of P‐ and S‐wave velocities and density show a fine‐layered structure with a significant increase in velocities and density at shallow depth, which may indicate the presence of a consolidated layer. The very similar velocities and density‐depth trends obtained by employing the two different misfit functions increase our confidence in the reliability of the predicted subsurface models.

“…, , and show that these

V p

increases often correspond to

V s

and density increases. However, the use of single‐component data and the limited offset range of the well‐site survey acquisition make us more confident on the predicted

V p

profiles than on the predicted

V s

and density depth trends (Aleardi and Mazzotti ). In fact, the greater ambiguity affecting

V s

and density estimates is clearly illustrated by the coloured maps in Figs.…”

Section: One‐dimensional Elastic Full‐waveform Inversionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Characterisation of shallow marine sediments using high‐resolution velocity analysis and genetic‐algorithm‐driven 1D elastic full‐waveform inversion

Near Surface Geophysics

Tognarelli

Mazzotti

2016

“…; Sajeva et al . ; Aleardi and Mazzotti ). We perform 1D elastic FWIs on synthetic seismic data, using a 1D reference elastic model composed of 12 layers, with a water depth of 400 m and a maximum depth of 1400 m. In the inversion, the P‐wave velocity ( Vp) , S‐wave velocity ( Vs) , and density values are unknown, whereas the number of layers, their depths, the source signature, and the water properties ( Vp , density, and water depth) are assumed known.…”

Section: Tests On the Analytic Objective Functionsmentioning

confidence: 98%

“…Many other applications of GA to geophysics were proposed in the following years (Mallick ; Mallick and Dutta ; Padhi and Mallick ; Aleardi ; Li and Mallick ; Aleardi, Tognarelli and Mazzotti ; Sajeva et al . ; Sajeva, Aleardi and Mazzotti ; Aleardi and Ciabarri ; Aleardi and Mazzotti ). Other noteworthy MC methods that have been applied to solve geophysical optimisation problems are the neighbourhood algorithm (NA) (Sambridge ), and particle swarm optimisation (PSO) (Kennedy and Eberhart ).…”

Section: Introductionmentioning

confidence: 97%

Comparing the performances of four stochastic optimisation methods using analytic objective functions, 1D elastic full‐waveform inversion, and residual static computation

Sajeva

Geophysical Prospecting

Galuzzi

et al. 2017

Self Cite

We compare the performances of four different stochastic optimisation methods using four analytic objective functions and two highly non-linear geophysical optimisation problems: 1D elastic full-waveform inversion (FWI) and residual static computation. The four methods we consider, namely, adaptive simulated annealing (ASA), genetic algorithm (GA), neighbourhood algorithm (NA), and particle swarm optimisation (PSO), are frequently employed for solving geophysical inverse problems. Because geophysical optimisations typically involve many unknown model parameters, we are particularly interested in comparing the performances of these stochastic methods as the number of unknown parameters increases. The four analytic functions we choose simulate common types of objective functions encountered in solving geophysical optimisations: a convex function, two multi-minima functions that differ in the distribution of minima, and a nearly flat function. Similar to the analytic tests, the two seismic optimisation problems we analyse are characterized by very different objective functions. The first problem is a 1D elastic FWI, which is strongly ill-conditioned and exhibits a nearly flat objective function, with a valley of minima extended along the density direction. The second problem is the residual static computation, which is characterized by a multi-minima objective function produced by the so-called cycle-skipping phenomenon. According to the tests on the analytic functions and on the seismic data, GA generally displays the best scaling with the number of parameters. It encounters problems only in the case of irregular distribution of minima, that is, when the global minimum is at the border of the search space and a number of important local minima are distant from the global minimum. The ASA method is often the best-performing method for low-dimensional model spaces, but its performance worsens as the number of unknowns increases. The PSO is effective in finding the global minimum in the case of low-dimensional model spaces with few local minima or in the case of a narrow flat valley. Finally, the NA method is competitive with the other methods only for low-dimensional model spaces; its performance stability sensibly worsens in the case of multi-minima objective functions

“…On the one hand, MCMC methods have been successfully applied to solve many geophysical problems (Malinverno ; Sambridge and Mosegaard ; Bosch et al . ; Aleardi and Mazzotti ) as they can theoretically assess the posterior uncertainties in cases of complex (i.e. non‐parametric) prior distributions and non‐linear forward modellings.…”

Section: Introductionmentioning

confidence: 99%

Markov chain Monte Carlo algorithms for target‐oriented and interval‐oriented amplitude versus angle inversions with non‐parametric priors and non‐linear forward modellings

Geophysical Prospecting

Salusti

2019

Self Cite

In geophysical inverse problems, the posterior model can be analytically assessed only in case of linear forward operators, Gaussian, Gaussian mixture, or generalized Gaussian prior models, continuous model properties, and Gaussian‐distributed noise contaminating the observed data. For this reason, one of the major challenges of seismic inversion is to derive reliable uncertainty appraisals in cases of complex prior models, non‐linear forward operators and mixed discrete‐continuous model parameters. We present two amplitude versus angle inversion strategies for the joint estimation of elastic properties and litho‐fluid facies from pre‐stack seismic data in case of non‐parametric mixture prior distributions and non‐linear forward modellings. The first strategy is a two‐dimensional target‐oriented inversion that inverts the amplitude versus angle responses of the target reflections by adopting the single‐interface full Zoeppritz equations. The second is an interval‐oriented approach that inverts the pre‐stack seismic responses along a given time interval using a one‐dimensional convolutional forward modelling still based on the Zoeppritz equations. In both approaches, the model vector includes the facies sequence and the elastic properties of P‐wave velocity, S‐wave velocity and density. The distribution of the elastic properties at each common‐mid‐point location (for the target‐oriented approach) or at each time‐sample position (for the time‐interval approach) is assumed to be multimodal with as many modes as the number of litho‐fluid facies considered. In this context, an analytical expression of the posterior model is no more available. For this reason, we adopt a Markov chain Monte Carlo algorithm to numerically evaluate the posterior uncertainties. With the aim of speeding up the convergence of the probabilistic sampling, we adopt a specific recipe that includes multiple chains, a parallel tempering strategy, a delayed rejection updating scheme and hybridizes the standard Metropolis–Hasting algorithm with the more advanced differential evolution Markov chain method. For the lack of available field seismic data, we validate the two implemented algorithms by inverting synthetic seismic data derived on the basis of realistic subsurface models and actual well log data. The two approaches are also benchmarked against two analytical inversion approaches that assume Gaussian‐mixture‐distributed elastic parameters. The final predictions and the convergence analysis of the two implemented methods proved that our approaches retrieve reliable estimations and accurate uncertainties quantifications with a reasonable computational effort.