Velocity Inversion Research Articles

Microseismic Data-Direct Velocity Modeling Method Based on a Modified Attention U-Net Architecture

In microseismic monitoring, the reconstruction of a reliable velocity model is essential for precise seismic source localization and subsurface imaging. However, traditional methods for microseismic velocity inversion face challenges in terms of precision and computational efficiency. In this paper, we use deep learning (DL) algorithms to achieve precise and efficient real-time microseismic velocity modeling, which holds significant importance for ensuring engineering safety and preventing geological disasters in microseismic monitoring. Given that this task was approached as a non-linear regression problem, we adopted and modified the Attention U-Net network for inversion. Depending on the degree of coupling among microseismic events, we trained the network using both single-event and multi-event simulation records as feature datasets. This approach can achieve velocity modeling when dealing with inseparable microseismic records. Numerical tests demonstrate that the Attention U-Net can automatically uncover latent features and patterns between microseismic records and velocity models. It performs effectively in real time and achieves high precision in velocity modeling for Tilted Transverse Isotropy (TTI) velocity structures such as anticlines, synclines, and anomalous velocity models. Furthermore, it can provide reliable initial models for traditional methods.

Learning-Based Seismic Velocity Inversion with Synthetic and Field Data.

Building accurate acoustic subsurface velocity models is essential for successful industrial exploration projects. Traditional inversion methods from field-recorded seismograms struggle in regions with complex geology. While deep learning (DL) presents a promising alternative, its robustness using field data in these complicated regions has not been sufficiently explored. In this study, we present a thorough analysis of DL's capability to harness labeled seismograms, whether field-recorded or synthetically generated, for accurate velocity model recovery in a challenging region of the Gulf of Mexico. Our evaluation centers on the impact of training data selection and data augmentation techniques on the DL model's ability to recover velocity profiles. Models trained on field data produced superior results to data obtained using quantitative metrics like Mean Squared Error (MSE), Structural Similarity Index Measure (SSIM), and R2 (R-squared). They also yielded more geologically plausible predictions and sharper geophysical migration images. Conversely, models trained on synthetic data, while less precise, highlighted the potential utility of synthetic training data, especially when labeled field data are scarce. Our work shows that the efficacy of synthetic data-driven models largely depends on bridging the domain gap between training and test data through the use of advanced wave equation solvers and geologic priors. Our results underscore DL's potential to advance velocity model-building workflows in industrial settings using previously labeled field-recorded seismograms. They also highlight the indispensable role of earth scientists' domain expertise in curating synthetic data when field data are lacking.

The effects of uplift and erosion on the petroleum systems in the southwestern Barents Sea: Insights from seismic data and 2D petroleum systems modelling

In the past three decades, the hydrocarbon prospectivity has been enigmatic in the southwestern Barents Sea as gas discoveries have dominated over oil. However, more recent discoveries indicate oil potential, especially in the Polheim Platform and Hoop Complex areas. Cenozoic uplift and erosion episodes are critical because they control the duration and depth of maximum burial of source rocks and the reduction of porosity of reservoir rocks due to diagenetic processes at larger depth and increased temperatures. Modelling of interpreted horizons from the southwestern Barents Sea provide a best-fit realization of the basin-scale sedimentary filling from the post-rifting in the Jurassic until the Last Glacial Maximum. 2D basin modelling was performed across one regional seismic section crossing the southwestern Barents Sea. For calibration of the 2D model, 1D modelling was performed for a selected number of wells in the region by integrating different estimates of net apparent erosion (velocity inversion of wells, interpreted profiles and structure maps as well as from temperature and vitrinite reflectance data) in order to assess the burial, thermal and maturity history of the source rocks at various well locations as well as along the 2D profile. Simulation results show that the Upper Jurassic source rock is immature to marginal mature in the central and eastern parts of the Norwegian Barents Sea. The western part is characterised by high chargeability of traps associated with rich source kitchens and porous reservoir rocks. Although not proven by commercial discoveries, there are evidences that the Permian Ørret and the Lower-Middle Triassic basal Klappmyss and basal Kobbe shales may be important gas-prone source rocks in the eastern Norwegian Barents Sea. Consequently, the exploration must rely on the Triassic and/or Palaeozoic source rocks in the eastern area.

A New Method for Selecting the Phase and Group Velocity Dispersion Curves of Rayleigh and Love Surface Waves: Real Data Case of Central Anatolia, Turkey (Türkiye)

We propose a new method to select the dispersion curve of Rayleigh and Love surface waves obtained from local and regional earthquakes. This method is efficient for the crustal tomography studies and the Central Anatolia is chosen to test it. The single-station method utilizing both seismograms and accelerograms is used for the group velocities from local earthquakes while the two-station approach utilizing the cross correlograms is employed for the group and phase velocities using both local and regional earthquakes. The proposed method is made of two stages. The first stage based on the multiple filter technique – MFT is designed for an automatic selection of the desired dispersion curve. In case of the single-station approach, the MFT diagrams are computed for both Rayleigh and Love seismograms or accelerograms. An algorithm based on several selection criteria is employed to extract the corresponding group velocity dispersion curve from the MFT diagram. In case of the two-station method, the MFT diagrams are computed for both Rayleigh and Love cross correlograms. The latter algorithm developed for the MFT diagram is again applied to the cross correlogram to select the respective two-station group velocity dispersion curve. To select the corresponding two-station phase velocity dispersion curve, another algorithm is developed where the joint inversion of phase and group velocities is employed. The RMS value quantifying the misfit between the selected and inverted dispersion curves is found minimum when the selected phase velocity curve is compatible with the group velocity curve extracted via the MFT. The selection procedures defined up until this point constitute the first stage. In the second stage, phase and group velocity gathering around base pathways is performed. This way it is possible to compute the averages and standard deviations for the observed pathways traversing the similar geology. The outliers determined by using the averages and standard deviations are eliminated from the data set and this elimination is performed for phase and group velocities, separately.

Quantitative inversion of the elastic parameters outside the borehole based on exact Zoeppritz equations

The acoustic remote detecting method in the borehole has developed rapidly in the past few decades. It uses the reflected waves recorded by array receivers based on monopole or dipole sources in the fluid filled borehole to image geological structures outside the well. The result can provide guidance on the exploration and evaluation of oil and gas reservoirs and mineral resources. However, the present structure imaging results lack of the elastic information, which limit the quantitative evaluation of the resources. The AVO (amplitude variation with offset) inversion theory is introduced into the analysis of borehole waves. The interested interfaces (fractures or minor faults) with a generally larger wave impedance difference makes the widely used approximate equation in the surface exploration no longer applicable. Therefore, the exact Zoeppritz equations are used as the forward equations in the inversion. To reduce the nonlinearity of inversion, the initial model combining structure tensor and mode wave velocity analysis is constructed. The simultaneous inversion of the wave velocity and density of the reflector provides a theoretical basis for quantitatively evaluating the elastic parameters of the reservoir outside the borehole. [Work supported by the National Natural Science Foundation of China (42004117 and 42127807).]

Joint inversion of Rayleigh group and phase velocities for S-wave velocity structure of the 2021 MS6.0 Luxian earthquake source area, China

On September 16, 2021, a MS6.0 earthquake struck Luxian County, one of the shale gas blocks in the Southeastern Sichuan Basin, China. To understand the seismogenic environment and its mechanism, we inverted a fine three-dimensional S-wave velocity model from ambient noise tomography using data from a newly deployed dense seismic array around the epicenter, by extracting and jointly inverting the Rayleigh phase and group velocities in the period of 1.6–7.2 s. The results showed that the velocity model varied significantly beneath different geological units. The Yujiasi syncline is characterized by low velocity at depths of ∼ 3.0–4.0 km, corresponding to the stable sedimentary layer in the Sichuan Basin. The eastern and western branches of the Huayingshan fault belt generally exhibit high velocities in the NE-SW direction, with a few local low-velocity zones. The Luxian MS6.0 earthquake epicenter is located at the boundary between the high- and low-velocity zones, and the earthquake sequences expand eastward from the epicenter at depths of 3.0–5.0 km. Integrated with the velocity variations around the epicenter, distribution of aftershock sequences, and focal mechanism solution, it is speculated that the seismogenic mechanism of the main shock might be interpreted as the reactivation of pre-existing faults by hydraulic fracturing.

Shear wave velocity inversion based on Scholte waves for a fully saturated seabed

As a non-destructive and convenient method, Scholte waves inversion method has been widely used in various engineering applications. However, previous inversion methods treated the seabed sediments as a fully elastic medium, and ignored the porous nature of the sediment. In this paper, a state-of-art inversion model of shear wave velocity, which takes into account the porous property of the seabed, is established based on Bloch's theorems and Biot's theory. Then, the validity of the results is established and the influences of porosity and permeability coefficient of seabed soil are discussed in detail. Finally, an inversion platform using a Python environment is built, and Differential Evolution algorithm and Bayesian approach are employed to obtain the shear velocity profile of the seafloor in the northern North Sea. The calculated results based on the proposed model are highly consistent with the in-situ measurements in the shallow seabed compared to those calculated by the elastic model. This suggests that the influence of porous medium properties on shear wave velocity should be carefully considered for more accurate marine geological surveys.

Seismic Elastic Parameter Inversion via a FCRN and GRU Hybrid Network with Multi-Task Learning

Seismic elastic parameter inversion translates seismic data into subsurface structures and physical properties of formations. Traditional model-based inversion methods have limitations in retrieving complex geological structures. In recent years, deep learning methods have emerged as preferable alternatives. Nevertheless, inverting multiple elastic parameters using neural networks individually is computationally intensive and can lead to overfitting due to a shortage of labeled data in field applications. Multi-task learning can be employed to invert elastic parameters simultaneously. In this work, a hybrid network that leverages the fully convolutional residual network (FCRN) and the gated recurrent unit network (GRU) is designed for the simultaneous inversion of P-wave velocity and density from post-stack seismic data. The FCRN efficiently extracts local information from seismic data, while the GRU captures global dependency over time. To further improve the horizontal continuity and inversion stability, we use a multi-trace to single-trace (M2S) inversion strategy. Consequently, we name our proposed method the M2S multi-task FCRN and GRU hybrid network (M2S-MFCRGRU). Through anti-noise experiments and blind well tests, M2S-MFCRGRU exhibits superior anti-noise performance and generalization ability. Comprehensive experimental inversion results also showcase the excellent lateral continuity, vertical resolution, and stability of the M2S-MFCRGRU inversion results.

Geophysical prediction of organic matter abundance in source rocks based on geochemical analysis: A case study of southwestern Bozhong Sag, Bohai Sea, China

The Bozhong Sag is the largest petroliferous sag in the Bohai Bay Basin, and the source rocks of Paleogene Dongying and Shahejie Formations were buried deeply. Most of the drillings were located at the structural high, and there were few wells that met good quality source rocks, so it is difficult to evaluate the source rocks in the study area precisely by geochemical analysis only. Based on the Rock-Eval pyrolysis, total organic carbon (TOC) testing, the organic matter (OM) abundance of Paleogene source rocks in the southwestern Bozhong Sag were evaluated, including the lower of second member of Dongying Formation (E3d2L), the third member of Dongying Formation (E3d3), the first and second members of Shahejie Formation (E2s1+2), the third member of Shahejie Formation (E2s3). The results indicate that the E2s1+2 and E2s3 have better hydrocarbon generative potentials with the highest OM abundance, the E3d3 are of the second good quality, and the E3d2L have poor to fair hydrocarbon generative potential. Furthermore, the well logs were applied to predict TOC and residual hydrocarbon generation potential (S2) based on the sedimentary facies classification, using ΔlogR, generalized ΔlogR, logging multiple linear regression and BP neural network methods. The various methods were compared, and the BP neural network method have relatively better prediction accuracy. Based on the pre-stack simultaneous inversion (P-wave impedance, P-wave velocity and density inversion results) and the post-stack seismic attributes, the three-dimensional (3D) seismic prediction of TOC and S2 was carried out. The results show that the seismic near well prediction results of TOC and S2 based on seismic multi-attributes analysis correspond well with the results of well logging methods, and the plane prediction results are identical with the sedimentary facies map in the study area. The TOC and S2 values of E2s1+2 and E2s3 are higher than those in E3d3 and E3d2L, basically consistent with the geochemical analysis results. This method makes up the deficiency of geochemical methods, establishing the connection between geophysical information and geochemical data, and it is helpful to the 3D quantitative prediction and the evaluation of high-quality source rocks in the areas where the drillings are limited.

Near-wall model for compressible turbulent boundary layers based on an inverse velocity transformation

In this work, a near-wall model, which couples the inverse of a recently developed compressible velocity transformation (Griffin et al., Proc. Natl Acad. Sci., vol. 118, 2021, p. 34) and an algebraic temperature–velocity relation, is developed for high-speed turbulent boundary layers. As input, the model requires the mean flow state at one wall-normal height in the inner layer of the boundary layer and at the boundary-layer edge. As output, the model can predict mean temperature and velocity profiles across the entire inner layer, as well as the wall shear stress and heat flux. The model is tested in an a priori sense using a wide database of direct numerical simulation high-Mach-number turbulent channel flows, pipe flows and boundary layers (48 cases, with edge Mach numbers in the range 0.77–11, and semi-local friction Reynolds numbers in the range 170–5700). The present model is significantly more accurate than the classical ordinary differential equation (ODE) model for all cases tested. The model is deployed as a wall model for large-eddy simulations in channel flows with bulk Mach numbers in the range 0.7–4 and friction Reynolds numbers in the range 320–1800. When compared to the classical framework, in the a posteriori sense, the present method greatly improves the predicted heat flux, wall stress, and temperature and velocity profiles, especially in cases with strong heat transfer. In addition, the present model solves one ODE instead of two, and has a computational cost and implementation complexity similar to that of the commonly used ODE model.

Seamount and Ridge Subduction at the Java Margin, Indonesia: Effects on Structural Geology and Seismogenesis

AbstractThe Java ‐ Lesser Sunda margin, which features multi‐scale subducting oceanic basement relief, is classified as neutral (Lombok and Sumbawa) to erosional (Central Java to Bali) in comparison to its accretionary counterpart offshore Sumatra. However, a comprehensive analysis of how plate boundary and upper plate structure across the neutral to erosional transition are modulated by the subduction of oceanic basement relief is lacking to date. To shed light on the tectonic parameters that push the margin into the neutral or erosional domain, we combine multi‐channel reflection seismic images derived through a grid‐based P‐wave velocity inversion, and multibeam bathymetric maps. The data document how different scales of subducting topography modify seafloor morphology, upper plate structure, and décollement position. Large‐scale subducting features cause a landward shift of the deformation front, shortening of the accretionary wedge, and seafloor steepening at the relief's trailing edge. Small‐scale subducting ridges primarily impact the frontal prism resulting in over‐steepening at the trench and localized slope failure. Ahead of subducting relief, deformation of the accretionary wedge encompasses enhanced compression and a reduction in seafloor slope but appears independent of the size of the relief. Ridge and seamount subduction induce frontal erosion and basal erosion offshore Lombok and Bali, respectively. Our P‐wave velocity models indicate that the rigidity of the upper plate's base along the eastern Sunda margin is significantly lower than the worldwide trend. We conclude that this favors the genesis of tsunami earthquakes that have occurred on the Java margin.

Inferring the Basal Friction Law From Long Term Changes of Glacier Length, Thickness and Velocity on an Alpine Glacier

AbstractBasal sliding of glaciers and ice sheets remains a source of uncertainty in simulating the long‐term evolution of ice masses. In particular, the response of ice flow to changes in driving stress depends strongly on the value of the exponent m in nonlinear friction laws (e.g., Weertman's law), which is poorly constrained by observations. Here we constrain the friction law at a natural scale on Argentière Glacier (French Alps, hard‐bed), taking advantage of well‐resolved observations of glacier mass balance, geometry and basal sliding over time spans that include large changes in driving stress. By combining three different independent methods based on (a) surface velocity inversion, (b) transient length change modeling, and (c) direct local sliding measurements, we consistently find a value of m = 3.1 ± 0.3. We suggest that Weertman's law is suitable for modeling the long‐term evolution of hard‐bedded glaciers and ice sheets.

Determination of Meteor Vector Velocity Using MU Interferometry Measurements of Head Echoes

A new method for measuring the vector velocity of meteoroids using meteor head echoes is proposed in this study. The lateral velocity is determined by utilizing the phase interference measurement between channels, while the radial velocity is obtained using a conventional Doppler frequency shift measurement. Compared to previous studies, this method does not require multi-site observations and can calculate the vector velocity of meteors in real-time. This paper provides the complete process for the inversion of the meteor vector velocity, detailing the analyzing process using MU radar head echo data. First, the MUSIC algorithm was used to estimate the DOA of the meteor target, which is a parameter required for lateral velocity measurement. Channel calibration is required before this estimation. Next, delay-Doppler matched filter processing was performed on each receiving channel’s data to determine the distance and radial velocity of the meteor target. Subsequently, the lateral velocity component was synthesized using the least squares method from the phase difference rate extracted from the matched filter output results of multiple channel pairs. Then, the vector velocity and trajectory of the meteor could be determined. The method was verified using MU radar head echo data. Different groups of channel pairs were selected for calculating the lateral velocity, and the results were found to be close, demonstrating the self-consistency of the method. Additionally, the calculated vector velocity is consistent with the direction and magnitude of the meteor’s motion trajectory, confirming the feasibility of the proposed approach. The method allows for the observation of more prominent characteristics of meteoroid motion, providing a more detailed observation capability of velocity variations in other directions than previous methods.

A graph approach for fast dense array inter-station phase delay interpretation

SUMMARY We present a phase-delay detection procedure adapted for seismic arrays composed of a large number of stations. We use graph formalism to introduce a direct method to compute station phase delays starting from inter-station phase differences deduced from noise cross-correlation functions. We focus this study on surface wave main arrival as phase-difference evaluation at each station requires high coherence level. Then, we perform numerical experiments with synthetic data computed as a realistic and dense network of 79 stations in a 400 by $400\, \mathrm{km^2}$ square box. For one of the 79 stations, we simulate a phase difference of 15 per cent of the signal period. Further, we evaluate the accuracy and precision of phase-delay estimation at each station with regard to the quality of the cross-correlation functions (i.e. the signal-to-noise ratio). When the inter-station coherence levels are larger than 0.6 (i.e. a high-quality signal), we show good agreement between the phase-delay estimation and its expected value of 15 per cent of the signal period. We introduce a coherence-weighted estimate of phase delay and show that applying this weighting allows us to be less vulnerable to phase-delay underestimation for intermediate-quality signals. Then, the method is applied to experimental data recorded by a high density nodal array with 923 vertical geophones with 19 d of continuous records, centred on the 600 by $600\, \mathrm{m^2}$ damage zone of the Clark branch of the San Jacinto Fault Zone, Southern California (USA). We verify that the San Jacinto network is well synchronized, as most of the estimated phase delays are less than 2 per cent of the central period of the signal, and they are associated with high levels of inter-station coherence. More surprisingly, the spatial features of the estimated phase delays show deterministic geographical patterns that are related to topography and that exhibit similarities with phase velocity maps at $4.5\, \mathrm{Hz}$ from previous 3-D velocity inversions. This suggests that the topographic effect may be accounted for to estimate accurate phase delays. Also, we note that the temporal variability of the estimated phase delays in the case of the San Jacinto data set are related to atmospheric forcing. Our direct method for estimating phase delays is applicable to structure-oriented monitoring studies, and it opens perspectives in the monitoring of seismic velocity variations.

An Optimum 1D Velocity Model for the Garhwal–Kumaun Himalaya Using Monte Carlo Style Inversion

Abstract A Monte Carlo based algorithm is developed to improve the 1D velocity inversion routines and minimize bias due to the choice of a starting model. Using this algorithm, a well-resolved six-layer minimum 1D velocity model, down to ∼24 km depth, is determined for the Garhwal–Kumaun Himalaya. A total of 4765 P- and 4724 S-phase travel times of local earthquakes recorded at 53 broadband seismic stations are used for this purpose. The travel time–distance curves from these carefully analyzed phase data of events are used to subsequently derive a prior 1D velocity model. Forward modeling of the travel time–distance curve yields an average Moho depth of ∼46 km and bulk crustal P- and S-wave velocity values of 7.60 and 4.47 km/s, respectively. To circumvent the subjectivity due to manual intervention in the inversion and automate the process, we propose a Monto Carlo style semirandom generation of initial trial velocity models, guided by the initial values derived from forward modeling. The estimated minimum 1D model reveals P- and S-wave velocities increasing from 5.17 to 6.85 km/s and 3.12 to 3.82 km/s, respectively, from the surface to a depth of 26 km. Subsequently, an optimum model is constructed for the region by incorporating the Moho layer in the minimum 1D model.

Compensating attenuation effects in full-waveform inversion with dissipation-dispersion decoupling

Seismic attenuation poses challenges to velocity model building from acoustic/elastic full-waveform inversion (FWI). In particular, when constructing the FWI gradient for velocity inversion, recent studies have indicated that the high-attenuation structure could distort the gradient by damping the amplitudes and shifting the kinematic phases, resulting in an imbalanced update and thus unreliable velocity model. These Q effects are particularly significant in the reflection acquisition geometry due to the “double-damping” issue. Here, we develop a Q-compensated FWI algorithm for constructing a Q-free FWI gradient. By using a recently developed viscoacoustic wave propagator, this compensation can be done conveniently by keeping the dispersion term and flipping the dissipation term in the wave equation when we simulate the forward and time-reversed adjoint wavefields. The resultant gradient obtained by interacting these two wavefields has correct kinematics and Q-free amplitudes. This Q-compensated FWI can balance the update between Q- and no- Q-areas, which we determine using synthetic examples. In addition, we illustrate how to take advantage of the dissipation-dispersion decoupling to determine the anomalous Q value in the Q model building workflow via Q-compensated reverse time migration.

An approach for prospective forecasting of rock slope failure time

Rock slope failures globally account for most single-event landslide disasters. Climatic changes in mountain areas boost failure activity and the demand for reliable failure time forecasts. State-of-the-art prediction models are often confused with high-frequency slope deformation data. Prospectively, they provide ambiguous forecasts as data filtering, starting point definition and forecast uncertainty remain arbitrary. Here, we develop a prospective failure time forecast model that applies multiple filtering and inverse velocity percentiles to minimize subjective decisions. We test the concept with 14 historic slope failures of 102-108 m3 including 46 displacement datasets from different sensors. After automatic detection of the onset of acceleration, the failure time of all events is forecasted to within −1 ± 17 h for higher-frequency data and −1 ± 4 d for daily data with a final mean uncertainty of 1 ± 1 d and 7 ± 4 d that is estimated in real-time. This prospective approach overcomes previous long-standing problems by introducing a robust and uniform concept across various types of catastrophic slope failures and sensors.

Crustal and Upper Mantle Velocity Structure of SE Tibet From Joint Inversion of Rayleigh Wave Phase Velocity and Teleseismic Body Wave Data

AbstractSince the continental collision between the Indian and Eurasian plates began about 50 Ma ago, southeastern Tibet (SET) has undergone complex tectonic deformation. In this study, we investigate fine scale structural features of the crustal and upper mantle depths (<250 km) beneath SET, which hold important clues to understanding the dynamic processes related to this collision. A 3D shear velocity model is constructed through jointly inverting Rayleigh wave phase velocity and teleseismic body wave data from more than 650 stations. Our 3D model identifies three independent low‐velocity zones (LVZs) in the mid‐lower crust with unprecedented details. More specifically, we observe a prominent LVZ beneath the North Chuan‐Dian Block, which is well separated from another LVZ beneath the Tengchong volcano in the south. This LVZ beneath the volcano represents a focused magma reservoir in the crust whose origin is potentially linked to the mantle upwelling associated with the eastward subduction of the Indian plate. The third LVZ, observed around the Xiaojiang Fault, likely represents a separated and mechanically weak layer in the mid‐lower crust due to the combined effects of regional crustal thickening under the southeastward plateau expansion, mantle upwelling, and shear heating of strike‐slip faults. In the upper mantle, we observe strong velocity reductions both in localized areas beneath the Tibetan Plateau and the broad region south of 26°N. These low velocity anomalies are sitting above high velocity anomalies at deeper depths, suggesting their association with lithospheric thickening and delamination processes.

Research on Seismic Velocity Inversion Method Based on Deep Learning

Methods for obtaining seismic velocity include offset velocity analysis, tomography velocity inversion and full waveform. inversion, but these methods all share common problems: As the amount of seismic data increases, the time required to process the data to obtain the seismic velocity increases exponentially, and the latter two methods are more dependent on the initial seismic velocity. To address the problems of the above methods, this paper improves a seismic velocity inversion method based on deep learning. At the same time, a method that can generate a large number of velocity models randomly with geological features (undulation layer, faults, anomalies, etc. ) similar to those of real subsurface structures is also proposed. The generated velocity model and fluctuation equation for forward modeling are used to perform. the forward modeling, which allows for the efficient establishment of data set. The basic principle of the improved deep learning inversion method in this paper is as follows: the characteristic information of the training data is extracted by convolution neural network, which is trained with large data to obtain a nonlinear mapping relationship between seismic record and seismic velocity. In the inversion stage, the seismic velocity can be inversed quickly by inputting the seismic records into the trained network. In order to make the network give full play to the advantages of processing seismic data, the authors obtained the dominant network structure by means of numerical simulation, and achieved satisfactory inversion results. Finally, through comparative experiments, this paper verifies the advantages and applicability of the method.

Seismic velocity inversion transformer

Velocity model inversion is one of the most challenging tasks in seismic exploration, and an accurate velocity model is essential for high-resolution seismic imaging. Recently, velocity inversion methods based on deep learning (DL), particularly convolutional neural networks (CNNs), have attracted considerable attention from the seismic exploration community. These researchers aim to directly estimate the velocity model from raw seismograms using a well-trained model. Although CNN-based velocity inversion methods have demonstrated remarkable performance in terms of intelligence and automation, their inversion performance is often constrained by a limited long-range dependence. Specifically, when conducting a convolutional operation on raw seismic data using small kernels (i.e., 1 × 1, 3 × 3, 5 × 5, and 7 × 7), CNN-based methods extract only the local features and neglect the weak spatial correlation between different local features that reflect the information of the same interface. This correlation could assist CNN in providing an overview of the seismic data and promote inversion performance when using DL. Furthermore, the time-varying properties of seismic data pose a challenge to the weight sharing of CNNs. Here, we have developed a new DL framework based on a transformer, called the seismic velocity inversion transformer (SVIT), to address the problem of velocity inversion. SVIT uses a self-attention mechanism to capture the long-range dependence of seismic data, rather than stacking multiple convolutional layers as in CNNs. Thus, SVIT can provide more informative remote features for building velocity models. The validity and reliability of the proposed method are demonstrated through numerical experiments using synthetic models. Compared with the conventional full-waveform inversion method and an existing CNN-based velocity inversion method, our SVIT indicates greater consistency with the target in terms of the velocity value, subsurface structures, and geologic interfaces and is expected to provide a new DL-based solution to resolve inversion problems.