Full-waveform inversion (FWI) of seismic data is a powerful method for estimating high-resolution models of the subsurface. An accurate initial model and low-frequency data are necessary to avoid cycle skipping and perform a successful FWI. In the absence of this information, FWI is likely to fail due to convergence in local misfit minima. With the recent advancements in artificial intelligence, studies have shown that absent low-frequency data can be extrapolated using deep learning (DL). These studies have been mostly focused on surface seismic data whose frequency content is different from cross-well data. In this study, we assess the use of DL for low-frequency extrapolation for a cross-well survey that was done at the Aquistore storage site in Saskatchewan. This assessment includes both numerical and field data examples. We extrapolate the low frequencies to increase the bandwidth of the acquired data at the Aquistore site and perform FWI. We evaluate the efficiency of this method by comparing the results with obtained velocity models from the conventional multiscale FWI. Our results for the Aquistore data show that the proposed strategy leads to an accuracy improvement of 39% and 20% in the model and data domains, respectively.
Conventional reflection waveform inversion solves a two-parameter seismic inverse problem alternately for subsurface reflectivity and acoustic background velocity as the model parameters. It seeks to reconstruct a low-wavenumber velocity model of the subsurface from pure reflection data cyclically, through alternating migration and tomography loops, such that the remodelled data fits the observed data. Low-resolution seismic images with unpreserved amplitudes, full-wave inconsistency in the short-offset data and cycle skipping in the long-offset are perceived as the main reasons for suboptimal tomographic updates and slow convergence in conventional reflection waveform inversion. In the context of one-way reflection waveform inversion, this paper addresses the listed limitations through four main components. First, it augments one-way reflection waveform inversion with a computationally affordable preconditioned least-squares wave equation migration algorithm to ensure high-resolution reflectors with preserved amplitudes. Second, the paper verifies how well the full-wave consistency condition in the short-offset data is satisfied in one-way reflection waveform inversion and suggests muting inconsistent short-offset residual waveforms in the tomography loop to attenuate their adverse imprint. Third, the paper suggests extending the migration offset beyond short offsets to improve both the illumination and the signal-to-noise ratio of the reflectors. Fourth, the paper presents a data-selection algorithm to exclude the damaging effect of the cycle-skipped long-offset data in the tomography loop. The effectiveness of the proposed one-way reflection waveform inversion algorithm is finally validated through three numerical examples, demonstrating its capability to recover high-fidelity tomograms.
Accurate and efficient modelling of subsurface electrical properties is critical for a wide range of applications, including mineral exploration, environmental studies and hydrogeological investigations. Traditional numerical approaches often use low-order discretization and impose artificial boundary conditions to approximate the unbounded spatial domain. These approximations can lead to inaccuracies and computational inefficiency, particularly in geologically complex environments. In this study, we present a spectral-infinite-element method (SIEM) for forward modelling of electrical resistivity and induced polarization. The approach couples high-order spectral elements within the finite domain with a single outer layer of mapped infinite elements, enabling precise representation of far-field boundary conditions. To achieve optimal numerical performance, we employ two distinct quadrature schemes: Gauss–Legendre–Lobatto quadrature for the spectral elements and Gauss–Radau quadrature for the infinite elements. We first verify the accuracy of our method by comparing the computed electric potential from a buried charged block with direct numerical integration. We conducted a convergence study by refining the mesh and increasing the order of the interpolation polynomials. To further evaluate the robustness of SIEM, we benchmark its results for a layered earth model against an analytical solution and an open-source Python-based geophysical modelling library, SimPEG. The comparisons demonstrate the accuracy, convergence and efficiency of SIEM. Finally, we apply SIEM to a complex heterogeneous conductivity model incorporating topography, generating apparent resistivity and chargeability pseudo-sections to illustrate its practical applicability under realistic survey conditions.
Accurate depth estimation is crucial for the quantitative interpretation of magnetic anomalies, which plays a significant role in geological mapping, mineral exploration and subsurface investigations. Traditional depth estimation techniques, such as the contact-depth (CD) and tilt-depth (TD) methods, often suffer from the generation of spurious solutions, especially when applied to complex geological environments. To address this, we propose an enhanced depth estimation technique, namely, the located contact-depth (LCD) method that integrates the CD technique with the enhanced horizontal gradient amplitude (EHGA). By utilizing points near the peaks of EHGA, a mask is generated to constrain the solutions from the CD method, effectively eliminating false solutions. Furthermore, a stable finite-difference technique for calculating vertical derivatives is used to improve the robustness and stability of the outputs. The proposed technique is tested on synthetic data, both with and without noise, as well as on real aeromagnetic data from the Galinge Fe-polymetallic deposit (China). The results demonstrate that our method provides depth estimates with improved reliability and accuracy compared to traditional methods, reducing the number of spurious solutions and enhancing precision around source boundaries. The result from the real example is in good agreement with known structures, highlighting the potential for deep mineral exploration in the Galinge Fe-polymetallic deposit.
The brittleness of a caprock layer is an important property to measure, as it influences sealing integrity for subsurface fluid injection projects. However, brittleness is a complex function of various factors, such as mineral composition, diagenesis and effective stress, and consequently can vary spatially. Because well log-based methods for brittleness estimation are often spatially limited, we develop a simple workflow to estimate the brittleness of a shale formation directly from seismic data. The shale in question is the Draupne Formation of the Upper Jurassic age, which acts as a primary seal of Viking Group sandstones in the Horda Platform area of the northern North Sea for hydrocarbon extraction (e.g., the Troll field) and geological CO2 storage (e.g., Smeaheia). First, well log data from 26 wells in the Horda Platform area is aggregated, focusing on the compressional sonic, bulk density and resistivity values of the Draupne Formation. This data are used to establish a linear model relating the acoustic impedance and elastic properties-estimated brittleness index (BI) of the Draupne Formation; these two quantities display a correlation of 0.86. By combining this acoustic impedance information with a wavelet extracted from field seismic data and using average acoustic properties for the relatively homogeneous underlying sandstone reservoir, synthetic seismograms corresponding to different BI values of the Draupne Formation are generated. The amplitudes extracted from the synthetic seismograms are then used to establish a quadratic model relating seismic amplitudes at the base Draupne reflection with the BI. Applying this quadratic model on a 2D seismic line from the Stord Basin (south of the Horda Platform) results in BI values that are close to elastic-properties-based values at wells which intersect the seismic line and an expected trend of increasing brittleness with respect to depth. This integrated method can be used as part of a workflow to characterize top seal effectiveness, which may be useful in fluid storage prospect evaluation.
Image-domain least-squares migration (IDLSM), which typically employs a diagonally dominant Hessian with narrow bandwidth for the inverse problem, provides an efficient deconvolution strategy for subsurface reflectivity imaging. Conventional methods often rely on the adjoint of the Born/Kirchhoff modelling operator to compute the Hessian matrix. However, the adjoint-derived Hessian is highly ill-conditioned, leading to slow convergence during linear inversion and resulting in images with undesired resolution and amplitude fidelity. To overcome these limitations, this study introduces a novel IDLSM approach that integrates the state-of-the-art migration operator. We derive and compute the preconditioned Hessian matrix through a Kirchhoff migration engine with source-side and receiver-side illumination. The preconditioned Hessian matrix exhibits identical values along its main diagonal. This illumination compensation will explicitly reduce the condition number of the Hessian matrix and significantly improve the quality of migrated images in terms of amplitude fidelity. In addition, we remove redundant source wavelets from the migrated image and the Hessian matrix. As a result, these improvements will greatly accelerate the convergence of linear inversion solvers while enhancing the resolution and amplitude fidelity of the resulting images. Experiments on synthetic and field datasets demonstrate that the proposed IDLSM method retrieves high-fidelity reflectivity images with superior resolution and amplitude fidelity compared to conventional IDLSM techniques.
The three-dimensional (3D) distributed acoustic sensing (DAS) vertical seismic profile (VSP) technique is an effective tool to characterize subsurface reservoirs, enabling the use of large and densely sampled borehole receiver arrays with many surface vibrator source points for onshore time-lapse monitoring. However, the processing of the DAS VSP signals for imaging purposes is based on a reliable wavefield separation, which may depend on the recognition and quality of the direct arrivals. To overcome this limitation for common-source gathers with poor signal-to- noise ratio or with interferences, we apply the dual-signal processing method, which allows us to estimate and separate the DAS wavefields by signals' combination without arrival picking. We present a case study of a 3D VSP DAS dataset recorded at a geothermal reservoir in Turkey, showing that the method, similar to a geophone and hydrophone combination, is robust and effective and can be advantageously integrated with the conventional processing. Supported by signal benchmarking, modelling and signal-to-noise ratio analysis, we treat common-source and common-receiver data. Our analysis shows the advantages and limitations of the proposed approach, valuable in the time-lapse perspective.
Seismic reflection traveltime tomography (RTT) is an effective technique for inverting subsurface low-frequency velocity models for prestack depth migration and full-waveform inversion of seismic data. However, the velocity model established using RTT demonstrates limited resolution for extremely shallow and deeply complex strata. Small-offset first-arrival wave effectively characterize velocity variations in shallow strata, whereas large-offset first-arrival wave can reflect the velocity distribution in deeper strata. Therefore, we propose a three-dimensional joint tomographic inversion of first-arrival and reflection waves based on the adjoint state method in this article. The method integrates first-arrival traveltime data, reflection traveltime data and slope data for inversion, enhancing the accuracy of the inversion model from shallow to deep. The adjoint state method is employed to calculate the gradient of the misfit function with respect to velocity and the spatial coordinates of reflection points, thereby reducing the computational memory requirements and improving the efficiency of velocity modelling. The results of synthetic data tests based on a theoretical model verify the accuracy and effectiveness of the proposed joint inversion method. The proposed method is applied to ocean bottom node and ocean bottom cable wide-line seismic data collected in an extremely shallow sea in eastern China, yielding a more accurate velocity model.
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