Guenther Schwedersky Neto

Stochastic Seismic AVO Inversion

One of the main challenge problems in geophysics is getting reliable seismic inverse models while the uncertainty is assessed. Seismic inverse problems may be tackled in a probabilistic framework resulting in a set of equiprobable acoustic and elastic impedance models. Here we show a new geostatistical seismic AVO method from where density, Vp and Vs models are retrieved. With the resulting Earth models we also compute the correspondent synthetic pre-stack data and the zero-reflectivity R(0) and Gradient (G) models. We successfully applied this workflow to a 3D synthetic seismic dataset from where density, Vp and Vs models were known. The final best models achieved a global correlation between the original and the synthetic seismograms of about 0.80.

Fast Seismic Inversion Methods Using Ant Colony Optimization Algorithm

This letter presents ACO\BBR - V, a new computationally efficient ant-colony-optimization-based algorithm, tailored for continuous-domain problems. The ACO\BBR - V algorithm is well suited for application in seismic inversion problems, owing to its intrinsic features, such as heuristics in generating the initial solution population and its facility to deal with multiobjective optimization problems. Here, we show how the ACO\BBR - V algorithm can be applied in two methodologies to obtain 3-D impedance maps from poststack seismic amplitude data. The first methodology pertains to the traditional method of forward convolution of a reflectivity model with the estimated wavelet, where ACO\BBR - V is used to guess the appropriate wavelet as the reflectivity model. In the second methodology, we propose an even faster inversion algorithm based on inverse filter optimization, where ACO\BBR - V optimizes the inverse filter that is deconvolved with the seismic traces and results in a reflectivity model similar to that found in well logs. This modeled inverse filter is then deconvolved with the entire 3-D seismic volume. In experiments, both the methodologies are applied to a synthetic 3-D seismic volume. The results validate their feasibility and the suitability of ACO\BBR - V as an optimization algorithm. The results also show that the second methodology has the advantages of a much higher convergence speed and effectiveness as a seismic inversion tool.

Elastic log editing and alternative invasion correction methods

Recent applications of seismic data in reservoir characterization, direct hydrocarbon indication, and production monitoring rely on the accuracy of elastic logs (density and sonic). Trying to develop (semi) quantitative seismic-based studies requires the use of well-to-seismic calibration; the well information is used as a bridge between the geology and the surface seismic data. Nevertheless, we must take into account that well logs are also indirect measurements of rock properties and subject to various sources of errors. Borehole wall rugosity due to washouts (or even threaded well bore) and mud filtrate invasion are the main sources of uncertainty on elastic logs. Velocity dispersion and shale alteration can also be very important. It is commonly believed that the correction of elastic logs is important only in refined studies, but sometimes even a simple acoustic well-to-seismic tie can be drastically improved with such corrections. Figure 1 presents two wavelets extracted from the same well based on raw and invasion-corrected acoustic impedance. Some amplitude and phase differences in the estimated wavelets can be seen. Even though these changes seem subtle, they can be important in quantitative processes like inversion and AVO interpretation. Figure 1. Wavelets extracted with raw (blue) and with invasion-corrected (red) acoustic impedance data. Figure 2 shows synthetic seismograms for four different wells from the same field. The synthetics based on the original logs are blue and those calculated with the corrected logs are red. The synthetics for three wells seem virtually unaffected by the correction but the synthetics for well 2 present significant differences near the objective. Figure 2. Synthetic zero-offset seismograms based on raw logs (blue) and after correction (red). Although elastic-log corrections can be done deterministically, based on rock physics theories and models (e.g., fluid substitution for invasion correction), there are some issues that we must take into consideration. In the case of …

Bayesian seismic inversion based on rock-physics prior modeling for the joint estimation of acoustic impedance, porosity and lithofacies

We propose a Bayesian approach for seismic inversion to estimate acoustic impedance, porosity and lithofacies within the reservoir conditioned to post-stack seismic and well data. The link between elastic and petrophysical properties is given by a joint prior distribution for the logarithm of impedance and porosity, based on a rock-physics model. The well conditioning is performed through a background model obtained by well log interpolation. Two different approaches are presented: in the first approach, the prior is defined by a single Gaussian distribution, whereas in the second approach it is defined by a Gaussian mixture to represent the well data multimodal distribution and link the Gaussian components to different geological lithofacies. The forward model is based on a linearized convolutional model. For the single Gaussian case, we obtain an analytical expression for the posterior distribution, resulting in a fast algorithm to compute the solution of the inverse problem, i.e. the posterior distribution of acoustic impedance and porosity as well as the facies probability given the observed data. For the Gaussian mixture prior, it is not possible to obtain the distributions analytically, hence we propose a Gibbs algorithm to perform the posterior sampling and obtain several reservoir model realizations, allowing an uncertainty analysis of the estimated properties and lithofacies. Both methodologies are applied to a real seismic dataset with three wells to obtain 3D models of acoustic impedance, porosity and lithofacies. The methodologies are validated through a blind well test and compared to a standard Bayesian inversion approach. Using the probability of the reservoir lithofacies, we also compute a 3D isosurface probability model of the main oil reservoir in the studied field.

Bayesian Framework to Wavelet Estimation and Linearized Acoustic Inversion

In this letter, we show how a seismic inversion method based on a Bayesian framework can be applied on poststack seismic data to estimate the wavelet, the seismic noise level, and the subsurface acoustic impedance. We propose a different linearized forward model and discuss in detail how some stochastic quantities are defined in a geophysical interpretation. The forward model and the Gaussian assumption for the likelihood distributions enable to obtain the conditional distributions. The method is divided into two sequential steps: the wavelet and noise level estimation, in which the posterior distribution is obtained via the Gibbs sampling algorithm, and the acoustic inversion, which uses the proposal forward model and the results of the first step. In the second step, the posterior distribution for acoustic impedance is analytically obtained. Therefore, the maximum a posteriori impedance can be calculated, yielding a very fast inversion algorithm. Results of tests on real data are compared with the deterministic constrained sparse-spike inversion, indicating that our proposal is viable and reliable.

A topological niching covariance matrix adaptation for multimodal optimization

Multimodal optimization attempts to find multiple global and local optima of a function. Finding a set of optimal solutions is particularly important for practical problems. However, this kind of problem requires optimization techniques that demand a high computational cost and a large amount of parameters to be adjusted. These difficulties increase in high-dimensional space problems. In this work, we propose a niching method based on recent developments in the basins (optimal locations) identification to reduce costs and perform better in high-dimensional spaces. Using Nearest-Better Clustering (NBC) and Hill-Valley (or Detect Multimodal) methods, an exploratory initialization routine is employed to identify basins on functions with different levels of complexity. To maintain diversity over the generations, we define a bi-objective function, which is composed by the original fitness function and the distance to the nearest better neighbor, assisted by a reinitialization scheme. The proposed method is implemented using Evolutionary Strategy (ES) known as Covariance Matrix Adaptation (CMA). Unlike recent multimodal approaches using CMA-ES, we use its step size to control the influence of niche, thus avoiding extra efforts in parameterization. We apply a benchmark of 20 test functions, specially designed for multimodal optimization evaluation, and compare the performance with a state-of-the-art method. Finally we discuss the results and show that the proposed approach can reach better and stable results even in high-dimensional spaces.

A method to estimate prediction intervals for artificial neural networks that is sensitive to the noise distribution in the outputs

The use of confidence estimation techniques on neural networks outputs plays an important role when these mathematical models are applied in many practical applications. However, few of these techniques have the capability to deal with variable noise rate in the predictions over the domain, making the assumptions about the reliability of these outputs become not suitable with their real accuracy. In this paper an extension to the non-linear regression method to estimate prediction intervals for feed forward neural networks is presented. The main idea of this method is that residuals variance should be estimated in function of the input data and not as a constant. Thus, using clustering techniques, distinct estimates of the residuals variance are made and then used to obtain new prediction intervals. Proceeding in this manner, the experiments results show that this approach can lead to prediction intervals that better reflect the confidence level of the neural network outputs.

ACO ℝ -V - An algorithm that incorporates the visibility heuristic to the ACO in continuous domain

Ant Colony Optimization (ACO) is an optimization metaheuristic based on the foraging behavior of ants. This metaheuristic was originally proposed to find good solutions to discrete combinatorial problems. Many extensions of the ACO heuristic for continuous domain have been proposed, but even those that claim close similarity with classical (discrete domain) ACO, like ACOR, do not use the heuristic information called visibility, commonly used in the original ACO algorithm. In this paper, we show the importance of the visibility in ACO, by proposing ACOℝ-V , a variant of ACOR that performs better in a number of benchmark functions. Results from our experiments shown better solutions when comparing ACOℝ-V to original ACOR. Moreover, the visibility increased the convergence speed as it reduced the number of times the objective function must be evaluated for a given precision in the solution.

Gradient Pore Pressure Modelling with Uncertain Well Data

Abnormal pore pressures can result in drilling problems such as borehole instability, stuck pipe, circulation loss, kicks, and blowouts. Gradient pore pressure prediction is of great importance for risk evaluation and for planning new wells in early stages of development and production of oil reservoirs. In this paper, a stochastic simulation with point distributions method is presented to integrate uncertain data in pore pressure cube characterization. The method consists in the use of direct sequential simulation with point distributions. Wells data, in this case, are considered “soft” data, of which uncertainty is quantified by local probability distribution functions or a set of values. A case study using a real dataset is also presented to illustrate the results.

Efficient confidence bounds for RBF networks for sparse and high dimensional data

Artificial Neural Networks have been used for function approximation and pattern recognition in a variety of domains. However, due to its empirical nature, it is difficult to derive an estimate of neural networks accuracy. There are in the literature a number of proposed methods to calculate a measure of confidence to the output of neural networks but in general these approaches require some strong assumptions which are rarely observed in real problems. This paper analyzes and extends the Validity Index Network, a model derived from radial basis function network that calculates the confidence of its outputs, we remove it restrictions in density calculations, specially in high dimensional input spaces, and improve the probability coverage of the prediction levels when the training data have variable density.