Jef Caers

Stanford University | SU · Department of Geological and Environmental Sciences

Prior model construction is a fundamental component in geophysical inversion, especially Bayesian inversion. The prior model, usually derived from available geological information, can reduce the uncertainty of model characteristics during the inversion. However, the prior geological data for inferring a prior distribution model are often limited i...

A critical challenge in mineral prospectivity mapping is to prioritize new areas for exploration drilling based on estimated depth and grade of potential deposits and the quantified uncertainty of estimations. This research study is aiming for exploiting already available drilling data in conjunction with data of different geophysical variables and...

Data Science for the Geosciences provides students and instructors with the statistical and machine learning foundations to address Earth science questions using real-world case studies in natural hazards, climate change, environmental contamination and Earth resources. It focuses on techniques that address common characteristics of geoscientific d...

Real-world planning problems$\unicode{x2014}$including autonomous driving and sustainable energy applications like carbon storage and resource exploration$\unicode{x2014}$have recently been modeled as partially observable Markov decision processes (POMDPs) and solved using approximate methods. To solve high-dimensional POMDPs in practice, state-of-...

Geological carbon capture and sequestration (CCS), where CO$_2$ is stored in subsurface formations, is a promising and scalable approach for reducing global emissions. However, if done incorrectly, it may lead to earthquakes and leakage of CO$_2$ back to the surface, harming both humans and the environment. These risks are exacerbated by the large...

The subglacial bed topography is critical for modelling the evolution of Thwaites Glacier in the Amundsen Sea Embayment (ASE), where rapid ice loss threatens the stability of the West Antarctic Ice Sheet. However, mapping of subglacial topography is subject to uncertainties of up to hundreds of metres, primarily due to large gaps of up to tens of k...

Building high-resolution lithological models using seismic data can facilitate decision-makings for earth resources development, but they are subject to considerable uncertainties due to the limited seismic resolution. Traditionally, high-resolution lithological models are built deterministically or stochastic simulation is performed using seismic...

The subglacial bed topography is critical for modeling the evolution of Thwaites Glacier in the Amundsen Sea Embayment (ASE), where rapid ice loss threatens the stability of the West Antarctic Ice Sheet. However, mapping of subglacial topography is subject to high uncertainty. This is mainly because the bed topography is measured by airborne ice-pe...

The spatial modeling of geo-domains has become ubiquitous in many geoscientific fields. However, geo-domains’ spatial modeling poses real challenges, including the uncertainty assessment of geo-domain boundaries. Geo-domain models are subject to uncertainties due mainly to the inherent lack of knowledge in areas with little or no data. Because they...

Implicit methods for modeling geological structures such as stratigraphy and faults have been developed for more than a decade, and they have made automatic model construction feasible. The implicit potential field method is such a method that is capable of incorporating multiple types of data including contact points for geological boundaries and...

Coming out means becoming human, to share common struggles, to become vulnerable. In this space, fear of rejection about sexual identity dissipates into “I am” but human, and it can start as simply as with a conversation with someone you like and trust, states Jef Caers.

This paper introduces a method to generate conditional categorical simulations, given an ensemble of partially conditioned (or unconditional) categorical simulations derived from any simulation process. The proposed conditioning method relies on implicit functions (signed distance functions) for representing the categorical spatial variable of inte...

Subglacial topography is an important feature in numerous ice-sheet analyses and can drive the routing of water at the bed. Bed topography is primarily measured with ice-penetrating radar. Significant gaps, however, remain in data coverage that require interpolation. Topographic interpolations are typically made with kriging, as well as with mass c...

Direct forecasting has recently been proposed as a method for uncertainty quantification in non-linear inverse problems. The method directly forecasts a desired future response without the need for full model inversion. The method has been successfully applied to a range of subsurface field cases, such as groundwater, shallow and deep geothermal an...

Direct sampling (DS) is a versatile multiple‐point statistics method for generating spatial‐temporal geostatistical models. DS is known for being able to address a variety of training images and hence spatiotemporal stochastic modeling problems. One limitation of DS is the central processing unit (CPU) time, mostly attributed to the use of a random...

Quantification of a mineral prospectivity mapping (MPM) heavily relies on geological, geophysical and geochemical analysis, which combines various evidence layers into a single map. However, MPM is subject to considerable uncertainty due to lack of understanding of the metallogenesis and limited spatial data samples. In this paper, we provide a fra...

Geological uncertainty quantification is critical to subsurface modeling and prediction, such as groundwater, oil or gas, and geothermal resources, and needs to be continuously updated with new data. We provide an automated method for uncertainty quantification and the updating of geological models using borehole data for subsurface developments wi...

Many Earth surface processes are studied using field, experimental, or numerical modeling data sets that represent a small subset of possible outcomes observed in nature. Based on these data, deterministic models can be built that describe the “average” evolution of a system. However, these models commonly cannot account for the complex variability...

Abstract. We provide an automated method for uncertainty quantification and updating of geological models using borehole data for subsurface developments (groundwater, geothermal, oil & gas, and CO2 sequestration, etc.) within a Bayesian framework. Our methodologies are developed with the Bayesian Evidential Learning protocol for uncertainty quanti...

The focus of this paper is on Duvernay shale formation in Alberta, Canada. The objective is to provide, based on existing data of production, completion and geological parameters, an automated machine- learning approach to determine the spatial variation in decline type curves for gas production. This model will enable the prediction and uncertaint...

Bayesian inverse modeling (BIM) provides a framework for uncertainty assessment in estimation of earth models from multiple sources of limited, noisy, and incomplete data. BIM, however, requires repeated solutions of computationally expensive full-physics forward (FPF) runs, rendering BIM overwhelmingly computationally prohibitive and intractable i...

Landslides are among the deadliest and most costly natural disasters, resulting in thousands of deaths and many billions of dollars in damages each year. Rainfall is the most widespread and frequent trigger of landslides. Climate change has increased rainfall intensity and, thus, we hypothesize an associated increase in landslide susceptibility. Ou...

We present a new stochastic object-based model (OBM), relying on the formalism of marked point processes (MPP), that mimics the formation of the dominant structures of coarse, braided river deposits. This grid-free three-dimensional MPP is a compound marked Strauss process introduced in the challenging context of stereology in which the three-dimen...

For many geoscience applications, prediction requires building complex 3D surface models. Because of such complexity, often only a single model is built, possibly with a small set of variants to represent the uncertainty. Recent advancement in implicit modeling has made the construction of 3D geological models simpler; however, automatic assessment...

We address the question of quantifying uncertainty associated with autogenic pattern variability in a channelized transport system by means of a modern geostatistical method. This question has considerable relevance for practical subsurface applications as well, particularly those related to uncertainty quantification relying on Bayesian approaches...

In this paper we propose Universal trace co-kriging, a novel methodology for interpolation of multivariate Hilbert space valued functional data. Such data commonly arises in multi-fidelity numerical modeling of the subsurface and it is a part of many modern uncertainty quantification studies. Besides theoretical developments we also present methodo...

Creating increasingly realistic groundwater models involves the inclusion of additional geological and geophysical data in the hydrostratigraphic modeling procedure. Using multiple-point statistics (MPS) for stochastic hydrostratigraphic modeling provides a degree of flexibility that allows the incorporation of elaborate datasets and provides a fra...

We have explored ways to integrate alternative geologic interpretations into the modeling of gravity data. These methods are applied to the Vaca Fault east of Fairfield, California, USA, where the structure across the fault is in question, and the Vaca Fault is used as a case study to demonstrate the method. The Vaca Fault is modeled using gravity...

A new book explores how uncertainty quantification can enable optimal decisions in the exploration, appraisal, and development of subsurface resources.

This chapter provides a theory of inversion in its most general form, mostly based on the work of Tarantola and his school of thought. It discusses not only the common explicit grid model but also how to parameterize more complex subsurface structures such as faults and horizons. The chapter provides some alternatives to the grid model and presents...

This chapter discusses some of the state‐of‐the‐art techniques that are well suited for the specificities of subsurface systems. Input parameters and model responses in subsurface modeling may have characteristics that require adaptation of existing sensitivity analysis (SA) techniques. Screening techniques rely on simplified approaches to identify...

A single matched model may not actually describe the true conditions in the city and may yield a prediction of apartment size that is different from reality. An alternative approach to solving such problem is Bayesian evidential learning (BEL), since it involves a statistical model. The first step of BEL always consists of constructing a set of pri...

This book introduces the reader to a variety of real‐case problems involving the subsurface, uncertainty, and decision making, as well as its societal importance, in terms of the future of geological resources. Researchers and practitioners of uncertainty quantification (UQ) are aware of the difficulty of making predictions, and how one's too narro...

The role of software in Bayesian approach to uncertainty quantification (UQ) can be classified into three categories: model generation, forward simulation, and post‐processing. In practice, no single software suite may encompass all three components, so implementation of UQ methodologies may require using multiple software packages or codebases. Mo...

This chapter aims to frame Bayesianism within the historical context of other forms of scientific reasoning, such as induction, deduction, falsification, intuitionism, and others. It discusses the application of Bayesianism in the context of uncertainty quantification (UQ). Bayesianism is based on inductive logic, although some argue that it is bas...

This chapter overviews the relevant mathematical, statistical, and computer science components needed to develop and understand the various approaches to uncertainty quantification. It provides some additional insight into how various, seemingly independent applied mathematical concepts share important common traits within the context of uncertaint...

Uncertainty plays a very important role in making sound decisions. This chapter provides a basic overview of those elements of decision analysis that are important in the context of the subsurface. It illustrates some basic concepts in decision making with an example of the thumbtack game. The chapter also illustrates the challenges with two very d...

This is a first draft of a new book that will be published end 2017/beginning 2018. Quantifying Uncertainty in Subsurface System provides a holistic view on Uncertainty Quantification for Geological resources. The book covers both theory and case studies. More specific, five real field case studies 1) Conventional oil/gas, 2) Groundwater, 3) Geoth...

Abstract: There is a critical need in hydrogeological modeling for geologically more realistic representation of the subsurface. Indeed, widely-used representations of the subsurface heterogeneity based on smooth basis functions such as cokriging or the pilot-point approach fail at reproducing the connectivity of high permeable geological structure...

Geophysical data have proven to be very useful for lithological characterization. However, quantitatively integrating the information gained from acquiring geophysical data generally requires colocated lithological and geophysical data for constructing a rock-physics relationship. In this contribution, the issue of integrating noncolocated geophysi...

Creating increasingly realistic hydrological models involves the inclusion of additional geological and geophysical data in the hydrostratigraphic modelling procedure. Using Multiple Point Statistics (MPS) for stochastic hydrostratigraphic modelling provides a degree of flexibility that allows the incorporation of elaborate datasets and provides a...

Suitable training images (TIs) for multiple-point statistics (MPS) are difficult to identify in real-case three-dimensional applications, posing challenges for modelers trying to develop realistic subsurface models. This study demonstrates that two-dimensional geophysical images, when employed as training and conditioning data, can provide sufficie...

Process-based modeling offers a way to represent realistic geological heterogeneity in subsurface models. The main limitation lies in conditioning such models to data. Multiple-point geostatistics can use these process-based models as training images and address the data conditioning problem. In this work, we further develop image quilting as a met...

Faults are one of the building-blocks for subsurface modeling studies. Incomplete observations of subsurface fault networks lead to uncertainty pertaining to location, geometry and existence of faults. In practice, gaps in incomplete fault network observations are filled based on tectonic knowledge and interpreter's intuition pertaining to fault re...

The conventional paradigm for predicting future reservoir performance from existing production data involves the construction of reservoir models that match the historical data through iterative history matching. This is generally an expensive and difficult task and often results in models that do not accurately assess the uncertainty of the foreca...

Sensitivity analysis plays an important role in geoscientific computer experiments, whether for forecasting, data assimilation or model calibration. In this paper we focus on an extension of a method of regionalized sensitivity analysis (RSA) to applications typical in the Earth Sciences. Such applications involve the building of large complex spat...

Limited knowledge about the spatial distribution of aquifer properties typically constrains our ability to predict subsurface flow and transport. Here, we investigate the value of using high resolution full-waveform inversion of cross-borehole ground penetrating radar (GPR) data for aquifer characterization. By stitching together GPR tomograms from...

We address the question of quantifying uncertainty associated with autogenic pattern variability in a channelized transport system by means of a modern geostatistical method. This question has considerable relevance for practical subsurface applications as well, particularly those related to uncertainty quantification relying on Bayesian approaches...

Time-lapse applications of electrical methods have grown significantly over the last decade. However, the quantitative interpretation of tomograms in terms of physical properties, such as salinity, temperature or saturation, remains difficult. In many applications, geophysical models are transformed into hydrological models, but this transformation...

In this paper we investigate the practical and methodological use of Universal Kriging of functional data to predict unconventional shale gas production in undrilled locations from known production data. In Universal Kriging of functional data, two approaches are considered: (1) estimation by means of Cokriging of functional components (Universal C...

A benchmark synthetic fractured reservoir dataset is built as an initial step towards evaluating methodologies for using deterministic Discrete Fracture Network (DFN) models from an explored area in predicting performance in relatively underexplored adjacent zones. In this exercise we create a robust synthetic dataset comprising about seven million...

Realistic geological representation of subsurface heterogeneity remains an important outstanding challenge. While many geostatistical methods exist for representing sedimentary systems, such as multiple-point geostatistics, rule-based methods or Boolean methods, the question of what the prior uncertainty on parameters (or training images) of such a...

Scientific curiosity, exploration of georesources and environmental concerns are pushing the geoscientific research community toward subsurface investigations of ever-increasing complexity. This review explores various approaches to formulate and solve inverse problems in ways that effectively integrate geological concepts with geophysical and hydr...

The difficulty in applying traditional reservoir simulation and modeling techniques for unconventional reservoir forecasting makes the use of statistical and modern machine learning techniques a relevant proposition for shale systems. However, the most current applications of these techniques often ignore the systematic time variations in productio...

History matching has traditionally been an important element of forecasting, but, due to computational, as well as modeling complexities in real reservoir systems, many ideas have remained academic. In this work we propose a new paradigm to side-step the iterative history matching process and to aim instead to directly establish a statistical relat...

The world, in particularly, the USA has seen an explosion in development of unconventional shale resources. In these reservoirs drilling and production occurs at development times orders of magnitude shorter than in conventional resources. As a result, decisions about where to drill and how to complete wells (hydro fracturing) need to be made in al...

In this extended abstract we propose novel kriging based technique for forecasting and uncertainty quantification in unconventional shale reservoirs. Our technique is data driven; we start from all available reservoir data including high dimensional sets of hydraulic fracturing and geological parameters, along with hydrocarbon production time serie...

Seismic data play a critical role in reservoir forecasting and decision making. However, large uncertainties are associated with seismic data, many of which arise from depth migration and the absence of accurate velocity models. Moreover, because of the computational and labor costs associated with velocity-model building, generally only a single s...

Geophysical subsurface modeling is often highly uncertain due to limited data resolution. At the same time, a wealth of geologic information, often from databases and outcrop studies, is available to state prior uncertainty on key geologic modeling parameters. In most inversion procedures, these uncertainties are ignored and only a limited number o...

Computationally efficient updating of reservoir models with new production data has received considerable attention recently. In this paper however, we focus on the challenges of updating reservoir models prior to production, in particular when new exploration wells are drilled. At this stage, uncertainty in the depositional model is highly impactf...

In inverse problems, investigating uncertainty in the posterior distribution of model parameters is as important as matching data. In recent years, most efforts have focused on techniques to sample the posterior distribution with reasonable computational costs. Within a Bayesian context, this posterior depends on the prior distribution. However, mo...

While seismic data is used to interpret the structural framework, the uncertainties associated with the seismic data itself are often neglected for computational reasons. Structural uncertainty studies are often limited to perturbing horizons and faults around a single interpretation. We propose a method to assess the uncertainty in the seismic ima...

Structural model has a zeroth order impact for flow through porous media. Although seismic image is used extensively to understand structure and is increasing in quality, it may not able to resolve the structure (faults and horizons) in areas of interest due to low image quality. However, there can be areas in seismic data where structure can be ex...

In the past decade, the training image (TI) has received considerable attention as a source for modeling spatial continuity in geostatistics. In this paper, the use of TIs in the context of kriging is investigated, specifically universal kriging (UK). Traditionally, kriging relies on a random function model formulation whereby the target variable i...

Inverse modeling is widely used to assist with forecasting problems in the subsurface. However, full inverse modeling can be time-consuming requiring iteration over a high dimensional parameter space with computationally expensive forward models and complex spatial priors. In this paper, we investigate a prediction-focused approach (PFA) that aims...

Modeling the subsurface of the Earth has many characteristic challenges. Earth models reflect the complexity of the Earth subsurface and contain many complex elements of modeling, such as the subsurface structures, the geological processes of growth and/or deposition, and the placement, movement, or injection/ extraction of fluid and gaseous phases...

In inverse problems, investigating the relationship between data and prior models and the uncertainty related to the posterior distribution of model parameters are as important as matching the data. In recent years, many efforts have been done to assess the posterior distribution of a given problem with reasonable computational costs through invers...

Fractures have crucial impact on the flow in reservoirs. In naturally fractured reservoirs the fracture network alone can be the dominant factor in fluid transport. Fractures as geological discontinuities introduce a high level of complexity into the entire reservoir modeling workflow. In current practice, the geological modeling of fractures and f...

In the early stage development of a reservoir, facies modeling often focuses on the specification and uncertainty regarding the depositional scenario. However, in addition to well data, facies models are also constrained to a spatially-varying trend, often obtained from geophysical data. While uncertainty in the training image has received consider...

Among various sources of uncertainty in reservoir modeling, structural uncertainty is often underrepre- sented. Evaluating different faulting scenarios requires gridding each of these scenarios. Preserving the structural geological realism requires careful consideration of structural hierarchy and abutting relationships. Enforcing such relationship...