Publications

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Reservoir uncertainty description via petrophysical inversion of seismic data Hydrocarbon reservoir characterization commonly combines seismic, petrophysical, and well-log information in a variety of procedures. As an inference problem, this combination can be formulated in a unified inverse framework, reducing the bias of nonlinear relationships among intermediate variables and providing a comprehensive calculation of uncertainties at final estimates of the medium parameters. In addition, the unified formulation leads to the joint estimation of reservoir and medium elastic properties as well as related parameters of interests...
Bosch, M., G. Bertorelli, G. Alvarez, A. Moreno, and R. Colmenares
Elastic seismic inversion and reservoir characterization in the Llanos Basin, Colombia The contribution of seismic inversion to lithology and fluid characterization in oil reservoirs is geology and data-dependent. Several studies of reservoir characterization based on elastic seismic inversion in the Llanos Basin in Colombia have proved to be successful for an accurate description of the siliciclastic lithology of lower members of the Carbonera Formation. Mass density estimated from the inversion has been an important lithology discriminator because of the compaction of shale, which exhibits larger densities than sand. In the analysis of properties calculated from well-log data, the separation in property space of oil sands and brine sands is moderate to small...
Bosch, M., D. Morales, Y. Gomez, T. Karmierczak, T. Salinas, G. Alvarez, A. Moreno, Y. Pino, and E. Medina
Seismic inversion using a geostatistical, petrophysical and acoustic model Interpretation of seismic data for structure and stratigraphy is commonly based on the geological knowledge of the area and the correlation of seismic reflections with well-log data. However, the relation between the seismic image and the well-log data is not straightforward, is often obscured by the wave-propagation phenomenon. Part of the problem is that reflectivities do not measure the interval properties but result from the property contrasts of consecutive strata. Seismic inversion provides insight into the interpretation process, transforming reflection amplitudes into physically meaningful variations in interval properties, which can be directly related to the well-log data after appropriate scale considerations.
Bosch, M., C. Campos, and E. Fernández
Monte Carlo approach to the joint estimation of reservoir and elastic parameters from seismic amplitudes Inversion of seismic data and quantification of reservoir properties, such as porosity, lithology, or fluid saturation, are commonly executed in two consecutive steps: a geophysical inversion to estimate the elastic parameters and a petrophysical inversion to estimate the reservoir properties. We combine within an integrated formulation the geophysical and petrophysical components of the problem to estimate the elastic and reservoir properties jointly. We solve the inverse problem following a Monte Carlo sampling approach, which allows us to quantify the uncertainties of the reservoir estimates accounting for the combination of geophysical data uncertainties...
Bosch, M., L. Cara, J. Rodrigues, A. Navarro, and M. Díaz, A.
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Full-waveform inversion of intensity-focused seismic data Full-waveform inversion (FWI) is a promising tool for the comprehensive analysis of seismic data because it involves modeling the complete elastodynamic phenomena in 3D for the estimation of medium parameters. However, the application for reservoir characterization is still limited in achieving the inverse problem solution using reasonable computational resources and the required model resolution....
Bosch, M., S. Mijares, R. Pachano and F. Peña
Seismic inversion for reservoir properties combining statistical rock physics and geostatistics: A review There are various approaches for the quantitative estimation of reservoir properties from seismic inversion. A general Bayesian formulation for the inverse problem can be implemented in two different workflows. In the sequential approach, first seismic data are inverted, deterministically or stochastically, into elastic properties; then rock-physics models transform those elastic properties to the reservoir property of interest. The joint or simultaneous workflow accounts for the elastic parameters and the reservoir properties, often in a Bayesian formulation, guaranteeing consistency between the elastic and reservoir properties...
Bosch, M., T. Mukerji, and E. Gonzalez
Petrophysical seismic inversion conditioned to well-log data: methods and application to a gas reservoir Hydrocarbon reservoirs are characterized by seismic, well-log, and petrophysical information, which is dissimilar in spatialHydrocarbon reservoirs are characterized by seismic, well-log, and petrophysical information, which is dissimilar in spatial distribution, scale, and relationship to reservoir properties. We combine this diverse information in a unified inverse-problem formulation using a multi-property, multiscale model, linking properties statistically by petrophysical relationships and conditioning them to well-log data. Two approaches help us: (1) Markov-chain Monte Carlo sampling, which generates many reservoir realizations for estimating medium properties and posterior marginal probabilities, and (2) optimization with a least-squares iterative technique to obtain the most probable model configuration.
Bosch, M., C. Carvajal, J. Rodrigues, A. Torres, M. Aldana, and J. Sierra
The optimization approach to lithological inversion: combining seismic data and petrophysics for porosity prediction Least-squares model optimization methods are commonly used to estimate physical media properties by fitting geophysical data with nonlinear models. I extendLeast-squares model optimization methods are commonly used to estimate physical media properties by fitting geophysical data with nonlinear models. I extend this formulation to the joint estimation of physical properties and the lithological description of the media. The incorporation of petrophysical information within the inversion scheme provides the coupling between lithology and media physics by describing the geostatistical relation between them. The resulting procedure adjusts iteratively the joint model to simultaneously fit geophysical data, the petrophysical statistical medium description, and prior information on the lithology, following equations derived for Newton’s optimization method...
Bosch, M.
Multi-step samplers for improving efficiency in probabilistic geophysical inference Geophysical inference is characterized by non-linear relationships between model and data parameters, large model spaces describing the spatial distribution of media properties, and intensive computation related to the numerical resolution of the forward problem. Although sampling approaches are convenient to solve such inverse problems, sometimes the involved computations are demanding. We consider here sampling techniques directed to improve the efficiency of sampling procedures in large real geophysical applications. We propose a sampling algorithm incorporating classical importance sampling within a two-step (or multi-step) Markov chain sampler set-up. The first step of the algorithm is a Metropolis sampler ergodic to an importance density function and the second step is a Metropolis sampler correcting from the bias introduced by the importance density function...
Bosch, M., Ch. Barnes, and K. Mosegaard
Lithology discrimination from physical rock properties The estimation of lithology from multiple geophysical survey methods needs to be addressed to develop advanced tomographic methods. An initial requirement for lithology discrimination is that lithology should be discriminable from the media properties physically related to the geophysical observations. To test this condition for different combinations of the most common crustal rocks, we performed several lithology discrimination exercises on rock samples under laboratory conditions. The physical properties included mass density, compressional velocity, shear velocity, electric conductivity, thermal conductivity, and magnetic susceptibility. A categorical description of the sample lithology was followed; hence, the inference consisted of predicting the sample rock category (lithotype) membership...
Bosch, M., M. Zamora, and W. Utama
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Inference networks in earth models with multiple components and data The integration of information for the inference of earth structure and properties can be treated in a probabilistic framework by considering a posterior probability density function (PDF) that combines the information from a new set of observations and a prior PDF. To formulate the posterior PDF in the context of multiple datasets, the data likelihood functions are factorized assuming independence of uncertainties for data originating across different surveys. A realistic description of the earth medium requires the modelization of several properties and other structural parameters, which relate to each other according to dependency and independency notions...
Bosch, M.
Joint gravity and magnetic inversion in 3D using Monte Carlo methods We jointly invert gravity and magnetic data following a Monte Carlo method that provides estimation for a 3D model of the structure and physical properties of the medium. In particular, layer interface depths, the density and magnetic susceptibility fields within layers are estimated, and their uncertainties are described with posterior probabilities. This method combines the gravity and magnetic data with prior information on the mass density, magnetic susceptibility statistics, and statistical constraints on the interface positions. The resulting model realizations jointly comply with the observations and the prior statistical information.
Bosch, M., R. Meza, R. Jiménez, and A. Hönig
Joint inversion of gravity and magnetic data under lithological constraints Interpreting exploration data requires combining different types of information to solve the geologic puzzle. It implies bringing together all data components into an image that makes conceptual sense in terms of the geology of the exploration area. The identification of geologic objects and the inference of a spatial description of the lithology—consistent with all available information—are the objectives of the process.
Bosch, M. and J. McGaughey
Lithologic tomography: An application to geophysical data from the Cadomian belt of northern Brittany, France A probabilistic description of subsurface lithologic structures can be established by inverting multidisciplinary geophysical data constrained by geological and geostatistical priors. The methodology is based on the joint modeling of several media properties and on a statistical description of the relationships between them. The information provided by the geophysical data and the geological and geophysical priors is represented by probability density functions (pdf) that are combined into a posterior pdf composed by...
Bosch, M., A. Guillen, and P. Ledru
Lithologic tomography: From plural geophysical data to lithology estimation The information provided by different geophysical data sets (gravimetric, magnetic, seismic, etc.) can be used, together with petrophysical and geostatistical information, to estimate the major lithological properties of the rocks within the studied volume. The formalization of this inverse problem requires a joint representation and parameterization of the different media properties in the model. The information relating rock properties together couples the inversion of the plural geophysical data sets and allows one to relate the observations with the lithological parameters of the model. The representation y probability density functions (pdfs) of the different types of information entering the problem is also required and provides the mathematical framework to formulate their combination...
Bosch, M.
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Title Summary Authors
Using a local Monte Carlo strategy to assess 1-D velocity models from wide-angle seismic travel-time data and application to the Rockall trough We present a statistically based search strategy to explore velocity–depth model space derived from the inversion of seismic refraction and wide-angle data. The method is based on the Metropolis algorithm and computes the likelihood of any given model of fitting the observed data. By iteratively perturbing the model, the model space is sampled and the resulting probability density function provides a quantified measure of the velocity resolution as a function of depth. Unlike manual analysis, where a single layer is perturbed to test its sensitivity ignoring the effect on the deeper layers, this method computes the fit for the whole model at each iteration and only selects the models that achieve a specified global fit...
Pearse, S., R. Hobbs, and Bosch, M.
Inversion of travel time data under a statistical model for seismic velocities and layer interfaces We invert large-aperture seismic reflection and refraction data from a geologically complex area on the  northeast Atlantic margin to jointly estimate seismic velocities and depths of major interfaces. Our approach  combines this geophysical data information with prior information on seismic compressional velocities and the structural interpretation of seismic sections. We constrain expected seismic velocities in the prior model  using information from well-logs from a nearby area. The layered structure and prior positions of the interfaces follow information from the seismic section obtained by processing the short offsets...
Bosch, M., P. Barton, S. Singh, and I. Trinks
Adaptive travel-time tomography of densely sampled seismic data We present a new 2-D traveltime tomography method for the inversion of densely sampled seismic streamer data. This method was specially designed for the efficient inversion of long-offset multichannel data. A layer-interface model is used to fit ray-traced traveltime data to observed seismic data. The solution of the forward problem is based on initial-value ray tracing in a triangulated grid with a linear interpolation of the squared slowness. We implement an adaptive model parametrization based on ray density, which allows for smaller velocity cells with subsequent iteration steps...
Trinks I., S. Singh, C. Chapman, P. Barton, M. Bosch, and A. Cherret
P-wave velocity tomography of the Venezuelan region from local arrival times Arrival times from the local seismological network of Venezuela were used to estimate a three dimensional P wave velocity model for the region between longitude 60° - 74° W and the latitude 6° - 14° N to a depth of more than 80 km. The inversion was carried out by damped least squared, describing the media by homogeneous velocity blocks. The resolved lateral velocity variations for the first layer (0-30 km depth) showed a correlation with the main stratigraphic features of the area, while the second layer (30-50 km depth) showed the influence of Moho depth variations through the region, generating a pattern well correlated to the Bouguer Anomaly Map...
Bosch, M.
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