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- Volume 70, Issue 1, 2021
Geophysical Prospecting - Volume 70, Issue 1, 2021
Volume 70, Issue 1, 2021
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Homotopy scattering series for seismic forward modelling with variable density and velocity
Authors Kui Xiang, Kjersti Solberg Eikrem, Morten Jakobsen and Geir NævdalABSTRACTWe have derived a convergent scattering series solution for the frequency‐domain wave equation in acoustic media with variable density and velocity. The convergent scattering series solution is based on the homotopy analysis of a vectorial integral equation of the Lippmann–Schwinger type. By using the Green's function and partial integration, we have derived the vectorial integral equation of the Lippmann–Schwinger type that involves the pressure gradient field as well as the pressure field from the wave equation. The vectorial Lippmann–Schwinger equation can in principle be solved via matrix inversion, but the computational cost of matrix inversion scales like , where is the number of grid blocks. The computational cost can be significantly reduced if one solves the vectorial Lippmann–Schwinger equation iteratively. A simple iterative solution is the Born series, but it is only convergent when the scattering potential is sufficiently small. In this study, we have used the so‐called homotopy analysis method to derive an iterative solution for the vectorial Lippmann–Schwinger equation which can be made convergent even in strongly scattering media. The computational cost of our convergent scattering series scales as . Our algorithm, which is based on the homotopy analysis method, involves a convergence control operator that we select using hierarchical matrices. We use a three‐layer model and a resampled version of the SEG/EAGE salt model to show the performance of the developed convergent scattering series.
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Multiscale linearized inversion of surface‐wave dispersion curves
Authors Zhinong Wang, Chengyu Sun and Dunshi WuABSTRACTIn recent years, surface‐wave analysis method has been developed rapidly in many fields. Multichannel analysis of surface waves can provide near‐surface one‐dimensional shear‐wave velocity profiles. Because linearized inversion of surface‐wave dispersion curves relies heavily on the choice of the initial model, setting an inappropriate initial model can lead to poor inversion results, or even failure of inversion. However, it is difficult to establish a reasonable initial model without a priori information, which is unavailable in most cases. To cope with this problem, a multiscale linearized inversion method is proposed for surface‐wave dispersion curves inversion. In contrast with the traditional single‐scale linearized inversion, the key idea of the proposed multiscale surface‐wave inversion method is the introduction of a merging and splitting process of layers. After every scale inversion, the merging and splitting operations automatically optimize the inversion model, making it gradually approach to a reasonable subsurface stratification. Multiscale surface‐wave inversion method reduces the difficulty of establishing the initial model and has high computational efficiency. In addition, it has strong ability to identify high‐velocity or low‐velocity interlayers and thin layers, especially suited for the geological conditions with obvious stratification. In synthetic tests, the proposed method was compared with the single‐scale surface‐wave inversion and particle swarm optimization algorithm to demonstrate the effectiveness and practicability of multiscale surface‐wave inversion method. We also applied the multiscale surface‐wave inversion method to field seismic data acquired in Guizhou, China and Texas, USA. Borehole and crosshole test data were compared with the inversion results of field data to prove the reliability of the proposed method.
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3D Marchenko applications: implementation and examples
Authors Joeri Brackenhoff, Jan Thorbecke, Giovanni Meles, Victor Koehne, Diego Barrera and Kees WapenaarABSTRACTWe implement the 3D Marchenko equations to retrieve responses to virtual sources inside the subsurface. For this, we require reflection data at the surface of the Earth that contain no free‐surface multiples and are densely sampled in space. The required 3D reflection data volume is very large and solving the Marchenko equations requires a significant amount of computational cost. To limit the cost, we apply floating point compression to the reflection data to reduce their volume and the loading time from disk. We apply the Marchenko implementation to numerical reflection data to retrieve accurate Green's functions inside the medium and use these reflection data to apply imaging. This requires the simulation of many virtual source points, which we circumvent using virtual plane‐wave sources instead of virtual point sources. Through this method, we retrieve the angle‐dependent response of a source from a depth level rather than of a point. We use these responses to obtain angle‐dependent structural images of the subsurface, free of contamination from wrongly imaged internal multiples. These images have less lateral resolution than those obtained using virtual point sources, but are more efficiently retrieved.
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High‐performance computing strategies for seismic‐imaging software on the cluster and cloud‐computing environments
ABSTRACTModern subsurface imaging techniques allow obtaining high‐quality images but with high computational costs. Nonetheless, depending on the amount of data, their execution is limited by memory in the current generation's hardware. However, with the advancement of new hardware and cloud‐based solutions, these problems are mitigated but still with the risk of work loss and instability. To mitigate the execution problems in memory‐limited and fail‐prone environments, we propose two high‐performance computing techniques. The first is based on independent checkpointing alongside a fault‐tolerant framework to store an execution state and recover from that state in case of failures. Besides, for memory‐limited graphics processing units, we present a technique to reduce the amount of memory requirement that we call the hybrid strategy. The experiments showed that the independent checkpointing alongside the fault‐tolerant framework is able to mitigate the performance penalty of node failures, with the independent checkpointing technique being more relevant when multiple nodes are terminated. Furthermore, the hybrid strategy technique has shown the possibility of execution of larger models that could make the graphics processing unit run out of memory otherwise. Finally, our implementation is scalable, allowing a significant improvement in performance when adding new nodes. In conclusion, our techniques can be used to deliver fast, high‐fidelity subsurface imaging in unstable and memory‐limited environments, such as the cloud.
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Broadband seismic source data acquisition and processing to delineate iron oxide deposits in the Blötberget mine‐central Sweden
ABSTRACTA prototype electromagnetic vibrator, referred to here as E‐Vib, was upgraded and developed for broadband hardrock and mineral exploration seismic surveys. We selected the iron oxide mine in Blötberget, central Sweden, for a test site in 2019 for the newly developed E‐Vib because of the availability of earlier seismic datasets (from 2015 to 2016) for verification of its performance for hardrock imaging purposes. The two‐dimensional data acquisition consisted of a fixed geometry with 550 receiver locations spaced at every 5 m, employing both cabled and wireless seismic recorders, along an approximately 2.7 km long profile. The E‐Vib operated at every second receiver station (i.e. 10 m spacing) with a linear sweep of 2–180 Hz and with a peak force of 7 kN. The processing workflow took advantage of the broadband signal generated by the E‐Vib in this challenging hardrock environment with varying ground conditions. The processed seismic section shows a set of reflections associated with the known iron oxide mineralization and a major crosscutting reflection interpreted to be from a fault system likely to be crosscutting the mineralization. The broadband source data acquisition and subsequent processing helped to improve signal quality and resolution in comparison with the earlier workflows and data where a drophammer seismic source was used as the seismic source. These results suggest new possibilities for the E‐Vib source for improved targeting in hardrock geological settings.
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Reverse time migration with Gaussian beams using optimized ray tracing systems in transversely isotropic media
Authors Qiang Liu, Zhen‐Chun Li, Jian‐En Xiao and Xue‐Cheng XuABSTRACTPrestack depth migration is a key technology for imaging complex reservoirs in media with strong lateral velocity variations. Prestack migrations are broadly separated into ray‐based and wave‐equation‐based methods. Because of its efficiency and flexibility, ray‐based Kirchhoff migration is popular in the industry. However, it has difficulties in dealing with the multi‐arrivals, caustics and shadow zones. On the other hand, wave‐equation‐based methods produce images superior to that of the ray‐based methods, but they are expensive numerically, especially methods based on two‐way propagators in imaging large regions. Therefore, reverse time migration algorithms with Gaussian beams have recently been proposed to reduce the cost, as they combine the high computational efficiency of Gaussian beam migration and the high accuracy of reverse time migration. However, this method was based on the assumption that the subsurface is isotropic. As the acquired azimuth and maximum offsets increase, taking into account the influence of anisotropy on seismic migration is becoming more and more crucial. Using anisotropic ray tracing systems in terms of phase velocity, we proposed an anisotropic reverse time migration using the Gaussian beams method. We consider the influence of anisotropy on the propagation direction and calculate the amplitude of Gaussian beams with optimized correlation coefficients in dynamic ray tracing, which simplifies the calculations and improves the applicability of the proposed method. Numerical tests on anisotropic models demonstrate the efficiency and accuracy of the proposed method, which can be used to image complex structures in the presence of anisotropy in the overburden.
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The appraisal of surface orbital vibrators with buried geophone array for permanent reservoir monitoring
ABSTRACTTime‐lapse seismic is one of the main methods for monitoring changes in reservoir conditions caused by production or injection of fluids. One approach to time‐lapse seismic is through permanent reservoir monitoring, whereby seismic sources and/or receivers are permanently deployed. Permanent reservoir monitoring can offer a more cost‐effective and environmentally friendly solution than traditional campaign‐based surveys that rely on temporarily deployed equipment while facilitating more frequent measurements. At the CO2CRC Otway Project, surface orbital vibrators were coupled to a buried geophone array to form a permanent reservoir monitoring system. These are fixed position seismic sources that provide both P and S waves using induction motor‐driven eccentric masses. After an initial injection of CO2 in February 2016, five months of continuous seismic data were acquired, and reflection imaging was used to assess the system performance. Analysis of the data showed the effects of weather variations on the near‐surface conditions and the sweep signatures of surface orbital vibrators. Data processing flows of the continuous data was adapted from Vibroseis four‐dimensional data processing flows. Ground roll proved a significant challenge to data processing. In addition, variations in the surface wave pattern were linked to major rainfall events. For the appraisal of surface orbital vibrators in imaging, a Vibroseis four‐dimensional monitor survey data with similar geometry was also processed. Surface orbital vibrators are observed to be reliable sources with a potential to provide a repeatable signal, especially if the ground roll should fall outside the target window of interest. To guide future permanent reservoir monitoring applications, a repeatability analysis was performed for the various key data processing steps.
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The added value of joint PP–PS inversion for reservoir characterization: A case study using Jubarte PRM seismic data (offshore Brazil)
Authors Andrea Damasceno, Ali Tura and James SimmonsABSTRACTThe added value of the joint pre‐stack inversion of PP (incident P‐wave and reflected P‐wave) and PS (incident P‐wave and reflected S‐wave) seismic data for the time‐lapse application is shown. We focus on the application of this technique to the time‐lapse (four‐dimensional) multicomponent Jubarte field permanent reservoir monitoring seismic data. The joint inversion results are less sensitive to noise in the input data and show a better match with the rock physics models calibrated for the field. Further, joint inversion improves S‐impedance estimates and provides a more robust quantitative interpretation, allowing enhanced differentiation between pore pressure and fluid saturation changes, which will be extremely useful for reservoir management.
Small changes in reservoir properties are expected in the short time between the time‐lapse seismic acquisitions used in the Jubarte project (only 1 year apart). The attempt to recover subtle fourth‐dimensional effects via elastic inversion is recurrent in reservoir characterization projects, either due to the small sensitivity of the reservoirs to fluid and pressure changes or the short interval between the acquisitions. Therefore, looking for methodologies that minimize the uncertainty of fourth‐dimensional inversion outputs is of fundamental importance. Here, we also show the differences between PP only and joint PP–PS inversion workflows and parameterizations that can be applied in other projects. We show the impact of using multicomponent data as input for elastic seismic inversions in the analysis of the time‐lapse differences of the elastic properties. The larger investment in the acquisition and processing of multicomponent seismic data is shown to be justified by the improved results from the fourth‐dimensional joint inversion.
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Factors that influence fluid flow in a single fracture
Authors Bo‐Ye Fu, Arthur Cheng, Yunyue Elita Li and Jingjing ZongABSTRACTTo investigate the influence of compression, Poisson effect and turbulence on the fluid flow process and the inversion for fracture surface geometries, we simulate two sets of fractures: one with a defined fracture height standard deviation σ constant and a varying autocorrelation length λ and another with a fixed λ and a changing σ. Under compression, the normal stress closes fractures with a large aperture and thus reduces the effective permeability. However, the Poisson effect, which is induced by the compression, has little influence on the fluid flow properties and does not affect the inversion for fracture height standard deviation or the autocorrelation length. When introducing turbulence, we observe a significant difference between the performance of the Navier–Stokes equation and the local cubic law; compared with the Navier–Stokes equation, the local cubic law overestimates the peak value of the breakthrough time curve and effective permeability, thereby underestimating the mean fracture aperture.
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Numerical determination of pressure‐dependent effective thermal conductivity in Berea sandstone
Authors Mirko Siegert, Marcel Gurris, Claudia Finger and Erik H. SaengerABSTRACTIn this paper, the methods of digital rock physics are applied to determine pressure‐dependent effective thermal conductivity in rock samples. Simulations are performed with an in‐house three‐dimensional finite volume code. In the first step, four numerical models are derived from a given tomographic scan of Berea sandstone. Consequently, simulations of the thermal conductivity at ambient conditions are performed and validated with experimental data. In a second step, a new workflow for the determination of the pressure‐dependent thermal conductivity in rock samples is elaborated, tested and calibrated. Results originating from the derived workflow show very good agreement with experimental data.
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Gravity for Lithosphere Architecture Determination and Analysis: the Central Eastern Mediterranean case study
Authors Daniele Sampietro and Martina CapponiABSTRACTThe Central‐Eastern Mediterranean region is known to be a complex area due to the interaction of four tectonic plates, namely Arabia, Africa, Anatolia and Eurasia, and by the presence of an ancient oceanic crust in the Herodotus and Ionian Basins. The analysis of the available literature highlights that the distribution of the freely available geophysical data (i.e. seismic, gravity and magnetic observations) is quite disparate. In this framework, high‐resolution global gravity field models, such as XGM2019e, mainly based (offshore) on satellite data, can be profitably used as a uniform dataset to study, in a coherent way, large regions.
In the current work, we exploit the XGM2019e model, together with a set of a priori information, derived mainly from geophysical data retrieved from the literature, to study the structure of the crust in the Central‐Eastern Mediterranean area. The study is organized in three different phases: in the first one, we enhanced the map of geological crustal provinces by means of an automatic Bayesian classification algorithm applied to the second radial derivatives of the gravitational potential. In the second phase, using as observation a grid of gravity anomalies, we applied a full three‐dimensional inversion procedure (always based on a Bayesian paradigm) to estimate the mass density variations and the geometries of the main geological units in the whole study area. Finally, in the third phase, we performed a refined three‐dimensional local inversion on the Cyprus area to improve the modelling of the shallowest layers. The main results of this study, carried out in the framework of the European Space Agency GIADA project, are freely available, upon request, at https://www.g‐red.eu/geophysics/.
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Discrete cosine transform for parameter space reduction in Bayesian electrical resistivity tomography
Authors A. Vinciguerra, M. Aleardi, A. Hojat, M. H. Loke and E. StucchiABSTRACTElectrical resistivity tomography is a non‐linear and ill‐posed geophysical inverse problem that is usually solved through gradient‐descent methods. This strategy is computationally fast and easy to implement but impedes accurate uncertainty appraisals. We present a probabilistic approach to two‐dimensional electrical resistivity tomography in which a Markov chain Monte Carlo algorithm is used to numerically evaluate the posterior probability density function that fully quantifies the uncertainty affecting the recovered solution. The main drawback of Markov chain Monte Carlo approaches is related to the considerable number of sampled models needed to achieve accurate posterior assessments in high‐dimensional parameter spaces. Therefore, to reduce the computational burden of the inversion process, we employ the differential evolution Markov chain, a hybrid method between non‐linear optimization and Markov chain Monte Carlo sampling, which exploits multiple and interactive chains to speed up the probabilistic sampling. Moreover, the discrete cosine transform reparameterization is employed to reduce the dimensionality of the parameter space removing the high‐frequency components of the resistivity model which are not sensitive to data. In this framework, the unknown parameters become the series of coefficients associated with the retained discrete cosine transform basis functions. First, synthetic data inversions are used to validate the proposed method and to demonstrate the benefits provided by the discrete cosine transform compression. To this end, we compare the outcomes of the implemented approach with those provided by a differential evolution Markov chain algorithm running in the full, un‐reduced model space. Then, we apply the method to invert field data acquired along a river embankment. The results yielded by the implemented approach are also benchmarked against a standard local inversion algorithm. The proposed Bayesian inversion provides posterior mean models in agreement with the predictions achieved by the gradient‐based inversion, but it also provides model uncertainties, which can be used for penetration depth and resolution limit identification.
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Distributed electric field sensing using fibre optics in borehole environments
Authors David L. Alumbaugh, Evan Schankee Um, G. Michael Hoversten and Kerry KeyAbstractIn the past decade, rapid advances in distributed optical fibre sensing technologies have made it possible to record various geophysical data (e.g. strain, temperature and pressure) continuously in both time and space along the fibre, providing an unprecedented quantity and spatial density of data compared to traditional geophysical measurements as well as reducing data acquisition cost. To date, no distributed fibre‐based electromagnetic field sensing system has been implemented although electromagnetic sensing could have a broad range of applications to geophysical imaging and monitoring in borehole environments. The goal of this paper is to provide a theoretical feasibility study regarding the design and use of an electromagnetic sensing optical fibre for geophysical applications. First, we present the sensitivity analysis of a ‘hypothetical’ optical fibre coated with polyvinylidene fluoride, a polymer that provides relatively high piezoelectric properties, yet unlike ceramics, is flexible. Using a two‐dimensional electromagnetic modelling algorithm, we simulate the earth electric‐field‐to‐fibre‐strain transfer function and estimate the theoretical sensitivity of the optical fibre to electric fields. Given the state‐of‐the‐art distributed acoustic sensing strain sensitivities in the picometres strain range, our numerical modelling analysis suggests that a perfectly coupled polyvinylidene fluoride–coated optical fibre can measure electric field values in the mV/m to V/m amplitude range. We then apply a cylindrically symmetric modelling algorithm to simulate numerical models demonstrating the applicability of such a fibre in an oilfield environment. Scenarios investigated employ an electric field source and suggest that the measurements can be used to distinguish the oil versus water ratio with a fibre mounted inside a producing steel cased oil well as well as distinguishing between brine and hydrocarbon filled reservoir zones with a fibre located outside of the casing.
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Research note: Inverse propagation in 1.5‐dimensional amplitude‐versus‐offset joint migration inversion
Authors Yimin Sun and Eric VerschuurABSTRACTThe state‐of‐the‐art joint migration inversion faces the so‐called amplitude‐versus‐offset challenge, due to adopting over‐simplified one‐way propagation, reflection and transmission operators to avoid over‐parameterization in the inversion process. To overcome this challenge, we apply joint migration inversion to horizontally layered media (or 1.5‐dimensional media) and parameterize the solution space via density and velocity models. In this scenario, one‐way propagation, reflection and transmission operators required by the joint migration inversion process can be analytically and correctly derived from the subsurface models, so the amplitude‐versus‐offset challenge is successfully overcome. We introduce a new concept, which is named ‘inverse propagation’, into our 1.5‐dimensional amplitude‐versus‐offset joint migration inversion. It can correctly reconstruct subsurface wavefields by using a surface‐recorded receiver wavefield with all the influence of transmission, reflection and multiples accounted for. A synthetic example is used to demonstrate the correctness of the inverse propagation. This work is the foundation to further develop the 1.5‐dimensional amplitude‐versus‐offset joint migration inversion technology.
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Volume 72 (2023 - 2024)
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