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Reservoir uncertainty description via petrophysical inversion of seismic data  Hydrocarbon reservoir characterization commonly combines
seismic, petrophysical, and welllog 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 datadependent. 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 welllog 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 welllog data. However, the relation between the seismic image
and the welllog data is not straightforward, is often obscured by the
wavepropagation 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 welllog 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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Fullwaveform inversion of intensityfocused seismic data  Fullwaveform 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 rockphysics 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 welllog data: methods and application to a gas reservoir  Hydrocarbon reservoirs are characterized by seismic, welllog, and petrophysical
information, which is dissimilar in spatialHydrocarbon reservoirs are characterized
by seismic, welllog, and petrophysical information, which is dissimilar in spatial
distribution, scale, and relationship to reservoir properties. We combine this
diverse information in a unified inverseproblem formulation using a multiproperty,
multiscale model, linking properties statistically by petrophysical relationships
and conditioning them to welllog data. Two approaches help us: (1) Markovchain
Monte Carlo sampling, which generates many reservoir realizations for estimating
medium properties and posterior marginal probabilities, and (2) optimization with a
leastsquares 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  Leastsquares model optimization methods are commonly used to estimate physical
media properties by fitting geophysical data with nonlinear models. I extendLeastsquares
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. 
Multistep samplers for improving efficiency in probabilistic geophysical inference  Geophysical inference is characterized by nonlinear 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 twostep (or multistep) Markov chain sampler setup.
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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Using a local Monte Carlo strategy to assess 1D velocity models from wideangle seismic traveltime 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 wideangle 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 largeaperture 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 welllogs 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 traveltime tomography of densely sampled seismic data  We present a new 2D traveltime tomography method for the inversion of densely sampled seismic streamer
data. This method was specially designed for the efficient inversion of longoffset multichannel data. A
layerinterface model is used to fit raytraced traveltime data to observed seismic data. The solution of
the forward problem is based on initialvalue 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 
Pwave 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 (030 km depth)
showed a correlation with the main stratigraphic features of the area, while the second layer (3050 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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