Ruben Nunes

Parallelization of sequential Gaussian, indicator and direct simulation algorithms

Improving the performance and robustness of algorithms on new high-performance parallel computing architectures is a key issue in efficiently performing 2D and 3D studies with large amount of data. In geostatistics, sequential simulation algorithms are good candidates for parallelization. When compared with other computational applications in geosciences (such as fluid flow simulators), sequential simulation software is not extremely computationally intensive, but parallelization can make it more efficient and creates alternatives for its integration in inverse modelling approaches. This paper describes the implementation and benchmarking of a parallel version of the three classic sequential simulation algorithms: direct sequential simulation (DSS), sequential indicator simulation (SIS) and sequential Gaussian simulation (SGS). For this purpose, the source used was GSLIB, but the entire code was extensively modified to take into account the parallelization approach and was also rewritten in the C programming language. The paper also explains in detail the parallelization strategy and the main modifications. Regarding the integration of secondary information, the DSS algorithm is able to perform simple kriging with local means, kriging with an external drift and collocated cokriging with both local and global correlations. SIS includes a local correction of probabilities. Finally, a brief comparison is presented of simulation results using one, two and four processors. All performance tests were carried out on 2D soil data samples. The source code is completely open source and easy to read. It should be noted that the code is only fully compatible with Microsoft Visual C and should be adapted for other systems/compilers.

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.

Simulation of Continuous Variables at Meander Structures: Application to Contaminated Sediments of a Lagoon

Simulation of continuous variables conditioned to meander structures is an important tool in the context of soil contamination assessment, namely, when the contamination is related with depositional sediments in water channels. Hence, this paper proposes using bi-point statistics stochastic simulation with local anisotropy trends to simulate continuous variables inside predefined channels. To accomplish this objective, the Direct Sequential Simulation (DSS) algorithm was modified to account for local anisotropy when searching for the simulation node. This methodological approach was applied to the spatial characterization of polluted sediments in a coastal lagoon located in the North of Portugal (Barrinha de Esmoriz).

Geostatistical Seismic Inversion with Direct Sequential Simulation and Co-simulation with Multi-local Distribution Functions

Stochastic sequential simulation is a common modelling technique used in Earth sciences and an integral part of iterative geostatistical seismic inversion methodologies. Traditional stochastic sequential simulation techniques based on bi-point statistics assume, for the entire study area, stationarity of the spatial continuity pattern and a single probability distribution function, as revealed by a single variogram model and inferred from the available experimental data, respectively. In this paper, the traditional direct sequential simulation algorithm is extended to handle non-stationary natural phenomena. The proposed stochastic sequential simulation algorithm can take into consideration multiple regionalized spatial continuity patterns and probability distribution functions, depending on the spatial location of the grid node to be simulated. This work shows the application and discusses the benefits of the proposed stochastic sequential simulation as part of an iterative geostatistical seismic inversion methodology in two distinct geological environments in which non-stationarity behaviour can be assessed by the simultaneous interpretation of the available well-log and seismic reflection data. The results show that the elastic models generated by the proposed stochastic sequential simulation are able to reproduce simultaneously the regional and global variogram models and target distribution functions relative to the average volume of each sub-region. When used as part of a geostatistical seismic inversion procedure, the retrieved inverse models are more geologically realistic, since they incorporate the knowledge of the subsurface geology as provided, for example, by seismic and well-log data interpretation.

Acceleration of stochastic seismic inversion in OpenCL-based heterogeneous platforms

Seismic inversion is an established approach to model the geophysical characteristics of oil and gas reservoirs, being one of the basis of the decision making process in the oil&gas exploration industry. However, the required accuracy levels can only be attained by dealing and processing significant amounts of data, often leading to consequently long execution times. To overcome this issue and to allow the development of larger and higher resolution elastic models of the subsurface, a novel parallelization approach is herein proposed targeting the exploitation of GPU-based heterogeneous systems based on a unified OpenCL programming framework, to accelerate a state of art Stochastic Seismic Amplitude versus Offset Inversion algorithm. To increase the parallelization opportunities while ensuring model fidelity, the proposed approach is based on a careful and selective relaxation of some spatial dependencies. Furthermore, to take into consideration the heterogeneity of modern computing systems, usually composed of several and different accelerating devices, multi-device parallelization strategies are also proposed. When executed in a dual-GPU system, the proposed approach allows reducing the execution time in up to 30 times, without compromising the quality of the obtained models. HighlightsNovel approach to accelerate a Stochastic Seismic AVO Inversion algorithm.Exploitation of GPU-based heterogeneous systems based on a unified OpenCL framework.Multi-device parallelization strategies to tackle system heterogeneity.The adopted parallelization strategy ensures the quality of the inversion results.Performance speedup as high as 30i? is obtained with a dual-GPU system.

Integration of Uncertain Data in Geostatistical Modelling

Most geostatistical estimation and simulation methodologies assume the experimental data as hard measurements, meaning that the measures of a given property of interest are not associated with uncertainty. The challenge of integrating uncertain experimental data at the geostatistical estimation or simulation models is not new. Several attempts have been made, either considering the uncertain data as soft data or interpreting it as inequality constraints, based on the indicator formalism or decreasing the weight of soft data in kriging procedures. This paper presents a stochastic simulation methodology where the uncertain experimental data are modelled by a probability distribution at each sample location. Data values are firstly drawn, by stochastic simulation, at these locations prior to the simulation of the rest of the grid nodes. This method is also extended to the simulation of categorical uncertain data, as well as to the simulation with uncertain block support data. To illustrate the proposed methodology, an application to a real case study of pore pressure prediction of oil reservoirs is presented, as well as an upscaling problem.

Geostatistical seismic inversion for non-stationary patterns using direct sequential simulation and co-simulation

Geostatistical seismic inversion methods are routinely used in reservoir characterization studies because of their potential to infer the spatial distribution of the petro-elastic properties of interest (e.g., density, elastic and acoustic impedances) along with the associated spatial uncertainty. Within the geostatistical seismic inversion framework, the retrieved inverse elastic models are conditioned by a global probability distribution function and global spatial continuity model as estimated from the available well-log data for the entire inversion grid. However, the spatial distribution of the real subsurface elastic properties is complex, heterogeneous and in many cases non-stationary since they directly depend on the subsurface geology, i.e., the spatial distribution of the facies of interest. In these complex geological settings, application of a single distribution function and spatial continuity model is not enough to properly model the natural variability of the elastic properties of interest. In this study, we propose a 3D geostatistical inversion technique that is able to incorporate the reservoirs heterogeneities. This method uses a traditional geostatistical seismic inversion conditioned by local multi-distribution functions and spatial continuity models under non-stationary conditions. The procedure of the proposed methodology is based on a zonation criterion along the vertical direction of the reservoir grid. Each zone can be defined by conventional seismic interpretation, with the identification of the main seismic units and significant variations of seismic amplitudes. The proposed method was applied to a highly non-stationary synthetic seismic dataset with different levels of noise. The results of this work clearly show the advantages of the proposed method against conventional geostatistical seismic inversion procedures. It is important to highlight the impact of this technique in terms of a higher convergence between real and inverted reflection seismic data and the more realistic approximation towards the real subsurface geology comparing with traditional techniques. This article is protected by copyright. All rights reserved

Geostatistical Data Fusion: Application to Red Edge Bands of Sentinel 2

The new ESA Sentinel-2 satellite delivers images of the red-edge band at a spatial resolution of 20m. These bands are particular useful for vegetation monitoring in general and present high potential of application in precision agriculture. For this, we propose a data fusion methodology for downscaling rededge bands to 10 m spatial resolution using the information of visible and near infrared band. The methodology is based on inverse modelling by combining geostatistical stochastic simulation methods and genetic programming. A case study case presents the preliminary results.

Geostatistical seismic inversion for frontier exploration

AbstractNumerical 3D high-resolution models of subsurface petroelastic properties are key tools for exploration and production stages. Stochastic seismic inversion techniques are often used to infer the spatial distribution of the properties of interest by integrating simultaneously seismic reflection and well-log data also allowing accessing the spatial uncertainty of the retrieved models. In frontier exploration areas, the available data set is often composed exclusively of seismic reflection data due to the lack of drilled wells and are therefore of high uncertainty. In these cases, subsurface models are usually retrieved by deterministic seismic inversion methodologies based exclusively on the existing seismic reflection data and an a priori elastic model. The resulting models are smooth representations of the real complex geology and do not allow assessing the uncertainty. To overcome these limitations, we have developed a geostatistical framework that allows inverting seismic reflection data without...

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.