Nonlinear Inversion Research Articles

Segmental Regularized Constrained Inversion of Transient Electromagnetism Based on the Improved Sparrow Search Algorithm

The initial inversion model is typically established in a transient electromagnetic nonlinear inversion, assuming the accurate capture of the number of layers in the geoelectric model; however, this assumption leads to significantly poorer inversion results for complex models when obtaining the exact number of layers from available a priori information, which is challenging. This study proposes a segmented regularized inversion method to enhance inversion accuracy and stability under varying conditions. The process involves two key steps: Firstly, a segmented initial model is established based on preliminary information. The layering criteria and layer thickness threshold for each segment are set during inversion to reduce dependence on the accuracy of the preliminary information. Secondly, a segmented regularization constraint is added to the objective function to improve the efficiency and stability of the inversion, as numerous parameters can exacerbate the problem of inversion ambiguity. Subsequently, an improved sparrow search algorithm (ISSA) is utilized to optimize the inversion objective function. This enhances the efficiency of searching for the objective function and the algorithm’s ability to escape local optimal solutions. The proposed method is evaluated using one-dimensional and two-dimensional models with different initial models and inversion algorithms and applied to the inversion of on-site exploration data in a coal mining area in Chongqing. Comparative results demonstrate that the proposed segmented regularization method, based on the improved sparrow search algorithm, exhibits superior practicality and a higher fitting accuracy.

Dynamic characteristics analysis and robust transition control of tail-sitter VTOL UAVs

The strong nonlinear dynamics of tail-sitter vertical takeoff and landing (VTOL) unmanned aerial vehicles (UAVs) have consistently constrained their applications. Particularly, the widely-varying flight speed and attitude during the transition flights pose substantial challenges for the controller design. In order to gain a clear understanding of the nonlinear transition flights, the long- and short- period dynamic characteristics of tail-sitter UAVs are investigated for the first time. The results reveal that the short-period mode exhibits either sluggish response or excessive overshoot in different transition stages, primarily due to the widely-varying damping ratio and natural angular frequency. Even worse, the long-period mode can diverge due to positive poles. To address these issues, a systematic controller is proposed. First, the transition trajectory is optimized and the optimal control inputs are employed in a feedforward manner to trim the nominal forces and moments. On this basis, a discrete-time linear quadratic regulation (LQR) controller with a predefined decay rate is developed to position the desired poles, and a novel angular acceleration estimation method is introduced to compensate for unmodeled dynamics. Simulations under different uncertainties indicate that the proposed control method performs better in both transition trajectory tracking and uncertainty suppression, compared to the PID and incremental nonlinear dynamic inversion (INDI) controllers.

Time-lapse seismic inversion for CO2 saturation with SeisCO2Net: An application to Frio-II site

Seismic monitoring of geological CO2 storage (GCS) involves highly nonlinear seismic inversion and petrophysical inversion, making it challenging to estimate CO2 volume efficiently and detect possible early CO2 leakages. Deep learning (DL) using convolutional neural networks (CNNs) has shown promise in solving highly nonlinear seismic inversion problems. However, direct estimation of CO2 plume extent/saturation from time-lapse seismic gathers using DL is still underexplored, with no reported field applications to date. The investigation of field data is primarily hindered by scarcity of field data for neural network training. Other obstacles include highly nonlinear seismic-petrophysics inverse relationship, and presence of noise in field seismic data. We introduce SeisCO2Net, a deep CNN that predicts CO2 saturation maps directly from time-lapse full waveform shot gathers. For training, we use site-specific geological information, fluid flow physics, rock physics, and seismic modeling to generate synthetic datasets that closely resemble the CO2 storage site. Synthetic tests show promising results, inspiring us to apply SeisCO2Net's trained weights on field data collected at Frio-II GCS site by leveraging transfer learning principles. As reference, we compare SeisCO2Net's predicted CO2 saturation maps with results obtained from physics-based inversion. Our analyses show both methods display similar CO2 plume shapes, reasonable CO2 plume characteristics, and comparable saturation values. Our results suggest pre-training CNNs on physics-informed synthetic datasets and then applying the learned weights to field data is a viable approach to estimating field CO2 saturation. This method effectively addresses the scarcity of field training data, thus encouraging the feasibility of long-term GCS monitoring.

The 1895 Ljubljana earthquake: source parameters from inversion of macroseismic data

The 14 April 1895 (Mw 6.1, in the area of Ljubljana, Slovenia) earthquake is still not fully understood. The aim of this work is to derive information about its source from the inversion of an updated dataset of intensities (evaluated with EMS-98). This was done via automatic non-linear geophysical inversion KF-NGA, which was performed using a Niching Genetic Algorithm and has been presented in other articles. The distribution of damage caused by this earthquake is not homogeneous and often shows significant intensity differences between neighbouring sites. Statistical analysis of the intensities, epicentral distances and geologic nature of the sites suggests some site effects. Nevertheless, the resulting solution is consistent with regional seismotectonics, i.e. an almost pure dip-slip mechanism: strike 282° ± 5°, dip 38° ± 7°, rake 86° ± 9° (± 180° because of the intrinsic ambiguity of the KF-NGA-inversion). Since the rake angle is close to 90°, there is an almost perfect ambiguity between the two planes of the focal mechanism. Therefore, our solution has a Dinaric direction and could be associated either with a fault plane that dips NE or with one that dips SW.

Geodetic imaging of magma ascent through a bent and twisted dike during the Tajogaite eruption of 2021 (La Palma, Canary Islands)

On Sept. 19th, 2021, the largest historical eruption on the island of La Palma began, which had a significant scientific, social, and economic impact. The 2021 Tajogaite eruption was characterised by short precursors, lasting only 8 days. The seismicity started on Sept. 11th with a westward and upward migration of hypocenters. Permanent GNSS stations started recording deformation on Sept. 12th on the island's western side, which reached more than 15 cm just before the eruption. After the eruption onset, the ground deformation increased, reaching a maximum on Sept. 22nd and showing a nearly steady deflation trend in the following months. To better understand the dynamics of the eruption, we exploited a joint dataset of GNSS and Sentinel-1 SBAS time series along both ascending and descending orbits. To obtain the geometry of the causative source of the ground deformation, we combined the result of a preliminary non-linear inversion and the precise location of the seismicity. The resulting geometry of the source is that of a twisted dike bending eastward. We performed inverse modelling to obtain the spatiotemporal kinematics of the opening function of the dike. The forward modelling has been realised using a 3D finite-element approach considering the island's topography. Our findings reveal a close correspondence between the magmatic intrusion and pre-eruptive seismicity. The ascent of the magma occurred along two branches, and the rheology of a previously identified ductile layer strongly affected the magma propagation process. Finally, we found evidence of an early shallow deformation, which we interpret as the effect of ascending hydrothermal fluids. Our findings highlight the need for advanced modelling to understand pre-eruptive processes in basaltic volcanoes.

Enhanced Estimation of Fluid Modulus and Porosity via Novel Nonlinear Elastic Impedance Inversion

Enhanced Estimation of Fluid Modulus and Porosity via Novel Nonlinear Elastic Impedance Inversion

3-D Adaptive Regularization Nonlinear Inversion of LWD Ultradeep Resistivity in Anisotropic Formation Based on Finite Volume Method of Secondary Field Coupled Potentials and Explicit Fréchet Derivative

3-D Adaptive Regularization Nonlinear Inversion of LWD Ultradeep Resistivity in Anisotropic Formation Based on Finite Volume Method of Secondary Field Coupled Potentials and Explicit Fréchet Derivative

Oilfield Reservoir Parameter Inversion Based on 2D Ground Deformation Measurements Acquired by a Time-Series MSBAS-InSAR Method

Time-series ground deformation monitoring and reservoir parameter inversion are crucial for the dynamic assessment of oilfield resources and sustainable exploitation in oilfields. As some of the regions with the richest oil reserves in China, the oilfield areas in the western Qaidam Basin were selected as a typical study area. Firstly, we used SAR images collected by the Sentinel-1A satellite from January 2021 to December 2022 and applied the multidimensional small baseline subset (MSBAS) method to obtain vertical and east–west deformation measurements. On this basis, a nonlinear Bayesian inversion method was applied to model the shallow reservoir in a series of complex deformation areas, based on a single-source model and a multi-source model, respectively. As a result, the ground deformation monitoring results obtained by long time-series InSAR clearly reflect the uneven ground deformation caused by the oil extraction and water injection operation processes. There was slight subsidence in the Huatugou oilfield, while significant uplift deformation occurred in the Ganchaigou oilfield and the Youshashan oilfield, with a maximum uplift rate of 48 mm/year. Further analysis indicated that the introduction of the 2D deformation field helps to improve the robustness of oilfield reservoir parameter inversion. Moreover, the dual-source model is more suitable than the single-source model for inverting reservoir parameters of complex deformation. This study not only fills the gap of InSAR deformation monitoring for the oilfields in the western Qaidam Basin but also provides a theoretical reference for the model and method selection of reservoir parameter inversion in other oilfields.

Multi-Phase Vertical Take-Off and Landing Trajectory Optimization with Feasible Initial Guesses

The advancement of electric vertical take-off and landing (eVTOL) aircraft has expanded the horizon of urban air mobility. However, the challenge of generating precise vertical take-off and landing (VTOL) trajectories that comply with airworthiness requirements remains. This paper presents an approach for optimizing VTOL trajectories considering six degrees of freedom (6DOF) dynamics and operational constraints. Multi-phase optimal control problems are formulated to address specific constraints in various flight stages. The incremental nonlinear dynamic inversion (INDI) controller is employed to execute the flight mission in each phase. Controlled flight simulations yield dynamically feasible trajectories that serve as initial guesses for generating sub-optimal trajectories within individual phases. A feasible and sub-optimal initial guess for the holistic multi-phase problem is established by concatenating these single-phase trajectories. Focusing on a tilt-wing eVTOL aircraft, this paper computes VTOL trajectories leveraging the proposed initial guess generation procedure. These trajectories account for complex flight dynamics, align with various operation constraints, and minimize electric energy consumption.

Tau Theory-Based Flare Control in Autonomous Helicopter Autorotation

A novel trajectory generation and control architecture for fully autonomous autorotative flare that combines rapid path generation with model-based control is proposed. The trajectory generation component uses optical Tau theory to compute flare trajectories for both longitudinal and vertical speed. These flare trajectories are tracked using a nonlinear dynamic inversion (NDI) control law. One convenient feature of NDI is that it inverts the plant model in its feedback linearization loop, which eliminates the need for gain scheduling. However, the plant model used for feedback linearization still needs to be scheduled with the flight condition. This key aspect is leveraged to derive a control law that is scheduled with linearized models of the rotorcraft flight dynamics obtained in steady-state autorotation, while relying on a single set of gains. Computer simulations are used to demonstrate that the NDI control law is able to successfully execute autorotative flare in the UH-60 aircraft. Autonomous flare trajectories are compared to piloted simulation data to assess similarities and discrepancies between piloted and automatic control approaches. Trade studies examine which combinations of downrange distances and altitudes at flare initiation result in successful autorotative landings.

Complex spherical-wave seismic inversion in anelastic media for the P-wave minimum quality factor

Attenuation always exists when seismic waves propagate in underground anelastic media, especially in hydrocarbon-bearing reservoirs. Quality factor Q or attenuation factor 1/ Q can be used to quantify the seismic wave attenuation and has become an important hydrocarbon indicator. The relationship between the plane-wave reflection coefficient ([Formula: see text]) in anelastic media and P- and S-wave quality factors has been widely used in the plane-wave seismic inversion to estimate the quality factors. The [Formula: see text] provides an adequate approximation for the deeper subsurface. However, for the shallow subsurface and anelastic wavefields excited by point sources, the [Formula: see text] is inaccurate and its meaning involves some fundamental difficulties. In view of this, a Q-dependent P-P spherical-wave reflection coefficient ([Formula: see text]) in anelastic media is used here. Considering that having too many parameters to be inverted will lead to unstable and inaccurate inversion results, we further derive an approximate anelastic [Formula: see text] and anelastic spherical-wave impedance ([Formula: see text]), which are frequency dependent and are the functions of P- and S-wave velocities, density, and P-wave minimum quality factor ([Formula: see text]). Finally, a complex spherical-wave seismic inversion approach in anelastic media for the P-wave minimum quality factor is developed. Using the Bayesian inversion approach and complex convolution model, we first estimate the multilayer [Formula: see text] from the complex seismic traces with different frequencies and incidence angles. Based on the inverted angle- and frequency-dependent [Formula: see text], the P- and S-wave velocities, density, and P-wave minimum quality factor are further estimated using a nonlinear inversion tool. Synthetic examples verify the feasibility and robustness of the complex spherical-wave seismic inversion approach in anelastic media. In the shallow subsurface, the spherical-wave inversion is superior to plane-wave inversion. A field example further demonstrates the accuracy and great potential of our approach in hydrocarbon-bearing reservoir prediction.

Miniaturization and Control of an Unmanned Tiltwing Aircraft

The objective of this paper is to describe the miniaturization and control of an unmanned tiltwing aircraft. For geometric miniaturization and mechanical realization, a lightweight design based on carbon fiber tubes, polystyrene rigid foam and 3D-printed parts is used. The attitude controller is adopted from an existing full-scale unmanned tiltwing aircraft and follows the control strategy of Incremental Nonlinear Dynamic Inversion (INDI). The effects of the miniaturization, including low mass inertia combined with comparatively large aerodynamic surfaces, require a re-evaluation of INDI-based assumptions. Due to the aircraft’s rear-positioned center of gravity, the modeled control ability of the main motors is adapted and explicitly considered in the controller design. The integrity of both, construction and controller, is validated in simulations and flight tests.

Whole-body magnetic resonance imaging in two minutes: cross-sectional real-time coverage of multiple volumes.

This work describes a novel technique for rapid and motion-robust whole-body magnetic resonance imaging (MRI). The method employs highly undersampled radial fast low angle shot (FLASH) sequences to cover large volumes by cross-sectional real-time MRI with automatic slice advancement after each frame. The slice shift typically amounts to a fraction of the slice thickness (e.g., 10% to 50%) in order to generate a successive series of partially overlapping sections. Joint reconstructions of these serial images and their respective coil sensitivity maps rely on nonlinear inversion (NLINV) with regularization to the image and sensitivity maps of a preceding frame. The procedure exploits the spatial similarity of neighboring sections. Whole-body scanning is accomplished by measuring multiple volumes at predefined locations, i.e., at fixed table positions, in combination with intermediate automatic movements of the patient table. Individual volumes may take advantage of different field-of-views, image orientations, spatial and temporal resolutions as well as contrasts. Preliminary proof-of-principle applications to healthy subjects at 3 T without cardiac gating and during free breathing yield high-quality anatomic images with acquisition times of less than 100 ms. Spin-density and T1 contrasts are obtained by spoiled FLASH sequences, while T2-type (i.e., T2/T1) contrast results from refocused FLASH sequences that generate a steady state free precession (SSFP) free induction decay (FID) signal. Total measuring times excluding vendor-controlled adjustment procedures are less than two minutes for a 100 cm scan that, for example, covers the body from head to thigh by three optimized volumes and more than 1,300 images. In conclusion, after demonstrating technical feasibility the proposed method awaits clinical trials.

Depth-to-basement Estimation of Basin Relief Using the BP Network

Nonlinear gravity inversion is a popular method for determining basin bottom relief and delineating basin configuration. However, traditional gravity inversion presents certain challenges, including the complexity and time demand of calculating and transforming large matrices, as well as instability and non-uniqueness caused by the inherently ill-posed nature of inversion problems. Over the past decade, deep learning, a subset of machine learning, has seen successful applications in geophysical interpretation and exploration. In this study, we propose an innovative method for estimating two-dimensional (2D) depth-to-basement using a BP network structure. This structure leverages the Leaky Rectified Linear Unit (ReLU) as an activation function, yielding more realistic geophysical models.

External Synchronization of Distributed Redundant Flight Control Computers

<div>This work introduces a practical approach to external synchronization for flight control computers (FCCs) deployed in a decentralized fashion. The internal synchronization among the FCCs in distributed flight control systems needs to be extended for specific applications, necessitating an urgent need for an external synchronization mechanism. For instance, when the air data and attitude reference system (ADAHRS) and the flight control computer (FCC) are not synchronized, a dead time or time offset occurs between the time the ADAHRS transmits data and the time the FCC begins executing its control functions, which can impair flight control system performance or even cause system instability, particularly for the system with incremental control approaches, such as incremental nonlinear dynamic inversion (INDI). Therefore, an external synchronization technique that does not rely on establishing a global view of time that is accurately synchronized with an external reference device has been proposed and implemented for distributed flight control systems. The findings of the implemented system demonstrate that the suggested approach can synchronize the distributed FCCs to an external reference device with high synchronization precision and deal with varying clock drift rates.</div>

Joint Inversion of Rayleigh Wave Dispersion and Ellipticity Based on Deep Learning

The joint inversion of Rayleigh wave dispersion curves and ellipticity curves is an important method to obtain information about the velocity structure of the stratum, which has the advantages of high resolution and speed. However, there are problems in the application of this technique, such as complicated data, low inversion efficiency, and large influence factors of nonlinear inversion. Deep learning has excellent nonlinear approximation capability, which can compensate for most of the above defects, and has higher efficiency and accuracy compared with traditional methods. In this paper, in order to obtain the near-surface stratigraphic structure quickly and accurately, we propose to introduce the deep learning method into the joint inversion, use the CNN-LSTM network to perform the joint inversion of Rayleigh wave dispersion curves and ellipticity curves. And in order to expand the variety of data set, we propose to add noise to the sample data set, through which the empirical risk can be reduced, and the generalization performance of the network can be increased. Model experiments show that the deep learning network can effectively and accurately perform the joint inversion of Rayleigh waves, and adding noise to the training set is an effective way to improve the generalization and stability of the network.

Control Design for Soft Transition for Landing Preparation of Light Compound-Wing Unmanned Aerial Vehicles Based on Incremental Nonlinear Dynamic Inversion

This paper proposes a soft switching mode for electric vertical takeoff and landing (eVTOL) compound-wing unmanned aerial vehicles (UAVs) to achieve a smooth transition between modes. The proposed mode pre-compensates the lift loss with the rotary wing during the deceleration stage before UAV landing. The control law adopted in this paper consists of implicit nonlinear dynamic inversion (NDI) and incremental nonlinear dynamic inversion (INDI). The outer loop (attitude angle loop) control law is based on implicit NDI, while the inner loop (attitude angle rate loop) controller is based on INDI. An extended state observer (ESO) is employed to estimate the angular acceleration. This paper innovates by proposing a soft switching strategy that improves the robustness, safety, and smoothness of the transition for the compound-wing UAV, and applying advanced control law to mode transition design. For the future application of eVTOL aircraft in UAM scenarios, this paper evaluates the smoothness of transition and passenger comfort using normal overload as a physical quantity. The Monte Carlo (MC) simulation results demonstrate that the proposed mode can reduce the peak normal overload by about 89%.

An adjoint-based optimization method for jointly inverting heterogeneous material properties and fault slip from earthquake surface deformation data

SUMMARY Analysis of tectonic and earthquake-cycle associated deformation of the crust can provide valuable insights into the underlying deformation processes including fault slip. How those processes are expressed at the surface depends on the lateral and depth variations of rock properties. The effect of such variations is often tested by forward models based on a priori geological or geophysical information. Here, we first develop a novel technique based on an open-source finite-element computational framework to invert geodetic constraints directly for heterogeneous media properties. We focus on the elastic, coseismic problem and seek to constrain variations in shear modulus and Poisson’s ratio, proxies for the effects of lithology and/or temperature and porous flow, respectively. The corresponding nonlinear inversion is implemented using adjoint-based optimization that efficiently reduces the cost function that includes the misfit between the calculated and observed displacements and a penalty term. We then extend our theoretical and numerical framework to simultaneously infer both heterogeneous Earth’s structure and fault slip from surface deformation. Based on a range of 2-D synthetic cases, we find that both model parameters can be satisfactorily estimated for the megathrust setting-inspired test problems considered. Within limits, this is the case even in the presence of noise and if the fault geometry is not perfectly known. Our method lays the foundation for a future reassessment of the information contained in increasingly data-rich settings, for example, geodetic GNSS constraints for large earthquakes such as the 2011 Tohoku-oki M9 event, or distributed deformation along plate boundaries as constrained from InSAR.

Applicability of ocean wave measurements based on high-frequency radar systems in an estuary region

ABSTRACT The applicability of high-frequency (HF) radar systems for wave measurement in an estuary was explored by extracting the significant wave height ( H sr ) using a traditional Barrick equation from the Doppler spectra observed by three radar systems installed in Ise Bay, Japan. The minimum value of H sr estimated around each grid point was relatively consistent with the wave height observed with a wave gauge/buoy, except for a deterioration of wave measurement accuracy caused by a decrease in seawater conductivity from the freshwater inflow after flooding. Furthermore, the relationship between the accuracy and the signal-to-noise ratios for the first- and second-order peaks (SNR1 and SNR2, respectively) highlighted the difficulty in determining the threshold values of SNRs in the bay. Thus, we suggest the use of H sr as a criterion for quality control when applying a nonlinear inversion method for estimating ocean wave spectra based on the Bayesian possibility theorem (BIM). Our suggestion is to select the appropriate Doppler spectra and increase the acquisition rates of wave data with low relative error compared to BIMs using SNR1 and SNR2. These results can promote the applicability of the nonlinear inversion in estuary regions.

Meta-Learning-Based Incremental Nonlinear Dynamic Inversion Control for Quadrotors with Disturbances

This paper proposes an online meta-learning-based incremental nonlinear dynamic inversion (INDI) control method for quadrotors with disturbances. The quadrotor dynamic model is first transformed into linear form via an INDI control law. Since INDI largely depends on the accuracy of the control matrix, a method composed of meta-learning and adaptive control is proposed to estimate it online. The effectiveness of the proposed control framework is validated through simulation on a quadrotor with 3D wind disturbances.