Dispersion Of Seismic Waves Research Articles

Three methods of visco‐acoustic migration based on the De Wolf approximation and comparison of their migration images

AbstractThe viscosity of a medium affects the amplitude attenuation and velocity dispersion of seismic waves. Therefore, it is necessary to consider these factors during migration. First, to eliminate the viscous effect of a medium, we combine the Futterman model with the integral equation of the De Wolf approximation to construct a compensation operator of the De Wolf approximation for a visco‐acoustic medium. Next, we use the visco‐acoustic screen approximation method to realize the continuation operator then establish a prestack depth migration algorithm. Finally, an error analysis, impulse response test and model test are performed. The results show that three different generalized visco‐acoustic screen methods (phase screen method, generalized screen method and extended local Born Fourier method) can satisfactorily compensate for the attenuation of deep interface amplitude. Among these methods, the visco‐acoustic extended local Born Fourier method has the highest accuracy and the best compensation effect.

Acoustic wave propagation and scattering in visco-acoustic medium: Integral equation representation and De Wolf approximation

A visco-acoustic medium is an approximate representation of the absorption and attenuation characteristics of the actual earth medium, which will cause energy attenuation and velocity dispersion of seismic waves. The propagation law of scattered waves in viscoelastic media can be revealed through seismic wave forward simulation. However, the numerical simulation of scattered waves in a visco-acoustic medium using the De Wolf approximation method based on the Lippmann-Schwingr (L-S) equation has not been studied. Therefore, based on the Futterman dispersion relation, the mathematical expression of the integral equation of acoustic wave propagation and scattering in the visco-acoustic medium is derived. We combine the De Wolf approximation with the quality factor Q. The thin slab approximation and screen approximation methods are two realizations of the De Wolf approximation. The thin slab approximation and the screen approximation continuation operator in the viscous-acoustic medium are constructed and applied to the numerical simulation of the scattered wave field. The research results of the concave model and complex model indicate that due to the influence of medium viscosity, the energy of the deep reflected waves is weaker in the forward modeling records of the thin slab approximation method and screen approximation method, and the dominant frequency of seismic waves moves towards the low-frequency direction; Compared with the finite difference results, they only calculate one reflection, and there are no multiple wave signals in the seismic records. Finally, We discuss the thin slab approximation and the screen approximation method for detail around the division of the thickness of the thin slab, the selection of the reference frequency, and the non-uniformity of the medium.

The onset of anelastic behavior in fine-grained synthetic dunite

Micromechanical models suggest that the onset of anelastic relaxation in polycrystalline olivine, critical to interpretation of the seismic wave attenuation and dispersion in the upper mantle, should be a mild dissipation peak caused by elastically accommodated grain-boundary sliding. Such behavior has been tentatively invoked to explain both a short-period shear modulus deficit and a dissipation plateau poorly resolved at 900–700 °C in previous forced-oscillation experiments on fine-grained dunite tested within mild-steel jackets. However, these observations may have been complicated by the austenite to ferrite plus cementite phase transition in the jacket material, compliance associated with interfacial Ni70Fe30 foils, and modeling of the mechanical properties of polycrystalline alumina as control specimen. To investigate the influence of these complications within the experimental setup and provide forced-oscillation data of better quality especially at moderate temperatures, we have conducted further forced-oscillation tests for which we removed the interfacial foils, employed single-crystal sapphire as reference sample, and used alternative jacket materials (stainless steel or copper) which experience no phase transition during the staged cooling. The newly acquired forced-oscillation data, although broadly consistent with the previous results, differ significantly especially in temperature sensitivity, and allow refinement of an appropriate Burgers creep-function model. A mild dissipation peak superimposed on monotonic dissipation background during the onset of anelastic relaxation in dry, melt-free and fine-grained dunite has now been consistently observed at temperatures of ∼950–1050 °C and seismic periods of 1–1000 s. Such a dissipation peak with relaxation strength 0.02 ± 0.01 is attributed to elastically accommodated grain-boundary sliding. The high activation energy (> 600 kJ/mol) of viscoelastic behavior involving both dissipation and related dispersion suggests that grain-boundary diffusion may be limited by interfacial reaction within grain boundaries. The reduced relaxation strength makes it difficult to attribute the oceanic lithosphere-asthenosphere boundary to water-mediated elastically accommodated grain-boundary sliding.

Application of AVO Characteristics Analysis and Seismic Dispersion AVO Inversion to the Carbonate Hydrocarbon Reservoirs in Region Y of the Tarim Basin, China

In recent years, breakthroughs in deep hydrocarbon exploration have been continuously achieved in the Tarim Basin of China. The Ordovician carbonate stratum has been shown to contain vast oil and gas resources. However, challenges remain in understanding the seismic response characteristics and accurately identifying the hydrocarbon reservoirs. These challenges can be attributed to factors including the significant burial depth of the target layers and complex geologic structures. To effectively support hydrocarbon exploration and resource assessment in the Tarim Basin, this study focused on the following three aspects in Region Y. First, according to the analysis of prestack amplitude versus offset (AVO) characteristics in well‐adjacent seismic traces and seismic forward modeling, we demonstrated that different fluid‐filled reservoirs have distinctly different AVO characteristics. This means that the hydrocarbon reservoirs in the study area can be identified by AVO inversion. Second, based on the theory that seismic waves exhibit amplitude attenuation and velocity dispersion when propagating through fluid‐filled media, the seismic dispersion AVO inversion technique was developed to obtain equations for the attributes of primary (P) and shear (S) seismic wave dispersion. Finally, this technique was applied in Region Y and further verified using actual drilling data from single wells and well profiles. The application results demonstrate that hydrocarbon reservoirs can be effectively identified using this technique and provide a technical reference for reservoir identification in other areas of the Tarim Basin. The AVO characteristic analysis is the prerequisite for the successful application of this method; the key is to find accurate inversion equations and parameters to recognize the AVO response patterns in the study area.

Frequency-dependent velocities and attenuations in fluid-saturated rocks: Fractures aligned in isotropic medium with random pore shape

The modeling of seismic wave velocity and attenuation is crucial for the interpretation of seismic data. In fluid-saturated rocks, the presence of fractures causes dispersion and attenuation of seismic waves due to fluid flow between cracks and pores. Meanwhile, the parallel distribution of cracks is an important reason for the anisotropy of rocks. Combined with poroelasticity theory, we extend Chapman’s model to media with penny-shaped fractures and an isotropic porous matrix, for which no restrictions are placed on the pore shape of the matrix. We conduct simulations at different frequencies to indicate the predicted anisotropy of velocity and attenuation. The variation of velocities and attenuations with orientation angle is consistent with Chapman’s model. Because a typical porous matrix is used in the new model, predicted velocities are lower than those under assumption of spherical matrix pores. Then, we analyze the effect of pore compressibility of the matrix on the velocity and attenuation. We also conduct discussions about the effect of different porosities on velocity and attenuation. The analysis indicates that the predictions of the new model are more closely related to the modulus of the porous matrix than Chapman’s model. The strength of fluid flow in the new model also will change with the matrix pores. The comparison of the new model and Chapman’s model with experimental data indicates that the new model is in better agreement with the experimental results.

Seismic wave dispersion and attenuation resulting from multiscale wave-induced fluid flow in partially saturated porous media

SUMMARY Sedimentary rocks are typical heterogeneous porous media induced by fluid patches and pore fabric. It is well acknowledged that the wave-induced fluid flow (WIFF) at different scales will cause seismic wave dispersion and attenuation in a wide frequency range. Consequently, modelling wave dispersion and attenuation due to multiscale WIFF is of significance for reservoir characterization from multiscale geophysical measurement and interpretation. In this study, the multiscale WIFF in partially saturated porous media, including global, 3-D mesoscopic and squirt flows, are investigated. And we derive the wave equations by introducing the Rayleigh's spherical bubble oscillation and the porous grain models into Santos poroelasticity theory. Numerical simulations demonstrate that the multiscale model can interpret the transition of rock states as frequency increases and capture the broad-band seismic wave dispersion and attenuation characteristics, which are directly associated with the heterogeneity scale. Besides, the multiscale model can be degraded to a single- or dual-scale model under specific parameters. We validate the proposed model with board-band experimental data of partially saturated sandstones, confirming its comprehensive characterization of velocity dispersion and attenuation over a wider range of frequencies. Moreover, the model successfully interprets the unrelaxed state of partially saturated rock at ultrasound frequencies.

Estimation of wave velocity and analysis of dispersion characteristics based on wavelet decomposition

Due to the complexity of the crustal medium and stratigraphic boundaries, seismic waves typically exhibit attenuation and dispersion after propagation through the medium. By studying the regularity of seismic wave dispersion, soil layer information can be extracted. Current spectral decomposition techniques take less account of signal filtering processing of seismic waves, and the complexity of the stratigraphy tends to reduce the accuracy of dispersion analysis. Based on the above, a new method for calculating the dispersion characteristics of a site from surface and downhole ground vibration recordings is proposed, which is simpler than the spectra analysis of surface waves (SASW) method and eliminates the need for multiple pickups and additional equipment. This method is based on wavelet decomposition and seismic wave filtering, and a numerical simulation example is established to verify the effectiveness of the method. Then, the records of the Tohoku earthquake on March 11, 2011 are used as actual strong earthquake examples for filtering and dispersion analysis. Finally, it is concluded that the seismic wave dispersion analysis method based on wavelet decomposition can effectively filter and analyze seismic waves in specific frequency bands.

A benchmark study for quasi-static numerical upscaling of seismic wave attenuation and dispersion in fractured poroelastic rocks

Numerical simulation is an effective tool for comprehending fluid flow behavior and solid skeleton deformation within porous media, as well as obtaining valid seismic information. The elastic response of seismic waves, serving as an intermediary linking material properties and seismic attributes, is influenced by a combination of the wave-induced fluid flow (WIFF) effects and stress interactions. However, the impact of stress interactions is frequently overlooked in numerous studies, primarily due to the complex distribution of subsurface fractures makes it difficult to clarify the effects caused by local stress perturbations. Therefore, we present a numerical upscaling procedure as a benchmark process to quantify seismic wave attenuation and dispersion in fractured porous media simulations. The procedure is based on COMSOL Multiphysics and allows for the simulation of the energy dissipation resulting from the compression of a model with arbitrary forms of fluid saturation, geometry, and petrophysical parameters by seismic waves. We analyze the fracture models with different spatial distributions and infills to understand the mechanism. Our simulation results show the efficient and accurate capabilities of the numerical upscaling procedure in simulating the acoustic properties of fractured porous media and demonstrate the physical processes at various frequencies. In addition, our study yielded corresponding results: 1) the diverse spatial distribution of fractures not only gives rise to peak anomalies but also influences both the attenuation peaks and characteristic frequencies of seismic waves, thus reflecting the attenuation phenomena occurring at different scales; 2) various infills exhibit distinct sensitivities to fracture morphology and stress interactions.

Influence of partial saturation on bulk modulus and attenuation: the experiment and the theoretical model

SUMMARY Modelling the dispersion and attenuation of seismic waves in partially saturated rocks is important for quantitative interpretation of seismic data. To observe the partial saturation effects on modulus and attenuation, three sandstone samples with different porosities were used in the laboratory experiment. The samples were measured by ultrasonic testing system under different water saturation using drainage process. The experimental results show that the bulk modulus more rapidly increased at higher saturations (>80 per cent), and attenuation peaks could be observed. Then we develop a new partial saturation model based on Chapman’s theory and poroelastic theory. The new model is consistent with the Gassmann equation when the water saturation is 0 or 100 per cent. By analysing the characteristic frequency, the new model can be concluded in the form of a standard linear solid model. A comparison of the new model with the White model and the measured data is conducted. The results show that the model performed well at predicting the effective bulk modulus and attenuation of the rock with different water saturation. Finally, we discussed the impact of frequency, fluids and pore structures on the new model. The results reveal that the new model will be helpful in discussing partial saturation in rocks.

Reflection dispersion of seismic waves at the ocean bottom due to mesoscopic-flow loss

Seismic reflections at the interface of heterogeneous porous media are significantly affected by the multi-scale fluid-flow losses. In this work, we study the seismic reflection dispersion from the ocean bottom separating seawater and heterogeneous porous seabed, described by the effective Biot theory where the mesoscopic loss is present. The analytical reflection coefficient is obtained based on the displacement potentials and suitable boundary conditions. Two reflection scenarios, including the water/water-bearing medium contact and water/gas-saturated medium interface, are considered. The shear-wave attenuation is also considered by using a Cole-Cole complex shear modulus. Numerical results showing the variation in reflection magnitude versus frequency and incidence angle are presented, revealing that the P-wave mesoscopic attenuation, complex shear modulus, boundary conditions and permeability can significantly affect the frequency and angle dependence of the reflection coefficients. Reflections at the water/gas-saturated medium interface exhibit quite different behaviors from those at the water/water-bearing medium contact. The open-pore interface gives frequency-dependent reflections, whereas in sealed-pore case, the reflection magnitudes remain unchanged for all frequencies, due to the fact that the interface degrades into a water/elastic solid one. The study can be relevant for reservoir prediction and fluid identification based on the reflected marine data.

Fluid identification by nonlinear frequency‐dependent amplitude variation with offset inversion based on scattering theory

AbstractPre‐stack seismic amplitude variation with offset inversion is a crucial technique in seismic exploration, employed to estimate reservoir elastic parameters and thus reservoir fluid properties. However, traditional amplitude variation with offset inversion methods are based on elastic theory and linear approximation, neglecting the inelasticity of medium and nonlinear theory. To overcome this limitation, a quadratic scattering coefficient equation of the viscoelastic fluid factor is derived, which provides the basis for the equation for amplitude variation with offset inversion. Traditional amplitude variation with offset inversion methods typically neglect seismic dispersion and attenuation, failing to account for the influence of the seismic wave velocity attenuation and frequency variation. Quality factors of P‐ and S‐waves represent the degree of attenuation of seismic waves. To comprehensively address the effects of seismic wave dispersion and attenuation, a novel method called pre‐stack seismic nonlinear frequency‐dependent amplitude variation with offset inversion has been developed. This method builds upon the new quadratic scattering coefficient and is utilized for reservoir fluid prediction. The reliability and stability of the method are verified through synthetic and filed data examples. Further analysis reveals that the method is more reasonable and accurate compared to the traditional linear amplitude variation with offset inversion method. The results demonstrate that the proposed pre‐stack seismic nonlinear frequency‐dependent amplitude variation with offset inversion method can effectively identify reservoir fluids, providing a novel solution for reservoir fluid identification.

A numerical assessment of local strain measurements on the attenuation and modulus dispersion in rocks with fluid heterogeneities

SUMMARY The forced oscillation method is widely used to investigate intrinsic seismic wave dispersion and attenuation in rock samples by measuring their dynamic stress–strain response. However, using strain gauges to locally measure the strains on samples surfaces can result in errors in determining the attenuation and moduli of rocks with mesoscopic scale heterogeneities. In this study, we developed a 3-D numerical model based on Biot's poroelastic theory to investigate the effect of strain gauge location, number and size on attenuation and dispersion in response to wave-induced fluid flow. Our results show that increasing the strain gauge length, number, and size can reduce the error between local and bulk responses. In a homogeneous and isotropic rock with a quasi-fractal fluid heterogeneity at 12 per cent gas saturation, the relative error between local and bulk responses stays below 6 per cent when the strain gauge length surpasses 8.6 times the correlation length. As the gas saturation becomes larger, the ratio minimally changes non-monotonically, initially increasing and then decreasing. We also used the Monte Carlo method to demonstrate that local laboratory measurements can approximate the reservoir-scale response with a minimum relative error of 1.5 per cent as the sample number increases. Our findings provide guidance for (i) interpreting local low-frequency measurements in terms of bulk properties of rock and (ii) upscaling lab measurements to reservoir-scale properties.

Incorporating the Nearly Constant Q Models Into 3-D Poro-Viscoelastic Anisotropic Wave Modeling

The Earth is often characterized by viscoelastic rocks, porous sediments and anisotropic structures. Poro-elasticity with Biot’s theory is considered fundamental to describe the interaction between the deformation of the elastic porous solid and the flow of fluid in the porous structure. The quality factor ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> ) in the theory of viscoelasticity relates seismic wave attenuation and dispersion to physical properties of the Earth’s interior, e. g. temperature, stress and composition. However, the constant <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> wave equation in its time-domain differential form remains difficult to solve when describing the attenuation in an explicitly specified <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> parameter. Here, we introduce the first-and second-order nearly constant <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> models capable of describing the attenuation of the solid skeleton, thereby extending the Biot and Biot-squirt (BISQ) models to poro-viscoelastic media. The bulk and shear moduli of the solid frame are represented by the modified relaxation function. By presenting examples with finite-difference time-domain (FDTD) numerical modeling for seismic wavefields in anisotropic, viscoelastic porous media including transversely isotropic media with a vertical symmetry axis (VTI) and orthorhombic meida, we demonstrate that the extended Biot and BISQ models provide good descriptions of the wave propagation in poro-viscoelastic anisotropic media and can thus help better understand the Earth’s interior.

Wave-induced fluid pressure diffusion and anelasticity in partially saturated rocks: The influences of boundary conditions

Open or partially open boundary conditions in fully or partially saturated rocks possibly occur in many realistic geologic scenarios, and it is critical to understand the influences of wave-induced fluid pressure diffusion and anelasticity for many fields of earth science and engineering applications. Under the framework of Biot’s poroelasticity, by proposing a scale factor to represent the opening degree of the boundary, we have investigated the influences of boundary conditions on the seismic wave dispersion and attenuation in partially saturated rocks. It is found that there exist two types of fluid pressure diffusion taking place simultaneously: the mesoscopic fluid pressure diffusion between the two immiscible fluids (e.g., gas and brine) and the fluid flow associated with the outer boundary. The boundary conditions significantly control the seismic wave dispersion and attenuation signatures. The coupled fluid pressure diffusion of mesoscopic flow and outer boundary flow expedite the pore pressure equilibration processes and make the characteristic frequency one order of magnitude higher than the undrained scenario. The drained and partially drained conditions also significantly decrease the velocity of partially saturated rocks, which can be even lower than that of Gassmann’s prediction and dry rock. The reliability of the theoretical model also is validated by comparing it with the numerical simulation for drained and undrained conditions. We have determined that the proposed model is capable of better interpreting the logging data of velocity-saturation relationship for a partially saturated carbonate reservoir and experimental data of wave dispersion for a fully saturated sandstone, both of which are possibly exposed to the open boundary conditions.

Biot-spherical squirt (BISSQ) model for wave attenuation and dispersion

SUMMARYIt has been widely recognized that seismic attenuation and dispersion can be induced by various mechanisms. Wave induced fluid flow (WIFF) is one of the popular mechanisms to interpret seismic wave attenuation and dispersion, especially at microscopic scale. In this study, we focus on the local flow induced by different compliances of adjacent pores and develop a unified model called BISSQ (Biot-spherical squirt) model based upon the Biot and spherical squirt flow theories. The proposed model is an extension of BISQ (Biot-squirt) model. The P-wave velocity and attenuation of BISSQ model are influenced by two mechanisms: the Biot and spherical squirt-flow mechanisms. To evaluate the impact of these two mechanisms on seismic wave propagation, we use different parameters (e.g. squirt flow length, fluid viscosity, permeability, saturation and so on) to simulate wave attenuation and dispersion. We then apply the proposed model to Fox Hills Sandstone, which shows that the model can realistically predict P-wave velocity dispersion. To sum up, our proposed model offers an alternative squirt flow attenuation mechanism, which can describe fluid state of squirt flow reasonably and help us to assess the effect of different parameters on seismic wave attenuation.

Improving seismic resolution based on enhanced multi-channel variational mode decomposition

The attenuation and dispersion of seismic waves change with frequency. So, it is unreasonable to compensate absorption and attenuation using the full-frequency band seismic data directly. In this study, we propose a seismic high-resolution processing workflow based on the enhanced multi-channel variational mode decomposition (EMVMD). Frist, we aim to adopt the multi-channel variational mode decomposition (MVMD) to decompose seismic data into several band-limited intrinsic mode functions (IMFs). Then, we explain the relationship between the IMFs and the different scale structures, and propose a strategy to determine the number of IMFs by introducing the contraction operator mapping (COM) and the scale-space representation (SSR). Note that we name the MVMD with a number selection strategy as the enhanced MVMD (EMVMD). Next, we adopt the adaptive spectrum-broadening method (ASBM) to separately improve the resolution of each decomposed IMF. Afterward, we can easily obtain the enhanced seismic data with a high resolution by summing the processed IMFs. Finally, we apply the proposed workflow (EMVMD-ASBM) to synthetic and field data to testify its validity and effectiveness for enhancing the resolution of the post-stack seismic data.

Dispersion of SH-Wave in a Heterogeneous Orthotropic Layer Sandwiched Between an Inhomogeneous Semi-Infinite Medium and a Heterogeneous Elastic Half-Space

The aim of this paper is to investigates the existence of the dispersion of SH-wave in a heterogeneous orthotropic layer lying over a heterogeneous elastic half-space and underlying an inhomogeneous semi-infinite medium. Hyperbolic variation in upper semi-infinite associated with directional rigidities and density has been considered while linear variation in the intermediate layer associated with initial stress, density, shear moduli and lower half-space associated with rigidity and density has been considered. The dispersion equation of SH-wave has been obtained in a closed form by using variable separation method. The effects of inhomogeneities of the assumed media are illustrated by figures using MATLAB programming. The Earth's composition is heterogeneous that incorporates extremely hard layers. The propagation of SH-wave across crustal layer of the Earth very much depends upon heterogeneity and orthotropic properties. In fact, the observation reveals that the phase velocity of SH-wave is directly proportionate to inhomogeneity parameter, orthotropic parameter and heterogeneity parameter. That means as inhomogeneity parameter and heterogeneity orthotropic parameter increases, the phase velocity of SH-wave increases proportionately. Moreover, the obtained dispersion equation of SH-wave coincides with the classical result of Love wave as initial stress, inhomogeneities, and the upper semi-infinite medium is neglected. This analysis may be helpful to expound the nature of the dispersion of seismic waves in elastic media.

Inversion of dry and saturated P- and S-wave velocities for the pore-aspect-ratio spectrum using a cracked porous medium elastic wave theory

Subsurface rocks contain pores and cracks of various sizes. The cracked porous medium elastic wave theory that describes wave propagation characteristics due to the pore-crack interaction is extended to include cracks of different aspect ratios. The extended theory is applied to model P- and S-wave velocity data of dry and fluid-saturated rock under pressure loading conditions, so as to determine the pore-aspect-ratio spectrum through an inversion procedure. The inversion result is consistent with that from the scanning electron microscope analysis, showing significant improvement versus previous inversion. The inverted pore-aspect-ratio spectrum is input into the wave theory to predict the velocity dispersion of the rock in the full frequency range. The predicted dispersion and its variation trend with pressure agree with the data measured in the (2–200, 106) Hz range at various differential pressures, whereas the modeling using a single-aspect-ratio theory has difficulty matching the data. This research work provides not only a method for analyzing the pore structure characteristics of rocks from the laboratory ultrasonic velocity data, but also a way to predict the seismic wave dispersion from the data.

An Exact Expression for the Effective Bulk Modulus for Acoustic Wave Propagation in Cylindrical Patchy-Saturation Rocks

Abstract Hydrocarbon reservoirs often contain partially gas-saturated rocks that have attracted the attention of exploration geophysicists and geologists for many years. Wave-induced fluid flow (WIFF) is an effective mechanism to quantify seismic wave dispersion and attenuation in partially gas-saturated rocks. In this study, we focus on the local fluid flow induced by variations in fluids in different regions and present a new model that describes seismic wave propagation in partially gas-saturated rocks, namely, the cylindrical patchy-saturation model. Because the seismic wave velocity and attenuation oscillate at high frequencies, it is not ideal for studying dispersion and attenuation caused by WIFF. To avoid the high-frequency oscillation in the cylindrical patchy-saturated model, we use an approximation to the Newman function instead of the full Newman function to calculate the effective bulk modulus. We then calculate the P-wave velocity and attenuation of the proposed model and interpret the lab-measured data. The proposed model is an alternative patchy-saturation model that can explain the problem of high-frequency oscillation and low-frequency attenuation.

Petroleum rock mechanics: An area worthy of focus in geo-energy research

Petroleum rock mechanics: An area worthy of focus in geo-energy research