1D Inversion Of 4D Radar Data To Image Fluid Flow

We present a general scheme for 3D geophysical inversion using a deep learning convolutional neural network that enables three-dimensional inversions of useful size to be solved on laptops and desktops. A priori constraints of maximum smoothness or compactness on model parameters used during conventional geophysical inversion are not necessary. In environments where a single stabilizing functional is not capable of adequately representing the subsurface variation (e.g., steel cased wells, buried pipes in smoothly varying geology), the method provides an attractive alternative. Projecting data to the Hilbert space of model parameters using the adjoint operator before training mitigates non uniqueness associated with the underdetermined nature of traditional 3D geophysical inverse problems. A field inversion example using magnetic data collected in Washington -on- Brazos state historic site to image buried pipe and other infrastructure is presented. While the training for a single inversion takes longer, the results show better resolution of the top of the structure and overall shape compared to conventional minimum structure inversion methods. For multiple inversions such as for systems with moving footprints, or time lapse surveys, neural networks can be substantially faster than traditional inversion as the network needs to be trained only once for several successive model predictions. The method can be applied to other geophysical data including seismic, electromagnetic and gravity, at various scales and resolution.

Tillage-induced seasonal changes in soil physical properties affecting soil CO 2 evolution under intensive cropping

Summary We have developed a novel probabilistic approach to the joint inversion of multi-modal geophysical data based on the Gramian constraint. The multi-modal geophysical survey is the most effective technique for geophysical exploration because different physical data reflect distinct physical properties of the different components of the geological system. The joint inversion of multi-modal data can produce enhanced subsurface images of the physical property distributions, which enhances our ability to explore natural resources. One effective method of joint inversion is based on the Gramian constraint. This technique enforces the relationships between different model parameters during the inversion process. We demonstrate that the Gramian can be interpreted as a determinant of the covariance matrix between different physical models representing subsurface geology in the framework of the probabilistic approach to inverse theory. This interpretation enables us to use all the power of the modern probability theory and statistics in developing new methods for the joint inversion of multi-modal geophysical data. We apply the developed joint inversion methodology to inversion of gravity gradiometry and magnetic data in the Nordkapp Basin, Barents Sea to image salt diapirs.

One of the major challenges in interpretation of geophysical data remains the ability to jointly invert multiple geophysical datasets for self-consistent 3D earth models of different physical properties. To date, various attempts at 3D joint inversion have been based on either correlations between different physical properties, or by introducing structural similarities. In addition, there could be both physical property and structural correlations between the different earth models, and these complexities cannot be captured by any existing joint inversion techniques. Note that, in practical applications, empirical or statistical correlations between different physical properties may exist, but their specific form may be unknown. In this situation, one can use a method of joint inversion, which does not require a priori knowledge about specific empirical or statistical relationships between the different model parameters and/or their attributes. This approach to the joint inversion of multimodal geophysical data uses Gramian spaces of model parameters and Gramian constraints, computed as determinants of the corresponding Gram matrices of the multi-modal model parameters and/or their attributes. This method, recently introduced by Zhdanov et al. (2012), has been shown to be a generalized method of joint inverting any number and combination of geophysical datasets, and includes extant methods based on correlations and/or structural constraints of the multiple physical properties as special case. The method is illustrated by two case studies. We present the results of joint inversion of airborne gravity gradiometer (AGG) and magnetic data collected by Fugro Airborne Surveys in the area of McFaulds Lake located in northwestern Ontario. We also jointly invert airborne magnetic and electromagnetic data from the Lac de Gras region of the Northwest Territories of Canada. These case studies demonstrate how joint inversion using Gramian constraints may enhance subsurface imaging of the mineral targets.

With the advent o underground heating operations, interest has developed in the alteration of rock properties by high-temperature treatment. In the present work a number of sandstones were heated to temperatures in the range of 400 to 800C under both atmospheric and simulated reservoir pressures. Permeabilities increased by at least 50 per cent and sonic velocities and breaking strengths decreased by an equivalent amount. Differential thermal expansion and other reactions of constituent mineral grains are the causes of these alterations. Introduction In the underground combustion of petroleum reservoirs. Temperatures of the order of 600C are reported to have been reached in the combustion zone. At this temperature rocks are subject to extensive thermal alteration. Temperatures of this magnitude and higher may also occur in subsurface formations when subjected to bottom-hole heating, thermal drilling operations, and underground nuclear explosions. Temperatures of this magnitude might also be generated by conventional rock drilling methods at points of bit-tooth contact. In earlier work, the permanent deformation of rocks resulting from heating was reported. Major structural damage of rocks occurs due to differential thermal expansion of mineral constituents. A number of mineral alterations including crystal versions, loss of water of crystallization and dissociation, may also contribute to changes in physical structure and properties of rock. In the present work, samples of three typical sandstones were had to several temperatures up to a maximum of 800C and then allowed to cool to room temperature. Heating was done under both atmospheric pressure and simulated reservoir pressure conditions. Physical properties of the samples were measured before and after healing and comparisons made. Measured properties included permeability, sonic velocity, breaking strength and fracture index. Changes in physical properties were compared to changes in mineralogical characteristics as determined by thin-section. X-ray diffraction and chemical tests. EQUIPMENT AND PROCEDURE Two outcrop sandstones (Bandera and Berea) and one sub-surface sandstone (St. Peter) were selected for the tests. These samples have a wide range in composition and physical properties as shown in Table 1.The first series of tests was made on 2-in. diameter by 5-in. long test specimens. Test specimens used in all later work were 3/4-in. diameter by 1 1/8-in. long. this being the specimen size required for heating at simulated reservoir pressures. After careful washing, the cores were oven dried at 100 +/- 5C for a minimum of 24 hours before the tests were run. Test specimens were heated in an electric furnace at a constant rate of temperature increase of 3C per minute. When maximum temperature of the run was reached, the sample was allowed to soak for one hour. The furnace was then cooled to room temperature at the same rate of 3C per minute. The entire heating operation was designed for reproducibility without subjecting the test specimens to excessive thermal shock. For samples heated under simulated reservoir pressures. a pressure cell designed by Dean was used (Fig. 1). The core sample was inserted into a thin-walled (0.006 to 0.01-in.) copper cup which was then mounted in a high- pressure cell. Provisions were made for the application of internal pore pressure as well as confining pressure. Tests showed that the thin-walled copper cup closed tightly around the core and satisfactorily transmitted confining pressure to the core. The core was heated by placing the entire cell into the electric furnace. The heating program was the same as that used in the atmospheric pressure runs: temperature rise of 3C per minute to maximum temperature of the test, soaking at maximum temperature for one hour. and cooling at a rate of approximately 3C per minute. The cell was designed to withstand 5,000 psi at 1,000C. However, since it was considered likely that repeated heating and cooling would in time weaken the steel, 2,000 psi at 850C was set as a working limit. In the present series of tests, the pore pressure was held constant at 750 psi and the confining pressure at 1,500 psi. The pressure source was a high-pressure nitrogen tank. The two pressures were controlled manually but are accurate well within +/- 50 psi. JPT P. 589ˆ

Dams are built to contain water or mining tailings and provide several benefits to society. The safety and stability of these structures are essential since eventual accidents can generate catastrophic damage. The main cause of ruptures is associated with abnormal seepage, which can progress to an internal erosion process. To assess the stability and safety of dams, periodic inspections are carried out, which typically include visual inspections and geotechnical instrumentation. Some geophysical methods have the potential to assist conventional geotechnical instrumentation using non-destructive and rapid acquisition investigations. The present study applied a finite element forward modeling to evaluate the percolation conditions and water stability in an earth dam of a decommissioned uranium mine in Brazil. The dam is the final structure of the contention system of mine water treatment. The electrical resistivity data were acquired using electrical resistivity tomography (ERT) and Schlumberger array. The results were presented from the inversion of data in 3D models. The data were processed by open-source software (modeling and inversion of geophysical data). The results indicate the presence of water in the vertical filter located in the crest area. The different levels of investigation indicated water infiltration in the rock mass of the dam foundation. These results are supported by structural surveys carried out in the area that indicate a fracturing pattern in the rock mass of the mine area. The results of the study were satisfactory for the desired purposes and demonstrate that geophysical methods constitute an important complementary tool for the geotechnical monitoring dams.

Experimental results on some physical and optical properties of (As₂Se₃)_1-x:Sn_x and (As₄S₃Se₃)_1-x:Sn_x(x = 0-10 at %) glasses and amorphous films (d~2.0 μm) are presented. The bulk chalcogenide glasses are studied by X-ray diffraction spectroscopy and nanoindentation methods. It is established that the addition of these amounts of tin (x = 0-10 at %) does not lead to significant changes in the physical properties of the glass, such as values of stress and Young’s modulus related to the modification of the density and compactness. It has been found that the addition of these amounts of tin in (As₄S₃Se₃)_1-x:Sn_x does not lead to significant changes in the glass physical properties, such as values of stress and Young’s modulus related to the modification of the density and compactness. The study of the photoplastic effect is performed in situ, with illumination of the bulk and thin film samples during indentation as well as their indentation after illumination with a green laser (λ = 532 nm) at a power of P = 50 mV/cm². The hardness is calculated from load-displacement curves by the Oliver-Pharr method. A sharp increase in hardness is registered if the tin concentration exceeds a value of 34% Sn. The hardness H of (As₂Se₃)_1-x:Sn_x films varies between 115 and 130 kg/mm². It is found that the hardness H of amorphous thin films is generally higher than the hardness of bulk samples with the same chemical composition. In this study, we are focused on the mechanical characteristics of high-purity As₂Se₃: Sn_x thin films. Keyword: Chalcogenide glasses, hardness,

The time-lapse joint inversion of geophysical data is required to image the evolution of oil reservoirs during production and enhanced oil recovery, CO2 sequestration, geothermal fields during production, active volcanoes, and the evolution of contaminant plumes. Joint inversion schemes reduce the uncertainty of the model in each monitoring stage, while time lapse inversion algorithms reduce time-related artifacts. There are several approaches that are possible to perform the time-lapse joint inverse problem. In this work, we select the structural joint inversion approach of Meju and Guallardo (the inversion looks for models with strcutural similarities) to perform the joint inversion of DC resistivity and seismic data. Timelapse inversion is performed with an actively timeconstrained (ATC) approach. In this approach, the subsurface is defined as a space-time model. All the snapshots are inverting together assuming a regularization over time of the sequence of snapshots. Still, this approach is flexible enough to allow for abrupt time-related changes in the areas where there are significant indications that these changes are effectively occurring. At the same time, the ATC approach removes inversion artefacts corresponding to spatial artefacts that are randomly distributed over time. We show the advantage of combining strcutural joint inversion and time-lapse inversion using a synthetic case corresponding to cross-hole seismic and DCresistivity data. We show that this approach reduces strongly artefact both with respect to individual inversion of the resistivity and seismic datasets and also with respect to the joint inversion of both data sets at each time step.

Reliable prediction of subsurface flow and contaminant transport depends on the accuracy with which the values and spatial distribution of process‐relevant model parameters can be identified. Successful characterization methods for complex soil systems are based on (i) an adequate parameterization of the subsurface, capable of capturing both random and structured aspects of the heterogeneous system, and (ii) site‐specific data that are sufficiently sensitive to the processes of interest. We present a stochastic approach in which the high‐resolution imaging capability of geophysical methods is combined with the process‐specific information obtained from the inversion of hydrological data. Geostatistical concepts are employed as a flexible means to describe and characterize subsurface structures. The key features of the proposed approach are (i) the joint inversion of geophysical and hydrological raw data, avoiding the intermediate step of creating a (nonunique and potentially biased) tomogram of geophysical properties and (ii) the concurrent estimation of hydrological and petrophysical parameters, in addition to (iii) the determination of geostatistical parameters from the joint inversion of hydrological and geophysical data. This approach is fundamentally different from inference of geostatistical parameters from an analysis of spatially distributed property data. The approach has been implemented into the iTOUGH2 inversion code and is demonstrated for the joint use of synthetic time‐lapse ground penetrating radar (GPR) travel times and hydrological data collected during a simulated ponded infiltration experiment at a highly heterogeneous site.

Changes in soil physical properties of two Alfisols and an Ultisol in southern Nigeria as affected by desurfacing to simulate varying levels of soil erosion were monitored for two consecutive seasons (3 and 7 months after exposure). These investigations were conducted at Ilora (Alfisol), Ikenne (Alfisol), and Onne (Ultisol) in southern Nigeria. All measurements were made on the top 5 cm of the undisturbed control and the desurfaced soils. Following topsoil removal some deleterious changes in soil physical properties occurred on the exposed subsoils. Seven months after removal of 10 cm of topsoil, bulk densities had increased from 1.37 to 1.45 Mg m −3 at Onne, 1.23 to 1.50 Mg m −3 at Ikenne, and 1.27 to 1.42 Mg m −3 at Ilora. These increased bulk densities were reflected in decreased total and macroporosities. Seven months after 10 cm of topsoil removal, total porosity was reduced from 48 to 45% at Onne, 52 to 43% at Ikenne, and 52 to 46% at Ilora. Available water‐holding capacities of the surface 5 cm of exposed subsoils following 5 cm of topsoil removal were reduced during 7 months by 61% at Onne, 23% at Ikenne, and 12% at Ilora. Corresponding reductions in saturated hydraulic conductivities of these soils were 75%, 65%, and 35% three months after exposure. Also reduced were the moisture retention at 0.01 MPa suction, and the clay contents of the exposed subsoils. Generally, the magnitude of these changes in physical properties was less for the undisturbed control than for the desurfaced soils. These results strengthen the argument that these structurally unstable soils of the tropics should be managed extremely carefully.

The potential of brown sugar as a substitute for granulated sugar is enormous considering the abundant coconut sap production. However, the quantity of brown sugar production through the traditional method is one of the main obstacles. This study used a vacuum evaporator that emphasizes the hygienic and effective mass production of brown sugar. For this reason, it is necessary to approach changes in the physical properties of sap juice during the cooking process. This knowledge is indispensable in the cooking process, which involves the proper evaporation and crystallization of brown sugar. This research is devoted to determining the viscosity, density, and dissolved solids expressed in Brix and proposes a mathematical model to predict the physical properties during the evaporation process of brown sugar as a function of the initial concentration the solution before proceeding to the crystallization process. Results confirm that the prediction model for Brix is Cθ=(Co–Ce)·exp(0.0067·t)+Ce, the model for viscosity µθ=µo·exp(0.011·t), and ρө=(0.44996·t)+ρ0 for the density prediction model. The resulted mathematical model can accurately predict the rate of change in coconut sap's physical properties, indicated by the high coefficient of determination (R2). Keywords : brix, brown sugar, density, vacuum evaporator, viscosity

Geophysical modelling and data inversion are important tools for interpreting the physical properties of Earth’s subsurface. Solving the inverse problem involves several computational steps and is generally a time consuming task. Artificial neural networks have the potential to speed up large computations. Such networks provide the means to model the relationship between the inputs and outputs without needing to know the physical model of the underlying problem. There are two main aspects that affect the performance of neural networks: optimization of network architecture and pre-processing of data. In this article, we investigate several traditional pre-processing techniques including the min-max scaling, z-score scaling, and the logarithmic transform scaling, and propose some novel data pre-processing approaches for the 1-D forward modelling of time-domain electromagnetic data based on signal characteristics. We evaluate the performance of the conventional and the proposed pre-processing methods against a 3% relative error metric, which corresponds to the typical data uncertainty, to show that forward data pre-processing has significant effect on the performance of neural networks. The proposed gate-wise min-max scaling achieves the best performance with 96% of gates within a 3% relative error, while the commonly used logarithmic transform results only in 75% of gates within a 3% relative error. We provide insights into how various pre-processing methods affect the performance of these networks and recommend optimal pre-processing strategies that may be used where similar data content is encountered to achieve superior performance. Finally, we show the effect of forward modelling accuracy in inverse modelling.

This paper presents a simple, generalized parameter constraint using a priori information to obtain a stable inverse of geophysical data. In the constraint the a priori information can be expressed by two limits: lower and upper bounds. This is a kind of inequality constraint, which is usually employed in linear programming. In this paper, we have derived this parameter constraint as a generalized version of positiveness constraint of parameter, which is routinely used in the inversion of electrical and EM data. However, the two bounds are not restricted to positive values. The width of two bounds reflects the reliability of ground information, which is obtained through well logging and surface geology survey. The effectiveness and convenience of this inequality constraint is demonstrated through the smoothness-constrained inversion of synthetic magnetotelluric data.

Monitoring the perturbation zone near a foundation excavation with electrical resistivity tomography: Comparison between time-lapse 3D and 2D inversions in single-profile study

Inverse problems play a crucial role in geophysics because one of the main tasks in this field is to probe the Earth's interior both for economic reasons, such as oil prospecting, and for the pursuit of academic knowledge about our planet. A variety of different physical fields are used for this: elastic waves form the basis of seismic prospecting, electromagnetic or magnetic fields are used to make inferences about the electrical conductivity in the Earth and the magnetic properties of the core, the gravity field constrains the mass distribution within the Earth, and many other examples can be given where inverse problem theory is crucial for inferring the properties of the Earth from measurements at its surface. Examples of the theory and practice of geophysical inverse problems are given by Iyer and Hirahara (1993), Lines and Levin (1988) and Parker (1994). This special section is aimed at presenting the inverse problems community with the theoretical barriers that geophysicists encounter, and providing some unorthodox examples of geophysical inverse problems. Every image obtained from an inverse problem with an incomplete data set gives an incomplete impression of the object under consideration. Trampert shows how limitations in global tomography influence the interpretation and implications of global maps of the seismic velocity in the Earth. In addition he shows how difficult it is to quantify the limitation of the images that are obtained. As shown by Snieder, nonlinearity aggravates this problem. He makes the point that currently there are no satisfactory theoretical tools for the error and resolution analysis of truly nonlinear inverse problems. Mosegaard attacks this problem, not by seeking a single solution to inverse problems, but by constructing many models and making inferences on the likelihood of these models using Bayesian statistics. That such an approach is needed for many practical problems is shown by Sambridge who shows that in practical problems the misfit function (or probability density function) can be extremely complex. In addition he develops tools to characterize this complexity. That inverse problem theory can be applied to problems other than making images of the Earth's interior is shown by Peltier, who makes inferences about the viscosity in the Earth from the measurement of sea-level variations, and by Gallagher, who reconstructs the thermal history of oil reservoirs from measurements at the surface. A major challenge in geophysics is to use different datasets to make inferences about the Earth's interior. Barghazi and Sansó present theoretical tools that can be used for the joint inversion of seismological and gravity data. It will be clear from this special section that inverse problems is a rich and diverse field of research within geophysics. Despite the success of many of its applications (western industrial society would not exist without effective methods for seismic exploration), geophysicists run into theoretical barriers. Within the geophysics community, solutions are usually sought that rely heavily on numerical techniques. It could be that this is the wisest strategy. However, it is also likely that an increased interaction with theoreticians who are active in the field of inverse problems could be beneficial both for the geophysics community and for those active in inverse problem theory. The goal of this special section is to help to close the gap between theory and practice within the inverse problems community. References Iyer H M and Hirahara K (ed) 1993 Seismic Tomography; Theory and Practice (London: Chapman and Hall) Lines L R and Levin F L (ed) 1988 Inversion of Geophysical Data SEG reprint series, 9 Parker R L 1994 Geophysical Inverse Theory (Princeton, NJ: Princeton University Press)