Geophysical Prospecting - Volume 73, Issue 6, 2025

We have developed two inversion algorithms to calculate the density ratio across a reflecting interface using Zoeppritz's equation for P‐to‐P wave reflections. At any point on the interface, we can calculate the most likely density ratio value with a corresponding standard deviation from a distribution of estimated (density ratio) values. This makes it possible to plot uncertainty maps at any interface of interest. Both inversion algorithms are applied within the near–far angle range to ensure the reliability of density ratio estimates. Although the methods can theoretically handle a wider range of angles, ultra‐far angles are avoided due to amplitude distortions that become more pronounced at large incidence angles. A natural consequence of this restriction is that the herein‐presented empiricism‐free algorithms can be used for all classes of amplitude variation with offset (AVO) responses. At the heart of the first inversion scheme is a solver of a 12th‐degree polynomial equation. The roots of the equation are calculated at an arbitrary number of incident angles. The solution space gives rise to a distribution from which the most frequent value (representing the maximum of the distribution) is taken as the most likely value. The second scheme involves solving a 5th‐degree polynomial equation for the square of the VP/VS ratio of layer 2 (in a two‐layered earth model) also at an arbitrary number of incident angles. The most likely density ratio estimate and the associated uncertainty are obtained as a byproduct of the calculation. We test both methods on a seismic dataset from the Barents Sea. The two methods yield very similar density ratio maps on the studied interface. Moreover, except for one well, they give a good match with estimated values from well‐log data. This study is the second part of a two‐part research. While Part I focuses on the theoretical foundations and synthetic validation of the inversion methods, this paper applies them to real seismic data to evaluate their practical performance.

Considering the demand for lithology identification in quantitative seismic interpretation, I introduced ternary diagrams based on rock physics modelling to derive lithology from seismic data. For this purpose, physical and acoustic parameters of minerals were utilized to reconstruct the most common rocks in hydrocarbon reservoirs, including source, reservoir and caprock. Subsequently, the generated rocks were input into a ternary diagram based on easily obtained parameters from seismic data, including acoustic impedance, VP/VS ratio and lambda–mu–rho parameters. Next, two ternary diagrams were implemented according to the elastic parameters for reservoir (and source) and caprock identification. The theoretical results indicated that the proposed ternary diagrams can be applied for interpreting seismic inversion data to discriminate limestone from sandstone and shale using lambda–rho. Additionally, mu–rho can serve as a criterion to differentiate dolomite from limestone and anhydrite (or sandstone from shale and limestone). The obtained ternary diagram was validated using ultrasonic and well‐log data from blind wells and subsequently used to interpret 3D seismic data. For this purpose, acoustic impedance was calculated using a simultaneous inversion method from pre‐stack data and converted to elastic parameters, which were then input into the ternary diagrams. The validation procedures yielded promising results and demonstrated that ternary diagrams can effectively identify different lithologies compared to conventional binary cross‐plots. The advantage of the proposed diagrams lies in their comprehensiveness and generality, making them compatible with seismic limitations and applicable to a wide range of sedimentary rocks. The findings of this research can enhance the interpretation of seismic inversion results when mineral fraction or petrophysical interpretation is unavailable. Finally, the advantages and limitations of the methodology were discussed, and the impact of reservoir heterogeneities and fluid types on ternary diagrams was analysed. It was concluded that the proposed diagrams are not restricted to specific depositional settings and can be developed for the seismic interpretation of unconventional reservoirs and igneous rocks through the implementation of the mentioned methodology.

Seismic tomography has long been an effective tool for constructing reliable subsurface structures. However, simultaneous inversion of P‐ and S‐wave velocities presents a significant challenge for conventional seismic tomography methods, which depend on numerical algorithms to calculate traveltimes. A physics‐informed neural network—based seismic tomography method (PINNtomo) has been proposed to solve the eikonal equation and construct the velocity model. We propose extending PINNtomo to perform multiparameter inversion of P‐ and S‐wave velocities jointly, which we refer to as PINNPStomo. In PINNPStomo, we employ two neural networks: one for the P‐ and S‐wave traveltimes and another for the P‐ and S‐wave velocities. By optimizing the misfits of P‐ and S‐wave first‐arrival traveltimes calculated from the eikonal equations, we can obtain the predicted P‐ and S‐wave velocities that determine these traveltimes. Recognizing that the original PINNtomo utilizes a multiplicative factored eikonal equation, which depends on background traveltimes corresponding to a homogeneous velocity at the source location, we propose to use an effective‐slowness‐based factored eikonal equation for PINNPStomo to eliminate this dependency. The proposed PINNPStomo, incorporating the effective‐slowness‐based factored eikonal equation, demonstrates superior convergence speed and multiparameter inversion accuracy. We validate these improvements using two‐dimensional Marmousi, two‐dimensional Overthrust and three‐dimensional foothill elastic velocity models across three different seismic data acquisition geometries.

Singhbhum Shear Zone (SSZ) also referred as Copper Belt Thrust (CBT), located at the southern margin of North Singhbhum Fold Belt (NSFB) is well‐known for highly mineralized copper, uranium and other sulphide minerals deposits. In order to the identify favourable structures that could host the sulphide–uranium mineralization in Gurulpada area of SSZ, an integrated geophysical study was conducted using magnetic, self‐potential (SP), electrical resistivity tomography (ERT) and induced polarization (IP) surveys. The present study identifies pronounced magnetic anomalies in the central part due to presence of magnetite mineral along the shear planes of quartz‐chlorite‐schist (±sericite) and basic dykes, exhibiting an ENE–WSW orientation, which follows the geological strike and the trend of the shear zone within the area. Low magnetic intensity in the southern part of area suggests demagnetization caused by hydrothermal alteration, indicate mineralized zones. SP anomaly map has identified six zones exhibiting negative anomalies. Tilt derivative (TDR) and Euler deconvolution (ED) technique were applied on magnetic and SP data to depict geological structures that control mineralization and its depth. Magnetic and SP anomalies along the profile are plotted with a 2D inverted resistivity and chargeability section for comparative analysis. The inverted resistivity and chargeability model, illustrated as 2D cross sectional view and a 3D fence diagram, has delineated several anomalous zones at varying depths. The high magnetic anomaly, corroborated with negative SP values, is associated with low resistivity and high chargeability zones, indicating the disseminated sulphide ore bodies with quartz and magnetite mineral along the shear planes. Conversely, positive SP, high chargeability and high resistivity zones signify disseminated sulphide deposits that infilled quartz veins and intense silicification in the fractured zones. The 3D pseudo iso‐surface chargeability models indicate high chargeability values (M ≥ 15 mV/V) oriented in an ENE–WSW direction. The integration of geophysical (magnetic, SP, ERT and IP) anomalies and geological (bedrock and trench sampling) data, in conjunction with borehole analysis, confirms the presence of sulphide–uranium mineralization in the study area. The present study reaffirms the presence of ENE–WSW trending ductile‐brittle intense shear and hydrothermal alteration zones, which are key indicators of sulphide–uranium mineralization in the study area. The findings revealed that the mineralization accommodated within the quartz‐chlorite‐schist (±sericite) of the Chaibasa Formation of the Singhbhum Group, appearing as dissemination and fracture filling in association with quartz and magnetite in certain locations. Thus, these integrated geophysical studies are essential for understanding and delineating the complex structural and mineralogical framework of the SSZ. They provide a foundation for further exploration and exploitation of economically significant mineral deposits in this highly mineralized region.

Anisotropic magnetic susceptibility, as an intrinsic property that records the strain history a rock formation experienced, has been widely used in structural geological studies based on direct specimen measurements. By comparing measurements of anisotropic parameters on drill samples from different locations, rock formations can be differentiated into different or the same groups. However, the applications of anisotropic magnetic susceptibility in geophysical data interpretation are rare due to its complexity in inverse problems, despite its long‐recognized influence on induced magnetization. In this work, we present a one‐dimensional inversion algorithm that simultaneously recovers two principal susceptibility components. To connect geophysical data with geology differentiation through different anisotropies, the inversion is constrained by fuzzy C‐means clustering to enforce coherency in the parameter space for model values within the same rock formation. Under the assumption of a sedimentary scenario, the synthetic tests show that, when the data are influenced by anisotropy, the inversion for an isotropic model could fail to reproduce the data, while inverting for an anisotropic model with clustering can lead to better data recovery and produce valuable information about different formations. We also test our method with field data published by the United States Geological Survey over the Wyoming Salient. The inversion results and their comparison against geochronological records reveal connections between airborne magnetic data and geology, including structures and rock formations originating from different geologic ages.

According to Huygens' principle, all points on a wave front act as secondary sources emitting spherical waves and the envelope of these spherical waves forms a new wave front. In the mathematical formulation of Huygens' principle, the waves emitted by the secondary sources are represented by Green's functions. In many present‐day applications of Huygens' principle, these Green's functions are replaced by their time‐reversed versions, thus forming a basis for backpropagation, imaging, inversion, seismic interferometry, etc. However, when the input wave field is available only on a single open boundary, this approach has its limitations. In particular, it does not properly account for multiply reflected waves. This is remedied by a modified form of Huygens' principle, in which the Green's functions are replaced by focusing functions. The modified Huygens' principle forms a basis for imaging, inverse scattering, monitoring of induced sources, etc., thereby properly taking multiply reflected waves into account.

Microseismic event detection and location are two primary components in microseismic monitoring, which offer us invaluable insights into the subsurface during reservoir stimulation and evolution. Conventional approaches for event detection and location often suffer from manual intervention and/or heavy computation, while current machine learning assisted approaches typically address detection and location separately; such limitations hinder the potential for real‐time microseismic monitoring. We propose an approach to unify event detection and source location into a single framework by adapting a convolutional neural network backbone and an encoder–decoder transformer with a set‐based Hungarian loss, which is applied directly to recorded waveforms. The proposed network is trained on synthetic data simulating multiple microseismic events corresponding to random source locations in the area of suspected microseismic activities. A synthetic test on a two‐dimensional profile of the SEG Advanced Modeling (SEAM) Time Lapse model illustrates the capability of the proposed method in detecting the events properly and locating them in the subsurface accurately; while, a field test using the Arkoma Basin data further proves its practicability, efficiency, and its potential in paving the way for real‐time monitoring of microseismic events.

Seismic characterization of carbonate reservoirs is a challenging task due to the complex structure of carbonate rocks, where the seismic response is affected by multiple factors such as pore volume and shape as well as changes in mineralogy due to dolomitization and silicification. Hence, the prediction of petrophysical properties from seismic data is often uncertain. For this reason, we propose a statistical inversion method for the estimation of rock properties, where we combine Bayesian inverse theory with geophysical modelling. The geophysical model aims to compute the seismic response based on the rock and fluid properties and pore structure of the carbonate rocks, and it includes rock physics and the amplitude variation with offset models for the seismic response. The Bayesian formulation allows for the solution of the associated inverse problem by computing the posterior distribution of rock and fluid properties and pore structure of the rocks conditioned by the measured geophysical data. The novelty of the proposed method is that the rock physics model can be any petroelastic relation, without requiring any linearization. For the application to the carbonate reservoir, we adopt the self‐consistent inclusion model with ellipsoidal pore shapes and Gassmann's equation for the fluid effect; however, the inversion can be applied to any rock physics model. The statistical model assumes that the prior probability distribution of the model variables is a Gaussian mixture model such that distinct petrophysical characteristics can be associated with geological or seismic facies. The result of the proposed inversion is the most likely reservoir model of rock and fluid and pore geometry parameters, for example, porosity, pore aspect ratio, and water saturation and the uncertainty of the model predictions. The method is demonstrated and validated on synthetic and real examples using well logs and two‐dimensional seismic sections from a pre‐salt dataset in Brazil.

Stochastic inversion approaches provide a valuable framework for geophysical applications due to their ability to explore multiple plausible models rather than offering a single deterministic solution. In this paper, we introduce a probabilistic joint inversion framework combining the very fast simulated annealing optimization technique with generalized fuzzy c‐means clustering for coupling of model parameters. Since very fast simulated annealing requires extensive computational resources to converge when dealing with a large number of inversion parameters, we employ sparse parameterization, where models are sampled at sparse nodes and interpolated back to the modelling grid for forward computations. By executing multiple independent inversion chains with varying initial models, our method effectively samples the model space, thereby providing insights into model variability. We demonstrate our joint inversion methodology through numerical experiments using synthetic seismic traveltime and controlled‐source electromagnetic datasets derived from the SEAM Phase I model. The results illustrate that the presented approach offers a practical compromise between computational efficiency and the ability to approximate model uncertainties, making it suitable as an alternative for realistic larger‐scale joint inversion purposes.

The uncertainty of model parameters obtained by full‐waveform inversion can be determined from the Hessian of the least‐squares error functional. A description of uncertainty characterisation is presented that takes the null space of the Hessian into account and does not rely on the Bayesian formulation. Because the Hessian is generally too costly to compute and too large to be stored, a segmented representation of perturbations of the reconstructed subsurface model in the form of geological units is proposed. This enables the computation of the Hessian and the related covariance matrix on a larger length scale. Synthetic two‐dimensional isotropic elastic examples illustrate how conditional and marginal uncertainties can be estimated for the properties per geological unit by themselves and in relation to other units.

Numerical simulations of fluid–solid coupled media are vital for marine seismic exploration. Anisotropy in real strata and the limitations of standard elastic wave equations in simulating pressure components in marine seismic data (e.g., towed streamer 1C and ocean‐bottom 4C data) necessitate alternative approaches. We propose an acoustic–elastic coupled equation for vertical transverse isotropic (VTI) media overlying fluid layers, eliminating the need for explicit boundary handling. Numerical results indicate that the proposed method has slightly higher computational and storage costs compared to standard elastic wave equations. However, the synthetic seismograms preserve converted wave information, which is crucial for S‐wave velocity inversion, and effectively simulate Scholte waves at fluid–solid boundaries in shallow marine environments. The equation is highly adaptable, accommodating various marine seismic acquisition methods and providing valuable insights into processing complex marine seismic data.

Efficient noise removal in seismic data is crucial for accurately analysing subsurface structures because noise generated during field acquisition can considerably degrade data quality. Traditional single‐domain denoising methods often struggle to preserve weak signals in prestack seismic data, potentially leading to the loss of critical information. To address this issue, we propose a novel dual‐domain (DD) denoising approach called non‐local means via patch ordering in DD (DD–PONLM). This method leverages the strengths of both time–space and transform domains to minimize the leakage of weak events. By employing non‐local self‐similarity and iterative processing in the time–space domain and discrete cosine transform domain, the proposed method effectively reduces noise while preserving weak signals. We validate the effectiveness of our method through extensive testing on both asynthetic and a field example. The results are compared with several traditional single‐domain methods, demonstrating that DD–PONLM considerably improves the preservation of weak signals and reduces artefacts, such as the Gibbs phenomenon, associated with transform domain processing. This DD strategy not only enhances the signal‐to‐noise ratio but also preserves structural fidelity, making it a robust solution for seismic data denoising.

Fault interpretation is crucial for subsurface resource extraction. Recent research has demonstrated that deep learning techniques can successfully detect faults. However, the network's prediction results still suffer from discontinuity and low accuracy problems due to insufficient exploitation of the spatial and global distribution characteristics of faults. This paper presents a novel approach for seismic fault detection using a dual‐attention mechanism and multi‐scale feature fusion. The proposed network uses ResNeSt residual blocks as encoders to extract multi‐scale features of faults. During multi‐scale feature fusion, a global context and a spatial dual‐attention module are introduced to suppress interference from non‐fault features. This improves the ability to detect faults. Five adjacent seismic slices were used as inputs to obtain the spatial distribution characteristics of faults. Data augmentation methods were used to enrich the fault morphology of synthetic seismic data. The Tversky loss function was used in the proposed model to alleviate the effect of data imbalance on fault identification tasks. Transfer learning methods were also used to evaluate the model's performance on field data from the F3 block in the Dutch North Sea and field data from the New Zealand Great South Basin. The model's performance was compared with some state‐of‐the‐art methods, including DeepLabV3+, Pyramid Scene Parsing Network, Feature Pyramid Network and U‐Net. The results show that the proposed fault detection method has excellent accuracy and fault continuity.

The brittleness index is a crucial parameter for evaluating the brittleness of subsurface reservoirs. Accurate brittleness determination optimizes fracture design and guides oil and gas extraction, especially in shale formations. Traditionally, the brittleness index assumes isotropy, which fails to capture the anisotropic nature of shale reservoirs and often leads to prediction errors. To mitigate this challenge, this study introduces a stiffness coefficient matrix specifically designed for anisotropic media and proposes a brittleness index equation tailored for transverse isotropic (VTI) media. Experimental results show that the proposed anisotropic brittleness index provides a more accurate assessment of shale reservoir brittleness than the conventional isotropic brittleness index. Ultimately, the anisotropic brittleness index is applied to field logging data, thereby validating the effectiveness of the method in distinguishing between reservoirs of high and low brittleness.

Fractures are omnipresent features in the shallower regions of the Earth's crust. In the context of rock physics, fracture characterization techniques rely largely on the determination of normal fracture compliances. Despite being thoroughly investigated through wave propagation experiments, this parameter is seldom estimated locally. In this work, we measure and compare local displacement‐jump‐ and transmission‐related fracture compliances using forced oscillations and ultrasonic propagation techniques, respectively. The experiments are carried out on an aluminium standard and on four different sandstone samples that contain a single planar fracture, considering a range of axial stresses. The results show that, for most rocks, both transmission‐related and locally measured dry normal compliances are of the same order and also present similar tendencies with axial loads. However, transmission methods predict larger dry normal fracture compliances than those retrieved from local strain estimations. The results of this study may help to assess the validity of linear slip theory, which is widely used in fracture characterization efforts in the specific literature.

The transient electromagnetic method (TEM) is a prominent geophysical technique, and the TEM inversion for resistivity models is a crucial aspect of physical exploration. However, TEM inversion faces challenges such as nonlinearity, multiple solutions and ill‐conditioning, which can lead to inaccurate results. In response to these challenges, metaheuristic algorithms have been extensively studied for their innovative approaches to solving inverse problems. Despite this, many existing metaheuristic inversion algorithms exhibit limitations, including premature convergence, slow convergence speed and inadequate computational accuracy. To address these issues, an improved bat algorithm (IBA) that incorporates logistic chaotic mapping and a spiral flight strategy (Logistic Chaotic Mapping and Spiral Flight Strategy‐Based Bat Algorithm, LSBA) has been proposed. The logistic chaotic mapping strategy is utilized to initialize the population of the bat algorithm to enhance the initial convergence rate. Moreover, the spiral flight strategy facilitates the bats’ escape from local optima, thereby improving the algorithm's local exploration capabilities and solution accuracy. Numerical simulations, synthetic models and field experiments have demonstrated that the LSBA significantly enhances solution precision (the degree of closeness between the algorithm's inverted parameters and the true values), convergence speed and anti‐noise performance. The LSBA effectively retrieves the stratigraphic parameters of the true model and accurately represents the geological information of actual mining areas, thereby validating the efficacy and feasibility of the proposed approach in TEM inversion.

Deep‐strata high‐pressure reservoirs are a key research area in subsurface resource exploration. The complex mix of in situ pressure, anisotropy and fluid saturation in rocks leads to unclear seismic responses and uncertainties in wave propagation. Using acoustoelasticity theory and assuming weak anisotropy, we derived equations for the elastic parameters of stressed orthotropic media. These equations use anisotropic parameters to describe the unstressed elastic properties of orthotropic media. Then, using the Gassmann equation and low‐frequency poro‐elasticity, we found elastic parameters for single fluid‐saturated orthotropic media. Non‐welded interfaces serve as a reasonable approximation for tiny fractures and are ubiquitous in subsurface formations, and the viscous fluid present within these interfaces contributes to the observable attenuation of seismic waves. Using elastic parameters of stressed, fluid‐saturated orthotropic media, we formulated reflection and transmission coefficient equations for these interfaces based on linear‐slip theory. Using these equations, we analysed how stress, fluid saturation and interface changes affect seismic response and wave propagation. We then analysed how frequency, porosity, viscosity, fracture weakness and other physical properties affect seismic behaviour within and at the medium's interface. By constructing exact equations, we have achieved a more realistic simulation of subsurface seismic response. This enhancement in simulation accuracy facilitates a deeper understanding of the seismic response patterns observed in deep and complex subsurface reservoirs. Furthermore, it provides a solid theoretical foundation for fluid identification and reservoir prediction in actual subsurface reservoir scenarios.

For this investigation, we exploit local‐distance P‐ and S‐wave observations generated by mining‐related and small‐magnitude events in the Klerksdorp, Orkney, Stilfontein and Harteesfontein (KOSH) mining region of South Africa to explore the robustness and variability of low‐yield P‐to‐S‐wave amplitude ratios. P/S amplitude ratios are traditionally used in discrimination studies between earthquakes and explosions recorded at regional and teleseismic distances ( 200 km) and for relatively large magnitude events. Few studies have explored the variability of P/S amplitude ratios using data recorded at local distances, distances 200 km, where more scrutiny of wave propagation, near‐surface geology, and source and strain release patterns is required. We took advantage of the dense surface accelerometer cluster network, KOSH, for our variability analysis. Final results show that most of the locally recorded low‐magnitude events in the Klerksdorp region have comparable shear wave energy to low‐magnitude earthquakes. Consequently, our time‐domain rms‐based P and S amplitude measurements result in stable event average P/S ratios likely to separate from explosive sources. We demonstrate the expected variability of the ratios with smaller network simulations (three‐, five‐, seven‐station) to show that ratios remain relatively stable between 1 and 30 Hz.