Nonlinear Inversion Research Articles

Prediction of Marine Thin Shale Gas Reservoir with Seismic Phase-Controlled Nonlinear Stochastic Inversion

Due to the complicated interference sources and low signal-to-noise ratio of seismic records, conventional seismic inversion methods are difficult to accurately identify shale gas reservoirs with a thickness of less than 10 m. This presents great challenges to shale gas exploration and development in China. Seismic phase-controlled nonlinear stochastic inversion (SPCNSI) is related to the heterogeneity of underground media. With the constraints of the stratigraphic sequence or seismic facies models, the minimum value between the seismic model and seismic record can be solved through iterative processes. Based on the solved acoustic velocity in formation, the constraints for SPCNSI can be formed with the matching relationship between target layers and different sequences in three-dimensional space. The prediction resolution of an unconventional reservoir can be effectively improved by combining logging, geological and seismic information. The method is suitable for predicting thin shale gas reservoirs in complex geological structures. In this study, SPCNSI was developed to predict the thin-layer marine shale gas reservoir in the southeast of Chongqing; the horizontal and vertical distribution characteristics were proven in the Longmaxi Formation and the Wufeng Formation; thin layers with a thickness of less than 7 m were also discovered. According to the results, three sets of potential development areas were determined by the inversion method, and the accuracy and reliability of the method were verified by logging and productivity testing.

JPEG Decoding With Nonlinear Inverse Transform Network and Progressive Recurrent Residual Network

JPEG is the most widely used image compression format, especially with the popularity of mobile or portable devices. However, the quality of a decoded JPEG image is usually degraded by compression artifacts such as blocking effect and ringing effect, especially at low bit rates. Recently, some convolutional neural network (CNN) based methods have been designed to solve the above problem. These methods take the problem as post-processing and only add a CNN-based post-processing network after a JPEG decoder to improve the image quality. In this paper, the JPEG decoding with nonlinear inverse transform network and progressive recurrent residual network (dubbed as JDNet) is proposed. JDNet can reconstruct JPEG images of different quality factors (QF) with only one model. In JDNet, first, the CNN-based inverse transform network (iTNet) is proposed to learn the nonlinear mapping from DCT coefficients to their corresponding original pixels, which is against the linear mapping in previous DCT networks. iTNet can reduce error propagation during inverse DCT and obtain more accurate reconstruction. Furthermore, iTNet can be combined with any JPEG post-processing method to improve its performance. Second, the progressive recurrent residual network (PRRN) is proposed for local feature extraction in the designed post-processing network which utilizes local and nonlocal similarities in multi-scale space (LNLMS) to further enhance the decoded image quality. The experimental results show that compared with JPEG, ARCNN, DnCNN and STRRN, the average gains of JDNet are 1.88dB, 0.63dB, 0.35dB, 0.24dB on Live1 dataset, 2.61dB, 1.11dB, 0.69dB and 0.29dB on Urban100 dataset, and 1.91dB, 0.69dB, 0.37dB and 0.13dB on BSD500 dataset, respectively.

High‐resolution reservoir stochastic modelling based on optimized estimation of vertical autocorrelation

AbstractThe high‐resolution model of elastic properties is of great significance for fine reservoir characterization and precise oil and gas exploration. However, it is difficult to obtain a satisfactory high‐resolution reservoir model with the existing technologies. In this paper, a novel high‐resolution stochastic modelling strategy based on the fast Fourier transform moving average is proposed. In this strategy, several structural parameters are optimized to improve the rationality of the stochastic model, including vertical autocorrelation length, horizontal autocorrelation length, roughness factor and angle parameter. Among them, the optimization of the vertical autocorrelation length is crucial for vertical high‐resolution modelling. To this end, a nonlinear optimal inversion strategy of the vertical autocorrelation length is designed based on the idea of minimizing the spectral Jensen–Shannon divergence between the modelling result and the logging curve. However, nonlinear inversion is usually unstable, so it is necessary to introduce a regularization operator in the inversion to improve the stability. Considering that the heterogeneity of the subsurface medium is consistent or gradual within the stratums, but discontinuous and abrupt at the interfaces, edge‐preserving regularization is applied to obtain a blocky estimation of the vertical autocorrelation length. The optimal estimation experiment of the vertical autocorrelation length based on the measured logging data shows that the edge‐preserving regularization significantly improves the stability of the nonlinear optimal inversion, and blocky estimation results with sharp edges are obtained. Then, the optimized vertical autocorrelation length and the other structural parameters are applied to fast Fourier transform moving average modelling on an actual reservoir profile. The result shows that the resolution of the model is significantly improved, which realizes the fine reservoir characterization. In addition, the optimized structural parameters effectively constrain the small‐scale heterogeneity and ensure the rationality of the stochastic model.

Robust Stability and Performance Analysis of Incremental Dynamic-Inversion-Based Flight Control Laws

Incremental nonlinear dynamic inversion (INDI) is a sensor-based control law design strategy that is based on the principles of feedback linearization. Contrary to its nonincremental counterpart (nonlinear dynamic inversion), this design method does not require a complete onboard model of the airframe dynamics and is therefore more robust against regular perturbations arising from aerodynamic variations. Therefore, INDI brings a natural design approach to desirable flying qualities. However, robustness against singular perturbations, which may arise due to transport delays, elastic airframe effects, or other types of badly modeled or unknown dynamics, is a known challenge for INDI-based control laws. Therefore, this paper addresses the question of robust stability and performance for INDI and its linear form (incremental dynamic inversion [IDI]) in the context of mixed regular and singular perturbations. This is done through analytical insights and by performing quantitative robustness assessments based on the structured singular value framework. Additionally, inversion loop augmentation solutions are investigated using robust synthesis techniques to improve the robustness characteristics of basic IDI designs.

Model-Free Sliding Mode Enhanced Proportional, Integral, and Derivative (SMPID) Control

This study proposes a type of Sliding Mode-based Proportional, Integral, and Derivative (SMPID) controllers to establish a model-free (treat dynamic plants as a whole uncertainty) sliding model control (MFSMC) platform for Bounded-Input and Bounded-Output (BIBO) dynamic systems. The SMPID design (1) proposes a sliding mode error (rather than error) as the PID input, (2) directly links to Lyapunov asymptotic stability to provide total robust nonlinear dynamic inversion (NDI), and (3) reduces the chattering effects in terms of Lyapunov definite positive stability. Further, the study proposes a general SMC framework to accommodate asymptotic time stabilisation and finite-time stabilisation for both model-based and model-free designs. A U-control framework is presented to integrate the SMPID control (for NDI) and an invariant control (IC) (for specifying the whole control system’s dynamic and static responses), which significantly relaxes the PID tunings and generates the specified performance. To provide assurance and guidance for applications and expansions, this study presents the relevant fundamental analyses and transparent simulated bench tests. It should be noted that the new SMPID in forms of u=SMPID(σ(e))=PID(sliding-mode) is different from that studied u=sliding-mode(PID(e)) in expression and functionality.

Crustal and lithospheric mantle structure below the Indian shield based on 3-D constrained gravity inversion and Deep Neural Network approach: Geological implications

The Indian shield region comprises of several Archean cratons, Proterozoic mobile belts, Proterozoic-Phanerozoic rift basins, and volcanic provinces and has been significantly modified by various tectono-thermal events and the supercontinental cycles. These overprinting processes and evolution can be understood, to some extent by characterizing the lithosphere structure. In this study, we carried out seismically constrained 3-D nonlinear gravity inversion using tesseroids in the spherical coordinate system to delineate the Moho geometry for the Indian shield. Further, the supervised machine learning approach using Deep Neural Network (DNN) is implemented on the geopotential data to obtain Lithosphere-Asthenosphere Boundary (LAB) across the Indian shield. The inversion results show that the Moho depth varies between 33 and 60 km below the Indian shield with a mean difference of ∼ −0.3 km and a standard deviation of ∼4.9 km relative to the Moho from receiver function data. For the DNN model, the estimated LAB depth values range between 95 and 280 km below the Indian shield. The model gave rise to the coefficient of determination R2 of 0.93, Mean Absolute Error of ∼14 km, and Root Mean Square Error of ∼22 km between the observed and predicted LAB depths. Apart from the general agreement of Moho and LAB depth estimates with previous seismological studies, the present study provides better resolved information of lithosphere structure across the Indian shield. The modelled lithosphere structure therefore will be useful to integrate with the geochronological data in order to to understand the Proterozoic tectonic evolution of the Indian Shield.

Bayesian linearized rock-physics amplitude-variation-with-offset inversion for petrophysical and pore-geometry parameters in carbonate reservoirs

Rock-physics amplitude-variation-with-offset (AVO) inversion aims at directly predicting reservoir properties from prestack seismic data. However, carbonate reservoir rocks often develop complex pore structures, which limits the application of conventional inversion methods with fixed pore-geometry parameters. We derive a PP-wave reflectivity equation in terms of porosity, water saturation, and pore-aspect ratio and we develop a rock-physics AVO inversion method to jointly estimate the petrophysical and pore-geometry parameters in carbonates. The reflectivity equation is obtained by linearizing the rock-physics model based on the differential effective medium model and Gassmann’s equation using Taylor series approximation, and we combine the linearization with the Aki-Richards equation. Thanks to the linearized model, the analytical solution to the inverse problem is derived using Bayesian linear theory. Our solution combines simulated annealing to estimate the prior information of the pore geometry and the iterative Bayesian inversion to update the posterior model. The method is tested on a benchmark data set and compared with conventional methods with a fixed aspect ratio. The results show that our method improves the petrophysical results. The method is also compared with two-step and nonlinear inversion methods to demonstrate its advantages. The method is applied to a field seismic section from a carbonate reservoir with a complex pore structure to demonstrate its advantages in terms of prediction accuracy.

Discrete-Time Incremental Backstepping Control with Extended Kalman Filter for UAVs

In this study, a discrete-time incremental backstepping (DTIBS) controller with an extended Kalman filter (EKF) is proposed for unmanned aerial vehicles (UAVs) with unknown actuator dynamics. The Taylor series and an approximate discrete method are employed, transforming the second-order continuous-time nonlinear system into a discrete-time nonlinear plant with an incremental input form. The incremental control laws are designed using the incremental nonlinear dynamic inversion (INDI) method and the time-delay control (TDC) method. The TDC is introduced to design the control law, eliminating the need for prior knowledge of the control effectiveness matrix involving some unknown aerodynamic coefficients. In addition, the airflow angle and body rotation rate are selected as key system states, and the EKF is used to design a state estimator to estimate the local state of the small unmanned aerial vehicle closed-loop flight control system under strong noise conditions. The effectiveness of the DTIBS control method with EKF is verified through numerical simulation. The results show that the proposed method can effectively estimate the state under the typical noise characteristics of low-cost sensors, and the closed-loop control systems has good tracking performance and can quickly and effectively track sudden commands.

Feasibility of structure inversions for gravity-mode pulsators

Context. Gravity-mode asteroseismology has significantly improved our understanding of mixing in intermediate mass stars. However, theoretical pulsation periods of stellar models remain in tension with observations, and it is often unclear how the models of these stars should be further improved. Inversions provide a path forward by directly probing the internal structure of these stars from their pulsation periods, quantifying which parts of the model are in need of improvement. This method has been used with success in the case of solar-like pulsators, but has not yet been applied to main-sequence gravity-mode pulsators. Aims. Our aim is to determine whether structure inversions for gravity-mode pulsators are feasible. We focus on the case of slowly rotating slowly pulsating B-type (SPB) stars. Methods. We computed and analyzed dipole mode kernels for three variables pairs: (ρ, c), (N2, c), and (N2, ρ). We assessed the potential of these kernels by predicting the oscillation frequencies of a model after perturbing its structure. We then tested two inversion methods, regularized least squares (RLS) and subtractive optimally localized averages (SOLA), using a model grid computed with the MESA stellar evolution code and the GYRE pulsation code. Results. We find that changing the stellar structure affects the oscillation frequencies in a nonlinear way. The oscillation modes for which this nonlinear dependency is the strongest are in resonance with the near-core peak in the buoyancy frequency. The near-core region of the star can be probed with SOLA, while RLS requires fine tuning to obtain accurate results. Both RLS and SOLA are strongly affected by the nonlinear dependencies on the structure differences, as these methods are based on a first-order approximation. These inversion methods need to be modified for meaningful applications of inversions to SPB stars. Conclusions. Our results show that inversions of gravity-mode pulsators are possible in principle, but that the typical inversion methods developed for solar-like oscillators are not applicable. Future work should focus on developing nonlinear inversion methods.

Mechanical stiffness and anisotropy measured by MRE during brain development in the minipig

The relationship between brain development and mechanical properties of brain tissue is important, but remains incompletely understood, in part due to the challenges in measuring these properties longitudinally over time. In addition, white matter, which is composed of aligned, myelinated, axonal fibers, may be mechanically anisotropic. Here we use data from magnetic resonance elastography (MRE) and diffusion tensor imaging (DTI) to estimate anisotropic mechanical properties in six female Yucatan minipigs at ages from 3 to 6 months. Fiber direction was estimated from the principal axis of the diffusion tensor in each voxel. Harmonic shear waves in the brain were excited by three different configurations of a jaw actuator and measured using a motion-sensitive MR imaging sequence. Anisotropic mechanical properties are estimated from displacement field and fiber direction data with a finite element- based, transversely-isotropic nonlinear inversion (TI-NLI) algorithm. TI-NLI finds spatially resolved TI material properties that minimize the error between measured and simulated displacement fields. Maps of anisotropic mechanical properties in the minipig brain were generated for each animal at all four ages. These maps show that white matter is more dissipative and anisotropic than gray matter, and reveal significant effects of brain development on brain stiffness and structural anisotropy. Changes in brain mechanical properties may be a fundamental biophysical signature of brain development.

Low-level control with actuator dynamics for multirotor UAVs

PurposeA low-level controller is critical to the overall performance of multirotor unmanned aerial vehicles. The purpose of this paper is to propose a nonlinear low-level angular velocity controller for multirotor unmanned aerial vehicles in various operating conditions (e.g. different speed and different mode).Design/methodology/approachTo tackle the above challenge, the authors have designed a nonlinear low-level controller taking the actuator dynamics into account. The authors first build the actuator subsystem by combining the actuator dynamics with the angular velocity dynamics model. Then, a recursive low-level controller is developed by designing a high-gain observer to estimate unmeasurable states. Furthermore, a detailed stability analysis is given with the Lyapunov theory.FindingsSimulation tests and real-world flying experiments are provided to validate the proposed approach. In particular, we illustrate the performance of the proposed controller using violent random command test, attitude mode flight and high-speed flight of up to 18.7 m/s in real world. Compared with the classical method used in PX4 autopilot and the estimation-based incremental nonlinear dynamic inversion method, experimental results show that the proposed method can further reduce the control error.Research limitations/implicationsLow-level control of multirotor UAVs is challenging due to the complex dynamic characteristics of UAVs and the diversity of tasks. Although some progress has been made, the performance of existing methods will deteriorate as operating conditions change due to the disregard for the electromechanical characteristics of the actuator.Originality/valueTo solve the low-level angular velocity control problem in various operating conditions of multirotor UAVs, this paper proposes a nonlinear low-level angular velocity controller which takes the actuator dynamics into account.

Improved Adaptive NDI Flight Control Law Design Based on Real-Time Aerodynamic Identification in Frequency Domain

The traditional aircraft controller design is usually based on the off-line aerodynamic model. Due to the deviation of the off-line aerodynamic model, the flight quality is difficult to meet the requirements when the aircraft is flying in the real atmosphere. To solve this problem, this paper proposes a frequency domain identification-based improved adaptive nonlinear dynamic inversion (NDI) control method (FDI-ANDI). In this paper, an online recursive aerodynamic parameter identification method in the frequency domain is first designed, and then an adaptive dynamic inversion control method based on the online aerodynamic parameter identification results is established. Finally, aiming at the problem of the slow response speed of the NDI controller, an improved adaptive dynamic inversion control law is designed by using the method of series lead correction. Compared with the traditional control method, the adaptive dynamic inversion method based on online aerodynamic identification has stronger robustness and a faster response speed in the face of model uncertainty. The final simulation analysis shows that the method has a better control effect than the traditional control method.

Incremental Nonlinear Dynamic Inversion Attitude Control for Helicopter with Actuator Delay and Saturation

In this paper, an incremental nonlinear dynamic inversion (INDI) control scheme is proposed for the attitude tracking of a helicopter with model uncertainties, and actuator delay and saturation constraints. A finite integral compensation based on model reduction is used to compensate the actuator delay, and the proposed scheme can guarantee the semi-globally uniformly ultimately bounded tracking. The overall attitude controller is separated into a rate, an attitude, and a collective pitch controller. The rate and collective pitch controllers combine the proposed method and INDI to enhance the robustness to actuator delay and model uncertainties. Considering the dynamic of physical actuators, pseudo-control hedging (PCH) is introduced both in the rate and attitude controller to improve tracking performance. By using the proposed controller, the helicopter shows good dynamics under the multiple restrictions of the actuators.

Calibration and Sensitivity Analysis of Macro and Meso Parameters of Discrete Element Model for Coal Measure Soil

The orthogonal test sequence of the meso parameters of the discrete element model was designed by using the orthogonal test method. The calculation method of directly determining the meso parameters from the macro mechanical parameters was established by using the test simulation calculation results and the multi factor nonlinear joint inversion method. The proposed method was applied to the discrete element numerical simulation of triaxial test of coal measure soil. The results show that the numerical simulation results are in good agreement with the stress-strain curves of the triaxial test of coal bearing soil. Through error analysis, it is found that the maximum error of the partial stress peak is 5.4%, the error of the cohesion is 2%, the error of the internal friction angle is 7%, and the error is all within 10%. It verifies that the method for rapid determination of the meso parameters proposed in this paper is feasible, and provides a new idea for the calibration of the meso parameters in the discrete element numerical simulation method.

Learning-Assisted Inversion for Solving Nonlinear Inverse Scattering Problem

Solving inverse scattering problems (ISPs) is challenging because of its intrinsic ill-posedness and the nonlinearity. When dealing with highly nonlinear ISPs, i.e., those scatterers with high contrast and/or electrically large size, the traditional iterative nonlinear inversion methods converge slowly and take lots of computation time, even maybe trapped into local wrong solution. To alleviate the above challenges, a learning-assisted (LA) inversion approach termed as the LA inversion method (LAIM) with advanced generative adversarial network (GAN) in virtue of a new recently established contraction integral equation for inversion (CIE-I) is proposed to achieve a good balance between the computational efficiency and the accuracy of solving highly nonlinear ISPs. The preliminary profiles composed of only small amount of low-frequency components can be got efficiently by the Fourier bases expansion of CIE-I inversion (FBE-CIE-I). The physically exacted information can be taken as the input of the neural network to recover super-resolution image with more high-frequency components. A weighted loss function composed of the adversarial loss, mean absolute percentage error (MAPE), and structural similarity (SSIM) is used under the pix2pix GAN framework. In addition, the self-attention module is used at the end of the generator network to capture the physical distance information between two pixels and enhance the inversion accuracy of the feature scatterers. To further improve the inversion efficiency, the data-driven method (DDM) is used to achieve real-time imaging by cascading U-net and pix2pix GAN, where U-net is used to replace FBE-CIE-I in the LAIM. Compared with other LA inversion, both the synthetic and experimental examples have validated the merits of the proposed LAIM and DDM.

Extended-State-Observer-Based Angular Acceleration Estimation for Supersonic Aircraft Lateral–Directional Control

Large-slenderness-ratio (LSR) aircraft exhibit more severe lateral–directional coupling compared with other aircraft, which poses a significant challenge to their flight safety, especially during high-speed maneuvers. Reliable attitude decoupling control is, therefore, essential for LSR aircraft. In this study, a novel control framework that combines incremental nonlinear dynamic inversion (INDI) and extended state observer (ESO) is proposed for supersonic roll maneuver control of LSR aircraft. The ESO is used to estimate the angular acceleration on the basis of an onboard mathematical model. The acceleration estimator based on ESO achieves superior noise reduction compared with the complementary filter (CF) and reduces the onboard model requirement without significantly sacrificing estimation accuracy. Monte Carlo (MC) simulations and frequency–domain analysis demonstrate the effectiveness and robustness of the proposed controller. The sensitivity of parameter uncertainties is also investigated, revealing that the natural frequency of the actuator is the most critical parameter affecting robustness. Finally, flight tests validate the effectiveness of the proposed control structure.

A nonlinear inversion procedure for modeling the effects of economic factors on credit risk migration

A nonlinear inversion procedure for modeling the effects of economic factors on credit risk migration

Nonlinear inversion of electrical resistivity sounding data for multi-layered 1-D earth model using global particle swarm optimization (GPSO)

Interpreting geophysical data requires solving nonlinear optimization problem(s) in inversion. Analytical methods such as least-square have some intrinsic limitations, which include slow convergence and dimensionality, making heuristic-based swarm intelligence a better alternative. Large-scale nonlinear optimization problems in inversion can be solved effectively using a technique within the swarm intelligence family called Particle Swarm Optimization (PSO). This study evaluates the inversion of geoelectrical resistivity data with global particle swarm optimization (GPSO). We attempted to invert field vertical electrical sounding data for a multi-layered 1-D earth model using the developed particle swarm optimization algorithm. The result of the PSO-interpreted VES data was compared with that of the least square inversion result from Winresist 1.0. According to the PSO-interpreted VES results, satisfactory solutions may be attained with a swarm of 200 or fewer particles, and convergence can be reached in fewer than 100 iterations. The GPSO inversion approach has a maximum capacity of 100 iterations, more than the least square inversion algorithm of the Winresist, which has a maximum capacity of 30 iterations. The misfit error of GPSO inversion is 6.14×10−7, much lower than that of the least square inversion of 4.0. The GPSO inversion model has lower and upper limit values of the geoelectric layer parameters model to fit the true model better. The limitations of the developed PSO inversion scheme include a slower execution time of the inversion procedures than the least-square inversion. There is a need for a priori knowledge of the number of layers from borehole reports in the study area. The PSO inversion scheme, however, estimates inverted models closer to the true solutions with greater accuracy than the least-square inversion scheme.

Estimating two groups of fracture weaknesses using azimuthal differences in partially incidence-angle-stacked seismic amplitudes

Geophysical and geologic data, e.g., results obtained using rock cores, outcrops, and borehole images, reveal the presence of multiple sets of fractures in rock. To analyze how fracture interactions affect seismic anisotropy and dispersion, we consider an effective model that contains two sets of orthogonal fractures. In seismic amplitude analysis, we focus on the case of subsurface target zones containing a fracture network composed of primary and secondary fracture sets. Focusing on gas-bearing rocks with small fracture densities, we formulate simplified stiffness parameters in terms of two groups of fracture weaknesses, which are related to the primary and secondary fractures, respectively. Using the simplified stiffness parameters, we derive the PP-wave reflection coefficient and the azimuthal elastic impedance (AEI) as functions of the two groups of normal and tangential fracture weaknesses. Based on the derived PP-wave reflection coefficient and AEI, we propose a method and workflow in which the azimuthal variations of the partial incidence-angle-stacked seismic data are used to estimate the AEI and differences in AEI (which we refer to as DEI) is input to a nonlinear inversion for two groups of fracture weaknesses. In the nonlinear inversion, the initial values of fracture weaknesses are obtained based on a two-term approximation of the PP-wave reflection coefficient. First- and second-order derivatives of DEI with respect to fracture weakness parameters are calculated to generate the update in the unknown parameter vector. Synthetic seismic gathers with varying signal-to-noise ratios are used to validate the robustness of the estimation. Applying the inversion method to a real data set, we obtain what we interpret to be reliable fracture weakness estimates that produce azimuthal amplitude differences matching those extracted from real seismic data. The results provide a potential tool for determining if two sets of fractures have developed in a reservoir.

Imaging the subcellular viscoelastic properties of mouse oocytes

In recent years, cellular biomechanical properties have been investigated as an alternative to morphological assessments for oocyte selection in reproductive science. Despite the high relevance of cell viscoelasticity characterization, the reconstruction of spatially distributed viscoelastic parameter images in such materials remains a major challenge. Here, a framework for mapping viscoelasticity at the subcellular scale is proposed and applied to live mouse oocytes. The strategy relies on the principles of optical microelastography for imaging in combination with the overlapping subzone nonlinear inversion technique for complex-valued shear modulus reconstruction. The three-dimensional nature of the viscoelasticity equations was accommodated by applying an oocyte geometry-based 3D mechanical motion model to the measured wave field. Five domains-nucleolus, nucleus, cytoplasm, perivitelline space, and zona pellucida-could be visually differentiated in both oocyte storage and loss modulus maps, and statistically significant differences were observed between most of these domains in either property reconstruction. The method proposed herein presents excellent potential for biomechanical-based monitoring of oocyte health and complex transformations across lifespan. It also shows appreciable latitude for generalization to cells of arbitrary shape using conventional microscopy equipment.