Full waveform inversion procedures with irregular topography

Full waveform inversion (FWI) is a form of seismic inversion that uses data residual, found as the misfit, between the whole waveform of field acquired and synthesized seismic data, to iteratively update a model estimate until such misfit is sufficiently reduced, indicating synthetic data is generated from a relatively accurate model. The aim of the thesis is to review FWI and provide a simplified explanation of the techniques involved to those who are not familiar with FWI. In FWI the local minima problem causes the misfit to decrease to its nearest minimum and not the global minimum, meaning the model cannot be accurately updated. Numerous objective functions were proposed to tackle different sources of local minima. The ‘joint deconvoluted envelope and phase residual’ misfit function proposed in this thesis aims to combine features of these objective functions for a comprehensive inversion. The adjoint state method is used to generate an updated gradient for the search direction and is followed by a step-length estimation to produce a scalar value that could be applied to the search direction to reduce the misfit more efficiently. Synthetic data are derived from forward modelling involving simulating and recording propagating waves influenced by the mediums’ properties. The ‘generalised viscoelastic wave equation in porous media’ was proposed by the author in sub-chapter 3.2.5 to consider these properties. Boundary layers and conditions are employed to mitigate artificial reflections arising from computational simulations. Linear algebra solvers are an efficient tool that produces wavefield vectors for frequency domain synthetic data. Regions with topography require a grid generation scheme to adjust a mesh of nodes to fit into its non-quadrilateral shaped body. Computational co-ordinate terms are implemented within wave equations throughout topographic models where a single point in the model in physical domain are represented by cartesian nodes in the computational domains. This helps to generate an accurate and appropriate synthetic data, without complex modelling computations. Advanced FWI takes a different approach to conventional FWI, where they relax upon the use of misfit function, however none of their proponents claims the former can supplant the latter but suggest that they can be implemented together to recover the true model.Open Acces

Application of upscaling methods for fluid flow and mass transport in multi-scale heterogeneous media : A critical review

Physical and biogeochemical heterogeneity dramatically impacts fluid flow and reactive solute transport behaviors in geological formations across scales. From micro pores to regional reservoirs, upscaling has been proven to be a valid approach to estimate large-scale parameters by using data measured at small scales. Upscaling has considerable practical importance in oil and gas production, energy storage, carbon geologic sequestration, contamination remediation, and nuclear waste disposal. This review covers, in a comprehensive manner, the upscaling approaches available in the literature and their applications on various processes, such as advection, dispersion, matrix diffusion, sorption, and chemical reactions. We enclose newly developed approaches and distinguish two main categories of upscaling methodologies, deterministic and stochastic. Volume averaging, one of the deterministic methods, has the advantage of upscaling different kinds of parameters and wide applications by requiring only a few assumptions with improved formulations. Stochastic analytical methods have been extensively developed but have limited impacts in practice due to their requirement for global statistical assumptions. With rapid improvements in computing power, numerical solutions have become more popular for upscaling. In order to tackle complex fluid flow and transport problems, the working principles and limitations of these methods are emphasized. Still, a large gap exists between the approach algorithms and real-world applications. To bridge the gap, an integrated upscaling framework is needed to incorporate in the current upscaling algorithms, uncertainty quantification techniques, data sciences, and artificial intelligence to acquire laboratory and field-scale measurements and validate the upscaled models and parameters with multi-scale observations in future geo-energy research.© 2021 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)This work was jointly supported by the National Key Research and Development Program of China (No. 2018YFC1800900 ), National Natural Science Foundation of China (No: 41972249 , 41772253 , 51774136 ), the Program for Jilin University (JLU) Science and Technology Innovative Research Team (No. 2019TD-35 ), Graduate Innovation Fund of Jilin University (No: 101832020CX240 ), Natural Science Foundation of Hebei Province of China ( D2017508099 ), and the Program of Education Department of Hebei Province ( QN219320 ). Additional funding was provided by the Engineering Research Center of Geothermal Resources Development Technology and Equipment , Ministry of Education, China.fi=vertaisarvioitu|en=peerReviewed

Understanding and Predicting Vadose Zone Processes

Vadose zone hydrologic and biogeochemical processes play a significant role in the capture, storage and distribution of contaminants between the land surface and groundwater. One major issue facing geoscientists in dealing with investigations of the unsaturated zone flow and transport processes is the evaluation of heterogeneity of subsurface media. This chapter presents a summary of approaches for monitoring and modeling of vadose zone dynamics in the presence of heterogeneities and complex features, as well as incorporating transient conditions. Modeling results can then be used to provide early warning of soil and groundwater contamination before problems arise, provide scientific and regulatory credibility to environmental management decision-making process to enhance protection of human health and the environment. We recommend that future studies target the use of RTMs to identify and quantify critical interfaces that control large-scale biogeochemical reaction rates and ecosystem functioning. Improvements also need to be made in devising scaling approaches to reduce the disconnect between measured data and the scale at which processes occur

The emergence of hydrogeophysics for improved understanding of subsurface processes over multiple scales

Geophysics provides a multi-dimensional suite of investigative methods that are transforming our ability to see into the very fabric of the subsurface environment, and monitor the dynamics of its fluids and the biogeochemical reactions that occur within it. Here, we document how geophysical methods have emerged as valuable tools for investigating shallow subsurface processes over the past two decades and offer a vision for future developments relevant to hydrology and also ecosystem science. The field of “hydrogeophysics” arose in the late 1990s, prompted, in part, by the wealth of studies on stochastic subsurface hydrology that argued for better field-based investigative techniques. These new hydrogeophysical approaches benefited from the emergence of practical and robust data inversion techniques, in many cases with a view to quantify shallow subsurface heterogeneity and the associated dynamics of subsurface fluids. Furthermore, the need for quantitative characterization stimulated a wealth of new investigations into petrophysical relationships that link hydrologically relevant properties to measurable geophysical parameters. Development of time-lapse approaches provided a new suite of tools for hydrological investigation, enhanced further with the realization that some geophysical properties may be sensitive to biogeochemical transformations in the subsurface environment, thus opening up the new field of “biogeophysics”. Early hydrogeophysical studies often concentrated on relatively small ‘plot-scale’ experiments. More recently, however, the translation to larger-scale characterization has been the focus of a number of studies. Geophysical technologies continue to develop, driven, in part, by the increasing need to understand and quantify key processes controlling sustainable water resources and ecosystem services

ADVANCED REFLECTION SEISMIC STUDIES OF PHASE I WEYBURN CO2 SEQUESTRATION MONITORING

Three-dimensional, time-lapse (TL) reflection seismic datasets and well logs collected for Phase I CO2 sequestration project in Weyburn oilfield (southern Saskatchewan, Canada) are utilized for developing new approaches in three research areas: 1) estimation of seismic source waveforms, 2) evaluation of TL acoustic impedance (AI) variations for monitoring CO2 propagation, and 3) rigorous modeling of seismic waves propagating through finely layered rock. All three study areas are interconnected and important for accurate analysis of seismic data and TL monitoring of this and other oil reservoirs undergoing fluid injection. The first approach focuses on estimating the source waveforms from reflection seismic data, which is critical for evaluating accurate well-to-seismic ties as well as in other applications. A simple and effective method is proposed, based on iterative identification of the strongest and sparse reflections in seismic records, which allows estimation of source waveforms through an optimization approach, without well-log control and statistical hypotheses. The method allows correcting for coherent noise which seems to occur in stacked Weyburn data, consisting in (de)amplification and time shifts of the low-frequency components of the records. The method is tested on real and self-similar synthetic well-log models and applied to the Weyburn seismic data. For the second topic, a post-stack waveform-calibration processing procedure is developed in order to achieve accurate consistency of TL datasets. Time shifts between the monitor and baseline records are also measured during this procedure, and an improved method for calculating the TL reflectivity differences is proposed. Further, instead of subtraction of the baseline and monitor AIs, TL AI variations are evaluated directly from the reflectivity differences and baseline AI. AI inversion is performed by an accurate and stable method using the stacked reflection and well-log data, and also seismic velocities measured during data processing. The inverted time shifts and TL AI variations correlate with CO2 distributions within the reservoir and allow estimating parameters of the reservoir. In the third research area, a completely new approach to seismic wave modeling is proposed. Rigorous first-principle continuum mechanics is used instead of the conventional viscoelastic approximation. This modeling considers the existence of internal variables, body-force internal friction, and boundary conditions for internal variables. These factors are disregarded in the viscoelastic model, but they should cause dominant effects on seismic-wave attenuation and velocity dispersion in layered media. Numerical modeling of seismic wave propagation is performed in a model of the Weyburn Field. The resulting wavefield and seismic attenuation parameters are found to strongly depend on the internal boundary conditions between layers. Several types of quality (Q) factors are measured in the modeled synthetic waveforms

Coarse graining equations for flow in porous media: a HaarWavelets and renormalization approach

Coarse graining of equations for flow in porous media is an important aspect in modelling permeable subsurface geological systems. In the study of hydrocarbon reservoirs as well as in hydrology, there is a need for reducing the size of the numerical models to make them computationally efficient, while preserving all the relevant information which is given at different scales. In the first part, a new renormalization method for upscaling permeability in Darcy’s equation based on Haar wavelets is presented, which differs from other wavelet based methods. The pressure field is expressed as a set of averages and differences, using a one level Haar wavelet transform matrix. Applying this transform to the finite difference discretized form of Darcy’s law, one can deduce which permeability values on the coarse scale would give rise to the average pressure field. Numerical simulations were performed to test this technique on homogeneous and heterogeneous systems. A generalization of the above method was developed designing a hierarchical transform matrix inspired by a full Haar wavelet transform, which allows us to describe pressure as an average and a set of progressively smaller scale differences. Using this transform the pressure solution can be performed at the required level of detail, allowing for different resolutions to be kept in different parts of the system. A natural extension of the methods is the application to two-phase flow. Upscaling mobility allows the saturation profile to be calculated on the fine or coarse scale while based on coarse pressure values. To conclude, an alternative approach to upscaling in multi-phase flow is to upscale the saturation equation itself. Taking its Laplace transform, this equation can be reduced to a simple eigenvalue problem. The wavelet upscaling method can now be applied to calculate the upscaled saturation profile, starting with fine scale velocity data