We present an optimized method to calculate traveltimes for seismic inversion. It is a hybrid version of the shortest path approach. The main improvements consist in computing traveltimes using the seismic ray paths and using temporary secondary nodes in vicinity of the source. The proposed method is done following two sequential steps. In the first step, traveltimes are computed for all nodes using the modified shortest path method. Ray paths are then traced back for all source-receiver couples and traveltimes for each receiver are updated using nodes along the ray path. Tests have shown that this approach can improve the accuracy by an order of magnitude and save up to a third of the computation time when compared to the standard shortest path algorithm.
Presentation Date: Thursday, October 18, 2018
Start Time: 8:30:00 AM
Location: 211A (Anaheim Convention Center)
Presentation Type: Oral
In this paper, we study the performance of joint time-lapse inversion of borehole ERT and magnetometric resistivity data in the context of quantitative monitoring of CO2 storage. We have considered the injection of CO2 in a thick sandstone aquifer at a depth of 75 m. The CO2 plume extension is modeled as a resistive zone with increased lateral extensions. Inversion results show that joint MMR and ERT data is a more robust tool to follow the evolution of CO2 plume propagation than the separate inversions.
Presentation Date: Monday, September 25, 2017
Start Time: 4:45 PM
Presentation Type: ORAL
Summary Speeding-up convergence rates and reducing the computational burden of Full Waveform Inversion (FWI) is increasingly important as we move toward large-scale 3D multi-parameter inversion. To this end, second-order optimization algorithms like L-BFGS or the truncated Newton method allow a much faster convergence rate at minimal computational costs. Still, large-scale multiparameter FWI remains computationally challenging, preventing its widespread adoption. Hence, reducing the computing times remains an important issue to broaden the applicability of FWI. Many strategies have been proposed to decrease the computational burden of FWI.
It is well known that the statistical properties of resistivity within the Earth are generally non-stationary due to spatial variations of parameters that control the bulk resistivity of rocks, such as water resistivity, water content, porosity, temperature, etc. Hence, it may be advantageous to take into account the non-stationary nature the parameters when defining the covariance model for Bayesian electrical resistivity tomography (ERT) inversion. In this paper, we propose to use recent work on non-stationary Matérn covariance family that is defined through linear stochastic partial differential equations (SPDE). The non-stationary precision matrix is obtained without calculating the inverse of the covariance matrix, and non-stationarity is easily implemented by spatially varying SPDE parameters. Two types of prior information are considered to take into account the non-stationarity of resistivity field, structure orientation and measurement sensitivity. The proposed approach was successfully tested on two synthetic models.
Electrical Resistivity tomography (ERT) or electrical imaging is among the most commonly used high resolution geophysical techniques in many geoscientific domains, such as hydrogeophysics (e.g. Binley and Kemna, 2006), engineering geophysics (e.g. Ramirez et al., 1996), and mining exploration (e.g. Oldenburg et al., 1997). An overview of recent ERT developments can be found in Loke et al (2013). The ERT inverse problem is ill-posed, nonlinear and generally underdetermined. In this paper, it is solved using Bayesian maximum a posteriori (MAP) estimation approach such as presented in (Tarantola and Valette, 1982). In general, covariance functions are chosen stationary and their parameters (correlation length or range, variance and anisotropy) are determined from resistivity well logs (Linde et al., 2006). However, in most real cases, resistivity models are not stationary because all parameters that affect bulk resistivity such as pore water resistivity, water content, temperature and clay content have statistics that can vary spatially. It is generally very difficult to assess non-stationarity when considering measured apparent resistivity data and well resistivity logs alone. In our methodology, all a priori information such as geology knowledge, other geophysical techniques and sensitivity of ERT are used to introduce the non-stationarity in the model parameters covariance matrix. A few approaches have been developed for non-stationary covariance calculation. An overview is given in Sampson (2010) and Fuglstad et al. (2014). In the literature on geophysical inverse problems, Shamsipour et al. (2012) used the Matérn-like process convolution of Paciorek and Schervish (2006) to invert gravity data. However, the covariance matrix is generally dense, especially when range parameter is high.
Down-hole magnetometric resistivity (MMR) measurements have been conducted in Tobermalug prospect in County Limerick, Ireland. The survey was used as an alternative to down-hole electromagnetic to delineate subhorizontal zinc/lead mineralization lenses that are poorly conductive. Two survey areas were investigated, DHMMR1 and DHMMR2.
Interpretation is based on the regularized least-squares inversion of MMR data, in which MMR modeling is performed by resolving electrostatic and magnetostatic equations using finite volume method. Inversion of synthetic data of two conductive horizontal discs model shows that conductive structures are well positioned but their extensions is biased to current electrodes orientation. Inversion allowed localizing a few conductive elongated targets. At DHMMR1, the conductivity is weaker and seems to be associated to disseminated mineralization. DHMMR2 contains a higher conductivity and more elongated target. It seems to be associated to semi-massive sulphides.
Ireland was one of leading European producer of zinc and lead. During the last fifty years, zinc and lead concentrates have been extracted from the Irish Midlands Orefield that covers a surface area greater than 35000km2 (Blaney, 2011). It is one of the world’s major zinc provinces with five major producing mines with large size and high grade ore. In 1999, Minco Ireland signed a joint venture agreement with Noranda (now Glencore) for the exploration of Pallas Green block located between Limerick city and Tipperary town in the centre south of Ireland. The zinc/lead mineralisation at Pallas Green ranges from disseminated and stringer-fracture fill textures to massive (Blaney, 2011). It consists of multiple, subhorizontal, stratiform lenses between 0.5 m to >18 m thick and comprises sphalerite, galena, pyrite and minor marcasite within a Carboniferous limestone. Disseminated and sphalerite rich ores are generally poor targets for electrical resistivity and electromagnetic methods (Denith and Mudge, 2014). In contrast, the MMR technique is more appropriate because it can respond to highly conductive and to weakly conductive targets in a conductive host. For example, it was successfully used in Australian environments for poorly conducting metal sulphide targets, such as sphalerite rich bodies (Asten, 1988; Bishop et al., 1997) and nickel sulphide mineralisation (Bishop et al., 2000).
In this paper, we study the performance of time-lapse inversion of borehole magnetometric resistivity data in the context of quantitative monitoring of CO2S/SUB> storage. We have considered the injection of CO2S/SUB> in a thick sandstone aquifer at a depth of 300 m, as is planned for a controlled release experiment at the Carbon Management Canada Field Research Station (FRS) in Alberta, Canada. The CO2S/SUB> plume extension is modeled as a resistive zone with increased lateral extensions. Inversion results show that MMR can be a robust tool to follow the evolution of CO2S/SUB> plume propagation. Structure orientation bias that affects the MMR method can be reduced using a distance weighting function. Also, the resistivity of the plume is generally under-estimated. Introduction The geological sequestration of Carbone dioxide (CO2S/SUB>) in deep saline aquifer requires the development of geophysical monitoring techniques that allow detecting and imaging the spatial extent of the CO2S/SUB> plume to ensure longterm integrity of the storage. Electrical and electromagnetic methods appear appropriate for such problem because a high resistivity contrast exists between brine and the injected supercritical CO2S/SUB>. For that reason, time-lapse electrical resistivity tomography (ERT) is being used in a few brine pilot tests (e.g. Schmidt-Hattenberger et al., 2012). In this paper, we present the results of a numerical feasibility study for borehole magnetometric resistivity (MMR) monitoring of CO2S/SUB> sequestration at the Field Research Station (FRS), Alberta, Canada. Instead of measuring the electrical potential field caused by current injection, MMR method measures the associated magnetic field. The latter is representative of current channelled through the ground and is a function of acquisition geometry and resistivity contrast. Besides, the MMR method is sensitive to current density variations and not to the absolute resistivity values. Consequently, the MMR response is not affected by the problem of noise in conductive media, as is the case of ERT survey (very weak electrical potential in conductive environments). MMR measurements are carried out using three-component fluxgate magnetic probe, which reduces the need for borehole electrode installation and suppresses corrosionrelated problems that can bias time-lapse measurements. Another important MMR feature for time-lapse CO2S/SUB> monitoring is that the vertical magnetic field resulting from the current distribution in the earth is only dependent on zones where lateral resistivity contrasts exist (Acosta and Worthington, 1983). The vertical magnetic component for a homogeneous or a layered earth is zero.
The geological sequestration of Carbone dioxide (CO2S/SUB>) in deep saline aquifer requires the development of geophysical monitoring techniques that allow detecting and imaging the spatial extent of the CO2S/SUB> plume to ensure longterm integrity of the storage. Electrical and electromagnetic methods appear appropriate for such problem because a high resistivity contrast exists between brine and the injected supercritical CO2S/SUB>. For that reason, time-lapse electrical resistivity tomography (ERT) is being used in a few brine pilot tests (e.g. Schmidt-Hattenberger et al., 2012).
In this paper, we present the results of a numerical feasibility study for borehole magnetometric resistivity (MMR) monitoring of CO2S/SUB> sequestration at the Field Research Station (FRS), Alberta, Canada. Instead of measuring the electrical potential field caused by current injection, MMR method measures the associated magnetic field. The latter is representative of current channelled through the ground and is a function of acquisition geometry and resistivity contrast. Besides, the MMR method is sensitive to current density variations and not to the absolute resistivity values. Consequently, the MMR response is not affected by the problem of noise in conductive media, as is the case of ERT survey (very weak electrical potential in conductive environments). MMR measurements are carried out using three-component fluxgate magnetic probe, which reduces the need for borehole electrode installation and suppresses corrosionrelated problems that can bias time-lapse measurements. Another important MMR feature for time-lapse CO2S/SUB> monitoring is that the vertical magnetic field resulting from the current distribution in the earth is only dependent on zones where lateral resistivity contrasts exist (Acosta and Worthington, 1983). The vertical magnetic component for a homogeneous or a layered earth is zero.
Until very recently, ray-based time-lapse traveltime tomography algorithms were scarce and limited, in opposition to electric resistance tomography (ERT) where multiple approaches have been developed over the last two decades. In this paper, three time-lapse ERT schemes are adapted for traveltime tomography. We show using synthetic crosswell data that the time-lapse algorithms allow reducing artifacts compared to independent inversions. Moreover, schemes relying on a reference model to regularize the inversion provide the best results.
Time-lapse geophysical monitoring has been used for about two or three decades to track the behaviour of underground fluids. Such monitoring is based on measurements that are collected before, perhaps during, and after an imposed change to the system. Inverted difference images reveal changes that vary over space and time and that can be related to fluid movement. Seismic methods are predominantly used to monitor oil and gas reservoirs (Lumley, 2001), while in hydrogeology, electric resistance tomography (ERT) is commonly used (LaBrecque and Yang, 2001), although ground-penetrating radar is also sometimes used (Huisman et al., 2003). Common practice rely on surface measurements mainly for economical reasons, although down-hole methods are also used.
Historically, consecutive time-lapse datasets were inverted independently to obtain as many “snap shots” tomograms that were subsequently subtracted to track changes in the medium. However, due to the ill-posedness nature of the tomographic problem, artifacts arise in the resulting images, and care should be taken to avoid attributing these artifacts to real changes. This fact was recognized early by researchers working on timelapse ERT inversion (Daily et al., 1992; LaBrecque and Yang, 2001), and improving time-lapse ERT inversion algorithms is still a topic of on-going research (Hayley et al., 2011; Karaoulis et al., 2011).
With respect to crosswell radar or seismic tomography, the efforts to develop time-lapse adapted algorithms are much more scarce. The work of Farmani et al. (2008); Chang and Alumbaugh (2011) compared snap shots radar tomograms obtained independently to map velocity changes due to variations in water content. In seismics, work from Mathisen et al. (1995); Bauer et al. (2005); Saito et al. (2006); Daley et al. (2008) also relied on independent snap shot comparison, while Vesnaver et al. (2003) used a “manual” iterative approach to minimize artifacts between the time-lapse models. Spetzler et al. (2007) and Ajo-Franklin et al. (2007) inverted traveltime differences, thus assuming stationary raypaths. Day-Lewis et al. (2002) and Johnson et al. (2007) proposed a difference tomography scheme specifically devised to invert time-lapse crosswell crosswell amplitude data to map changes in electric conductivity consecutive to a saline tracer test. Very recently, Karaoulis et al. (2015) used an active time-constraint approach to invert time-lapse traveltime data within a Fresnel-zone formalism.
The relative advantages and disadvantages of the fast marching (FMM), fast sweeping (FSM) and shortest-path methods (SPM) for raytracing on unstructured meshes are examined. The SPM implementation relies on secondary nodes to improve accuracy. Measurements are performed on 2D triangular and 3D tetrahedral meshes. In all cases, the SPM with a high number of secondary nodes (up to 9) yields the highest accuracy. In 2D, the computational cost of the SPM might be compensated in tomography problems where the raytracing routine is called for multiple sources with the same grid. In 3D, a small number of secondary nodes (1 or 2) can be used with the SPM to achieve accuracy comparable or better than the FMM and FSM, at better computational cost.
2.5D modeling is appealing to speedup calculations when physical properties are invariant in one horizontal dimension. The discrete Fourier transform imposed by the 2.5D geometry implies the selection of a particular set of wavenumbers to sample the out-of-plane dimension. In this article, we derive simple criteria for the number and the spacing between the wavenumbers in order to apply the 2.5D configuration to frequency-domain modeling. To show the efficiency of the derived criteria, we use finite-difference methods to obtain full 3D wavefront for viscoelastic media.
Modeling the propagation of viscoelastic waves in the frequency- domain presents numerous advantages compared to time-domain approaches (Ajo-Franklin, 2005; Jo et al., 1996). A major drawback however is the size of linear system that must be solved when 3D problems are to be tackled (Gosselin-Cliche and Giroux, 2014). Often, the survey configuration and geology of the area under study are such that 2D models could be good approximations. 2D modelling, however, does not capture the true seismic amplitudes (Auer et al., 2013), and adding a “half” dimension allows accurately describing amplitudes and phases of the seismic waves (Williamson and Pratt, 1995). This is usually done by using a Fourier transform in the out-of-plane direction to reduce the problem of solving the 3D equation to multiple 2D ones (Song and Williamson, 1995). In doing so, care must be taken to correctly sample the out-of-plane dimension in order to avoid aliasing and noise issues. In this contribution, we examine how the choice of the sampling parameters affects the quality of the modeled response.
Duchesne, Mathieu J. (Geological Survey of Canada) | Brake, Virginia I. (Geological Survey of Canada) | Hu, Kezhen (Geological Survey of Canada) | Giroux, Bernard (INRS-ETE) | Walker, Emilie (Laval University)