Imaging of a fluid injection process using geophysical data - A didactic example

In many subsurface industrial applications, fluids are injected into or withdrawn from a geologic formation. It is of practical interest to quantify precisely where, when, and by how much the injected fluid alters the state of the subsurface. Routine geophysical monitoring of such processes attempts to image the way that geophysical properties, such as seismic velocities or electrical conductivity, change through time and space and to then make qualitative inferences as to where the injected fluid has migrated. The more rigorous formulation of the time-lapse geophysical inverse problem forecasts how the subsurface evolves during the course of a fluid-injection application. Using time-lapse geophysical signals as the data to be matched, the model unknowns to be estimated are the multiphysics forward-modeling parameters controlling the fluid-injection process. Properly reproducing the geophysical signature of the flow process, subsequent simulations can predict the fluid migration and alteration in the subsurface. The dynamic nature of fluid-injection processes renders imaging problems more complex than conventional geophysical imaging for static targets. This work intents to clarify the related hydrogeophysical parameter estimation concepts

Highly efficient Bayesian joint inversion for receiver-based data and its application to lithospheric structure beneath the southern Korean Peninsula

With the deployment of extensive seismic arrays, systematic and efficient parameter and uncertainty estimation is of increasing importance and can provide reliable, regional models for crustal and upper-mantle structure.We present an efficient Bayesian method for the joint inversion of surface-wave dispersion and receiver-function data that combines trans-dimensional (trans-D) model selection in an optimization phase with subsequent rigorous parameter uncertainty estimation. Parameter and uncertainty estimation depend strongly on the chosen parametrization such that meaningful regional comparison requires quantitative model selection that can be carried out efficiently at several sites. While significant progress has been made for model selection (e.g. trans-D inference) at individual sites, the lack of efficiency can prohibit application to large data volumes or cause questionable results due to lack of convergence. Studies that address large numbers of data sets have mostly ignored model selection in favour of more efficient/simple estimation techniques (i.e. focusing on uncertainty estimation but employing ad-hoc model choices). Our approach consists of a two-phase inversion that combines trans-D optimization to select the most probable parametrization with subsequent Bayesian sampling for uncertainty estimation given that parametrization. The trans-D optimization is implemented here by replacing the likelihood function with the Bayesian information criterion (BIC). The BIC provides constraints on model complexity that facilitate the search for an optimal parametrization. Parallel tempering (PT) is applied as an optimization algorithm. After optimization, the optimal model choice is identified by the minimum BIC value from all PT chains. Uncertainty estimation is then carried out in fixed dimension. Data errors are estimated as part of the inference problem by a combination of empirical and hierarchical estimation. Data covariance matrices are estimated from data residuals (the difference between prediction and observation) and periodically updated. In addition, a scaling factor for the covariance matrix magnitude is estimated as part of the inversion. The inversion is applied to both simulated and observed data that consist of phase- and group-velocity dispersion curves (Rayleigh wave), and receiver functions. The simulation results show that model complexity and important features are well estimated by the fixed dimensional posterior probability density. Observed data for stations in different tectonic regions of the southern Korean Peninsula are considered. The results are consistent with published results, but important features are better constrained than in previous regularized inversions and are more consistent across the stations. For example, resolution of crustal and Moho interfaces, and absolute values and gradients of velocities in lower crust and upper mantle are better constrained

Retrieving shallow shear-wave velocity profiles from 2D seismic-reflection data with severely aliased surface waves

The inversion of surface-wave phase-velocity dispersion curves provides a reliable method to derive near-surface shear-wave velocity profiles. In this work, we invert phase-velocity dispersion curves estimated from 2D seismic-reflection data. These data cannot be used to image the first 50 m with seismic-reflection processing techniques due to the presence of indistinct first breaks and significant NMO-stretching of the shallow reflections. A surface-wave analysis was proposed to derive information about the near surface in order to complement the seismic-reflection stacked sections, which are satisfactory for depths between 50 and 700 m. In order to perform the analysis, we had to overcome some problems, such as the short acquisition time and the large receiver spacing, which resulted in severe spatial aliasing. The analysis consists of spatial partitioning of each line in segments, picking of the phase-velocity dispersion curves for each segment in the f-k domain, and inversion of the picked curves using the neighborhood algorithm. The spatial aliasing is successfully circumvented by continuously tracking the surface-wave modal curves in the f-k domain. This enables us to sample the curves up to a frequency of 40 Hz, even though most components beyond 10 Hz are spatially aliased. The inverted 2D VS sections feature smooth horizontal layers, and a sensitivity analysis yields a penetration depth of 20–25 m. The results suggest that long profiles may be more efficiently surveyed by using a large receiver separation and dealing with the spatial aliasing in the described way, rather than ensuring that no spatially aliased surface waves are acquired.Fil: Onnis, Luciano Emanuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Osella, Ana Maria. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física; ArgentinaFil: Carcione, Jose M.. Istituto Nazionale di Oceanografia e di Geofisica Sperimentale; Itali

Saturated hydraulic conductivity determined by on ground mono-offset Ground-Penetrating Radar inside a single ring infiltrometer

In this study we show how to use GPR data acquired along the infiltration of water inside a single ring infiltrometer to inverse the saturated hydraulic conductivity. We used Hydrus-1D to simulate the water infiltration. We generated water content profiles at each time step of infiltration, based on a particular value of the saturated hydraulic conductivity, knowing the other van Genuchten parameters. Water content profiles were converted to dielectric permittivity profiles using the Complex Refractive Index Method relation. We then used the GprMax suite of programs to generate radargrams and to follow the wetting front using arrival time of electromagnetic waves recorded by a Ground-Penetrating Radar (GPR). Theoretically, the 1D time convolution between reflectivity and GPR signal at any infiltration time step is related to the peak of the reflected amplitude recorded in the corresponding trace in the radargram. We used this relation ship to invert the saturated hydraulic conductivity for constant and falling head infiltrations. We present our method on synthetic examples and on two experiments carried out on sand soil. We further discuss on the uncertainties on the retrieved saturated hydraulic conductivity computed by our algorithm from the van Genuchten parameters

Non-Local Compressive Sensing Based SAR Tomography

Tomographic SAR (TomoSAR) inversion of urban areas is an inherently sparse reconstruction problem and, hence, can be solved using compressive sensing (CS) algorithms. This paper proposes solutions for two notorious problems in this field: 1) TomoSAR requires a high number of data sets, which makes the technique expensive. However, it can be shown that the number of acquisitions and the signal-to-noise ratio (SNR) can be traded off against each other, because it is asymptotically only the product of the number of acquisitions and SNR that determines the reconstruction quality. We propose to increase SNR by integrating non-local estimation into the inversion and show that a reasonable reconstruction of buildings from only seven interferograms is feasible. 2) CS-based inversion is computationally expensive and therefore barely suitable for large-scale applications. We introduce a new fast and accurate algorithm for solving the non-local L1-L2-minimization problem, central to CS-based reconstruction algorithms. The applicability of the algorithm is demonstrated using simulated data and TerraSAR-X high-resolution spotlight images over an area in Munich, Germany.Comment: 10 page

Characterising poroelastic materials in the ultrasonic range - A Bayesian approach

Acoustic fields scattered by poroelastic materials contain key information about the materials' pore structure and elastic properties. Therefore, such materials are often characterised with inverse methods that use acoustic measurements. However, it has been shown that results from many existing inverse characterisation methods agree poorly. One reason is that inverse methods are typically sensitive to even small uncertainties in a measurement setup, but these uncertainties are difficult to model and hence often neglected. In this paper, we study characterising poroelastic materials in the Bayesian framework, where measurement uncertainties can be taken into account, and which allows us to quantify uncertainty in the results. Using the finite element method, we simulate measurements where ultrasonic waves are incident on a water-saturated poroelastic material in normal and oblique angles. We consider uncertainties in the incidence angle and level of measurement noise, and then explore the solution of the Bayesian inverse problem, the posterior density, with an adaptive parallel tempering Markov chain Monte Carlo algorithm. Results show that both the elastic and pore structure parameters can be feasibly estimated from ultrasonic measurements.Comment: Published in JSV. https://doi.org/10.1016/j.jsv.2019.05.02