Hybrid Inversion Method Research Articles

A Hybrid Inversion Method Based on SDM and ANNs Considering Electromagnetic Response Laws

A Hybrid Inversion Method Based on SDM and ANNs Considering Electromagnetic Response Laws

Novel Hybrid Model to Estimate Leaf Carotenoids Using Multilayer Perceptron and PROSPECT Simulations

Leaf carotenoids (Cxc) play a crucial role in vegetation as essential pigments responsible for capturing sunlight and protecting leaf tissues. They provide vital insights into a plant physiological status and serve as sensitive indicators of plant stress. However, remote sensing of Cxc at the leaf level has been challenging due to the low Cxc content and weaker absorption features compared to those of chlorophylls in the visible domain. Existing vegetation indices have been widely applied but often lack a solid physical foundation, which limits their applicability and robustness in characterizing Cxc. Yet, physical models can confront this ill-posed problem, though with high operational costs. To address this issue, this study presents a novel hybrid inversion method that combines the multilayer perceptron (MLP) algorithm with PROSPECT model simulations to accurately retrieve Cxc. The effectiveness of the MLP method was investigated through comparisons with the classical PROSPECT model inversion (look-up table [LUT] method), the convolutional neural network (CNN) hybrid model, and the Transformer hybrid model. In the pooled results of six experimental datasets, the MLP method exhibited its robustness and generalization capabilities for leaf Cxc content estimation, with RMSE of 3.12 μg/cm2 and R2 of 0.52. The Transformer (RMSE = 3.14 μg/cm2, R2 = 0.46), CNN (RMSE = 3.42 μg/cm2, R2 = 0.28), and LUT (RMSE = 3.82 μg/cm2, R2 = 0.24) methods followed in descending order of accuracy. A comparison with previous studies using the same public datasets (ANGERS and LOPEX) also demonstrated the performance of the MLP method from another perspective. These findings underscore the potential of the proposed MLP hybrid method as a powerful tool for accurate Cxc retrieval applications, providing valuable insights into vegetation health and stress response.

Model reduction in geostatistical seismic inversion with functional data analysis

In subsurface modeling and characterization, predicting the spatial distribution of subsurface elastic properties is commonly achieved by seismic inversion. Stochastic seismic inversion methods, such as iterative geostatistical seismic inversion (GSI), are widely applied to this end. Global iterative GSI methods are computationally expensive because they require, at a given iteration, the stochastic sequential simulation of the entire inversion grid at once multiple times. Functional data analysis (FDA) is a well-established statistical method suited to model long-term and noisy temporal series. This method allows us to summarize spatiotemporal series in a set of analytical functions with a low-dimension representation. FDA has been recently extended to problems related to geosciences, but its application to geophysics is still limited. We have developed the use of FDA as a model reduction technique during the model perturbation step in global iterative GSI. FDA is used to collapse the vertical dimension of the inversion grid. We illustrate our hybrid inversion method with its application to 3D synthetic and real data sets. The results indicate the ability of our inversion methodology to predict smooth inverted subsurface models that match the observed data at a similar convergence as obtained by a global iterative GSI, but with a considerable decrease in the computational cost. Although the resolution of the inverted models might not be enough for a detailed subsurface characterization, the inverted models can be used as a starting point of global iterative GSI to speed up the inversion or to test alternative geologic scenarios by changing the inversion parameterization and obtaining inverted models in a relatively short time.

Transfer-learning-based approach for leaf chlorophyll content estimation of winter wheat from hyperspectral data

Leaf chlorophyll, as a key factor for carbon circulation in the ecosystem, is significant for the photosynthetic productivity estimation and crop growth monitoring in agricultural management. Hyperspectral remote sensing (RS) provides feasible solutions for obtaining crop leaf chlorophyll content (LCC) by the advantages of its repeated and high throughput observations. However, the data redundancy and the poor robustness of the inversion models are still major obstacles that prevent the widespread application of hyperspectral RS for crop LCC evaluation. For winter wheat LCC inversion from hyperspectral observations, this study described a novel hybrid method, which is based on the combination of amplitude- and shape- enhanced 2D correlation spectrum (2DCOS) and transfer learning. The innovative feature selection method, amplitude- and shape- enhanced 2DCOS, which originated from 2DCOS, additionally considered the relationships between external perturbations and hyperspectral amplitude and shape characteristics to enhance the dynamic spectrum response. To extract the representative LCC featured wavelengths, the amplitude- and shape- enhanced 2DCOS was conducted on the leaf optical PROperties SPECTra (PROSPECT) + Scattering from Arbitrarily Inclined Leaves (SAIL) (PROSAIL) simulated dataset, which covered most possible winter wheat canopy spectra. Nine wavelengths (i.e., 455, 545, 571, 615, 641, 662, 706, 728, and 756 nm) were then extracted as the sensitive wavelengths of LCC with the amplitude- and shape- enhanced 2DCOS. These wavelengths had specificity to LCC and showed good correlation with LCC from the aspect of photosynthesis mechanism, molecular structure, and optical properties. The transfer learning techniques based on the deep neural network was then introduced to transfer the knowledge learned from the PROSAIL simulated dataset to the inversion tasks of field measured LCC. Parts of the labeled samples in field observations were used to finetune the model pre-trained by the simulated dataset to improve the inversion accuracy of the winter wheat LCC in different field scenes, aiming to reduce the need for the field measured and labeled sample size. To further ascertain the universality, transferability and predictive ability of the proposed hybrid method, field samples collected from different locations at different phenological phases, including the jointing and heading stages in 2013, 2014, and 2018, were utilized as target tasks to validate the proposed hybrid method. Moreover, the LCC of winter wheat estimated with the proposed method was evaluated with the ground-based platform and the UAV-based platform to verify the model versatility for different monitoring platforms. Various validations demonstrated that the hybrid inversion method combining the amplitude- and shape- enhanced 2DCOS and the fine-tuned transfer learning model could effectively estimate winter wheat LCC with good accuracy and robustness, and can be extended to the detection and inversion of other key variables of crops.

Analyzing the Effects of Hyperspectral ZhuHai-1 Band Combinations on LAI Estimation Based on the PROSAIL Model.

Leaf area index (LAI) is a key biophysical variable to characterize vegetation canopy. Accurate and quantitative LAI estimation is significant for monitoring vegetation growth status. ZhuHai-1 (ZH-1), which is a commercial remote sensing micro-nano satellite, provides a possibility for quantitative detection of vegetation with high spatial and spectral resolution. However, the band characteristics of ZH-1 are closely related to the accuracy of vegetation monitoring. In this study, a simulation dataset containing 32 bands of ZH-1 was generated by using the PROSAIL model, which was used to analyze the performance of 32 bands for LAI estimation by using the hybrid inversion method. Meanwhile, the effect of different band combinations on LAI estimation was discussed based on sensitivity analysis and the correlation between bands. Then, the optimal band combination from ZH-1 hyperspectral satellite data for LAI estimation was obtained. LAI estimation was performed based on the selected optimal band combination of ZH-1 satellite images in Xiantao city, Hubei province, and compared with the Sentinel-2 normalized difference vegetation index (NDVI) values and LAI product. The results demonstrated that the obtained LAI map based on the optimal band combination of ZH-1 was generally consistent with the overall distribution of Sentinel-2 NDVI and the LAI product, but had a moderate correlation with Sentinel-2 LAI (R = 0.60), which may not favorably indicate the validity of indirect validation. However, the method of this study on the analysis of hyperspectral data bands has application potential to provide a reference for selecting appropriate bands of hyperspectral satellite data to estimate LAI and improve the application of hyperspectral data such as ZH-1 in vegetation monitoring.

Preliminary study of HVSR forward modeling: parameters properties and non-uniqueness of subsurface models

The application of horizontal to a vertical spectral ratio (HVSR) in Indonesia is often analyzed using theoretical equations that only focus on Vs. or the two rock layers’ thickness. On the other hand, there are already HVSR modeling programs that involve other parameters such as VP, density, QP, and Qs for multiple layers. Armed with existing modeling, the effect of each parameter and test the possible non-uniqueness of HVSR modeling is found. In the end, the right inversion method to get satisfactory results is found. Modeling is done by calculating the wave amplification of the transfer function, the phenomenon of attenuation, and dispersion. A synthetic model will be made from the modeling scheme, which is approached with various possible parameters using a random test of 200000 models for each test. From the existing parameters, it is found that only the parameters Vs, thickness, and Qs affect the position f0. Meanwhile, the parameters VP, density, and QP only affect the amplitude of the curve. The parameters VP, Vs, density, and thickness have a consistent relationship between parameters, but not for QP and Qs. From the various tests carried out, it was found that many combinations can produce similar responses, both parameter combinations, and combinations of parameters with a different number of layers. Inversion modeling is needed to produce a precise subsurface model that can reduce the non-uniqueness results, such as optimization with a global approach, a statistical approach, or a hybrid inversion method.

A New Hybrid Inversion Method for 2D Nuclear Magnetic Resonance Combining TSVD and Tikhonov Regularization.

This paper is concerned with the reconstruction of relaxation time distributions in Nuclear Magnetic Resonance (NMR) relaxometry. This is a large-scale and ill-posed inverse problem with many potential applications in biology, medicine, chemistry, and other disciplines. However, the large amount of data and the consequently long inversion times, together with the high sensitivity of the solution to the value of the regularization parameter, still represent a major issue in the applicability of the NMR relaxometry. We present a method for two-dimensional data inversion (2DNMR) which combines Truncated Singular Value Decomposition and Tikhonov regularization in order to accelerate the inversion time and to reduce the sensitivity to the value of the regularization parameter. The Discrete Picard condition is used to jointly select the SVD truncation and Tikhonov regularization parameters. We evaluate the performance of the proposed method on both simulated and real NMR measurements.

Estimating Crop LAI Using Spectral Feature Extraction and the Hybrid Inversion Method

The leaf area index (LAI) is an essential indicator used in crop growth monitoring. In the study, a hybrid inversion method, which combined a physical model with a statistical method, was proposed to estimate the crop LAI. The simulated compact high-resolution imaging spectrometer (CHRIS) canopy spectral crop reflectance datasets were generated using the PROSAIL model (the coupling of PROSPECT leaf optical properties model and Scattering by Arbitrarily Inclined Leaves model) and the CHRIS band response function. Partial least squares (PLS) was then used to reduce the dimension of the simulated spectral data. Using the principal components (PCs) of PLS as the model inputs, the hybrid inversion models were built using various modeling algorithms, including the backpropagation artificial neural network (BP-ANN), least squares support vector regression (LS-SVR), and random forest regression (RFR). Finally, remote sensing mapping of the CHRIS data was achieved with the hybrid model to test the inversion accuracy of LAI estimates. The validation result yielded an accuracy of R2 = 0.939 and normalized root-mean-square error (NRMSE) = 6.474% for the PLS_RFR model, which indicated that the crops LAI could be estimated accurately by using spectral feature extraction and a hybrid inversion strategy. The results showed that the model based on principal components extracted by PLS had a good estimation accuracy and noise immunity and was the preferred method for LAI estimation. Furthermore, the comparative analysis results of various datasets showed that prior knowledge could improve the precision of the retrieved LAI, and using this information to constrain parameters (e.g., chlorophyll content or LAI), which make important contributions to the spectra, is the key to this improvement. In addition, among the PLS, BP-ANN, LS-SVR, and RFR methods, RFR was the optimal modeling algorithm in the paper, as indicated by the high R2 and low NRMSE in various datasets.

Hybrid frequency-domain full-waveform inversion using ray+Born sensitivity kernels

Full-waveform inversion (FWI) using the scattering integral (SI) approach is an explicit formulation of the inversion optimization problem. The inversion procedure is straightforward, and the dependence of the data residuals on the model parameters is clear. However, the biggest limitation associated with this approach is the huge computational cost in conventional exploration seismology applications. Modeling from each of the source and receiver locations is required to compute the update at every iteration, and that is prohibitively expensive, especially for 3D problems. To deal with this issue, we have developed a hybrid implementation of frequency-domain FWI, in which forward modeling is combined with ray tracing to compute the update. We use the sensitivity kernels computed from dynamic ray tracing to build the gradient. The data residual is still computed using finite-difference wavefield modeling. With ray theory, the Green’s function can be approximated using a coarser grid compared to wave-equation modeling. Therefore, the memory requirements, as well as the computational cost, are reduced significantly. Considering that in transmission FWI long-to-intermediate wavelengths are updated during the early iterations, we obtain accurate inverted models. The inversion scheme captured the anomaly embedded in the homogeneous background medium. For more complex models, the hybrid inversion method helps in improving the initial model with little cost compared with conventional SI inversion approaches. The accuracy of the inversion results shows the effectiveness of the hybrid approach for 3D realistic problems.

Hybrid inversion method and sensitivity analysis of inherent deformations of welded joints

In order to efficiently predict the welding deformation of large and complex welded structures based on the inherent deformation method, it is necessary to obtain the inherent deformations of each weld seam beforehand. In this paper, a new method was proposed to inverse inherent deformations by combining inherent deformation method and complex method. The validity of the proposed hybrid inversion method was proved by the comparison with the results of thermal-elastic-plastic (TEP) model the effectiveness of which had been demonstrated by the welding deformation and residual stress obtained from the butt-welded experiment. And the independence of the method on initial value is verified by inversion results using different initial complex shapes. Finally, the sensitivity analysis of inherent deformations was also carried out, and the analysis result shows that longitudinal shrinkage, transverse shrinkage and transverse curvature have a more significant effect on calculation accuracy than longitudinal curvature for the present welded plates.

Acoustic tomography based on hybrid wave propagation model for tree decay detection

Acoustic wave technologies have been used in wood defect detection for many years. Various tomographic imaging algorithms have been proposed to construct two dimensional acoustic velocity maps that serve as the scientific evidence of tree’s internal condition. Many previously proposed algorithms were based on the assumption that acoustic waves propagate along straight rays in the cross sections of trees. To simulate the acoustic wave propagation more realistically, this paper proposed a tomographic imaging method based on a hybrid wave propagation model (HWPM) that includes two velocity inversion phases: straight-ray inversion and curved-ray inversion. The straight-ray inversion was first applied to obtain the preliminary velocity distribution, followed by the curved-ray inversion to refine the velocity distribution. A velocity correction factor was determined for each grid cell following each inversion iteration, and then was used to derive a new velocity value for each corresponding cell. The maximum and minimum velocity constraints were imposed on the newly-computed velocities, and some velocity constraints of grid cells were also imposed to address the nonuniqueness problem commonly existed in velocity inversion and generate a more accurate tomographic image. To evaluate the effectiveness of the hybrid inversion method, we conducted multipath acoustic wave testing on three short log sections (one sound and two with artificial defect) in the laboratory and four live trees in Yangzhou Slender West Lake Park, Jiangsu Province, China. Time-of-flight data was collected by PiCUS Tomograph tool and used to generate tomographic images with both Simultaneous iterative reconstruction technique (SIRT) and the proposed hybrid inversion method to make a comparison. Micro-drilling tests were conducted on the live trees to determine the internal condition and served as the basis for evaluating the tomographic images. Our results indicate that the hybrid wave propagation model is effective in constructing acoustic tomographic images that are reasonably accurate in detecting the internal defects of urban trees.

Hybrid Inversion Method to Estimate Hydraulic Transmissivity by Combining Multiple-Point Statistics and a Direct Inversion Method

Inversion methods that rely on measurements of the hydraulic head h cannot capture the fine-scale variability of the hydraulic properties of an aquifer. This is particularly true for direct inversion methods, which have the further limitation of providing only deterministic results. On the other hand, stochastic simulation methods can reproduce the fine-scale heterogeneity but cannot directly incorporate information about the hydraulic gradient. In this work, a hybrid approach is proposed to join a direct inversion method (the comparison model method, CMM) and multiple-point statistics (MPS), for determination of a hydraulic transmissivity field T from a map of a reference hydraulic head $$h^\mathrm {(ref)}$$ and a prior model of the heterogeneity (a training image). The hybrid approach was tested and compared with pure MPS and pure CMM approaches in a synthetic case study. Also, sensitivity analysis was performed to test the importance of the acceptance threshold $$\delta $$ , a simulation parameter that allows one to tune the influence of $$h^\mathrm {(ref)}$$ on the final results. The transmissivity fields T obtained using the hybrid approach take into account information coming from the hydraulic gradient while simultaneously reproducing some of the fine-scale features provided by the training image. Furthermore, many realizations of T can be obtained thanks to the stochasticity of MPS. Nevertheless, it is not straightforward to exploit the correlation between the T maps provided by the CMM and the prior model introduced by the training image, because the former depends on the boundary conditions and flow settings. Another drawback is the growing number of simulation parameters introduced when combining two diverse methods. At the same time, this growing complexity opens new possibilities that deserve further investigation.

Finite element inversion method for interfacial stress analysis of composite single-lap adhesively bonded joint based on full-field deformation

A hybrid inversion method combining the finite element method and full-field displacement data was proposed to analyze the adhesive interface stress at a composite single-lap bonded joint. The displacement field distribution for the outer surface of the overlapped composite plate was measured through the two-dimensional digital image correlation method at different times by performing a tensile test. At the same time, the finite element analysis of the single-lap joint was carried out, which provided the data on structural deformation characteristics. Then, a polynomial interpolation method was used to establish the relation between the internal and external surface displacements. The displacements of the inner surface of the plate can be calculated from the measured displacement data of the outer surface of the plate by using the polynomial function. The displacements of the inner surface of the plate are regarded as the displacement load conditions for the outer and inner surfaces of the plate to establish the finite element model of the adhesive layer. The validity of the hybrid inversion method was proved by FEM analysis and experiments.

Hybrid geoacoustic inversion method and its application to different sediments

Bottom acoustic parameters have large effects on sound propagation both in shallow water and in deep water with an incomplete sound channel. A hybrid geoacoustic inversion method is proposed to invert for sound speed, density and attenuation coefficient based on the facts that the bottom acoustic parameters have different sensitivities to sound field at different ranges. The hybrid inversion method is applied to inversion for bottom parameter with different sediments in the Yellow Sea, East China Sea, and South China Sea and verified by using the core sampling measurements. The relationships between the sediments types and the bottom acoustic parameters are given. The differences of the sediment acoustic parameters between sandy silty(or silty sand) and clay(or mud) sediment at low frequency are discussed in the end. [Work supported by the National Natural Science Foundation of China under Grant No. 10434012 and Grant No. 41561144006.]

Estimation and Mapping of Winter Oilseed Rape LAI from High Spatial Resolution Satellite Data Based on a Hybrid Method

Leaf area index (LAI) is a key input in models describing biosphere processes and has widely been used in monitoring crop growth and in yield estimation. In this study, a hybrid inversion method is developed to estimate LAI values of winter oilseed rape during growth using high spatial resolution optical satellite data covering a test site located in southeast China. Based on PROSAIL (coupling of PROSPECT and SAIL) simulation datasets, nine vegetation indices (VIs) were analyzed to identify the optimal independent variables for estimating LAI values. The optimal VIs were selected using curve fitting methods and the random forest algorithm. Hybrid inversion models were then built to determine the relationships between optimal simulated VIs and LAI values (generated by the PROSAIL model) using modeling methods, including curve fitting, k-nearest neighbor (kNN), and random forest regression (RFR). Finally, the mapping and estimation of winter oilseed rape LAI using reflectance obtained from Pleiades-1A, WorldView-3, SPOT-6, and WorldView-2 were implemented using the inversion method and the LAI estimation accuracy was validated using ground-measured datasets acquired during the 2014–2015 growing season. Our study indicates that based on the estimation results derived from different datasets, RFR is the optimal modeling algorithm amidst curve fitting and kNN with R2 > 0.954 and RMSE <0.218. Using the optimal VIs, the remote sensing-based mapping of winter oilseed rape LAI yielded an accuracy of R2 = 0.520 and RMSE = 0.923 (RRMSE = 93.7%). These results have demonstrated the potential operational applicability of the hybrid method proposed in this study for the mapping and retrieval of winter oilseed rape LAI values at field scales using multi-source and high spatial resolution optical remote sensing datasets. Details provided by this high resolution mapping cannot be easily discerned at coarser mapping scales and over larger spatial extents that usually employ lower resolution satellite images. Our study therefore has significant implications for field crop monitoring at local scales, providing relevant data for agronomic practices and precision agriculture.

Estimating crop chlorophyll content with hyperspectral vegetation indices and the hybrid inversion method

ABSTRACTA hybrid inversion method was developed to estimate the leaf chlorophyll content (LCC) and canopy chlorophyll content (CCC) of crops. Fifty hyperspectral vegetation indices (VIs), such as the photochemical reflectance index (PRI) and canopy chlorophyll index (CCI), were compared to identify the appropriate VIs for crop LCC and CCC inversion. The hybrid inversion models were then generated from different modelling methods, including the curve-fitting and least squares support vector regression (LS-SVR) and random forest regression (RFR) algorithms, by using simulated Compact High Resolution Imaging Spectrometer (CHRIS) datasets that were generated by a radiative transfer model. Finally, the remote-sensing mapping of a CHRIS image was completed to test the inversion accuracy. The results showed that the remote-sensing mapping of the CHRIS image yielded an accuracy of R2 = 0.77 and normalized root mean squared error (NRMSE) = 17.34% for the CCC inversion, and an accuracy of only R2 = 0.33 and NRMSE = 26.03% for LCC inversion, which indicates that the remote-sensing technique was more appropriate for obtaining chlorophyll content at the canopy scale (CCC) than at the leaf scale (LCC). The estimated results of various VIs and algorithms suggested that the PRI and CCI were the optimal VIs for LCC and CCC inversion, respectively, and RFR was the optimal method for modelling.

A new hybrid inversion method for parametric curved faults and its application to the 2008 Wenchuan (China) earthquake

A new hybrid inversion method for parametric curved faults and its application to the 2008 Wenchuan (China) earthquake

Estimation of crop LAI using hyperspectral vegetation indices and a hybrid inversion method

Leaf area index (LAI) is an important indicator of crop growth. In this paper, a hybrid inversion method was developed to estimate the LAI values of crops. Based on PROSAIL simulation datasets, 43 hyperspectral vegetation indices (VIs), including the optimized soil-adjusted vegetation index (OSVAI) and modified triangular vegetation index (MTVI2), were analyzed to identify optimal VIs for estimating LAI values. Hybrid inversion models were then built to determine the relationships between optimal simulated VIs and the LAI values (generated by the PROSAIL model) using modeling methods, including curve fitting, artificial neural network (ANN) and random forest regression (RFR) algorithms. Finally, remote sensing mapping of a Compact High Resolution Imaging Spectrometer (CHRIS) image was completed using the inversion model to verify the LAI estimation accuracy. The remote sensing mapping of the CHRIS image yielded an accuracy of R2=0.928 and RMSE=0.485 for OSAVI and R2=0.910 and RMSE=0.554 for MTVI2, demonstrating the feasibility of high-accuracy estimation of crop LAI using hyperspectral VIs and a hybrid inversion method. The estimation results of various VIs suggested that the identification of the appropriate VIs is critical to improve the inversion accuracy. In addition, to obtain the appropriate VIs, the factors must be evaluated with respect to two aspects, i.e., the sensitivity to target parameters and the insensitivity to interference. In this study, OSVAI and MTVI2 were sensitive to LAI and relatively insensitive to the effects of interference factors, such as chlorophyll, soil background, sky scattered light and observed geometry. Therefore, these indices could be primarily used as VIs for an LAI estimation. The inversion results of different datasets demonstrated that prior information is critical for improving the inversion accuracy and identifying the optimal VIs. Additionally, based on the comparison of the curve fitting, ANN, and RFR algorithms, RFR was an optimal method for modeling in this study, as indicated by the higher R2 and lower RMSE values for different datasets and various VIs.

A hybrid inversion method of damped least squares with simulated annealing used for Rayleigh wave dispersion curve inversion

Surface wave methods are becoming increasingly popular in many geotechnical applications and in earthquake seismology due to their noninvasive characteristics. Inverse surface wave dispersion curves are a crucial step in most surface wave methods. Many inversion methods have been applied to surface wave dispersion curve inversion, including linearized inversion and nonlinearized inversion methods. In this study, a hybrid inversion method of Damped Least Squares (DLS) with Very Fast Simulated Annealing (VFSA) is developed for multi-mode Rayleigh wave dispersion curve inversion. Both synthetic and in situ field data were used to verify the validity of the proposed method. The results show that the proposed method is superior to the conventional VFSA method in aiming at global minimum, especially when parameter searching space is adjacent to real values of the parameters. The advantage of the new method is that it retains both the merits of VFSA for global search and DLS for local search. At high temperatures, the global search dominates the runs, while at a low temperatures, the local search dominates the runs. Thus, at low temperatures, the proposed method can almost directly approach the actual model.

Numerical simulation of (T 2, T 1) 2D NMR and fluid responses

One-dimensional nuclear magnetic resonance (1D NMR) logging technology is limited for fluid typing, while two-dimensional nuclear magnetic resonance (2D NMR) logging can provide more parameters including longitudinal relaxation time (T 1) and transverse relaxation time (T 2) relative to fluid types in porous media. Based on the 2D NMR relaxation mechanism in a gradient magnetic field, echo train simulation and 2D NMR inversion are discussed in detail. For 2D NMR inversion, a hybrid inversion method is proposed based on the damping least squares method (LSQR) and an improved truncated singular value decomposition (TSVD) algorithm. A series of spin echoes are first simulated with multiple waiting times (T W s) in a gradient magnetic field for given fluid models and these synthesized echo trains are inverted by the hybrid method. The inversion results are consistent with given models. Moreover, the numerical simulation of various fluid models such as the gas-water, light oil-water, and vicious oil-water models were carried out with different echo spacings (T E s) and T W s by this hybrid method. Finally, the influences of different signal-to-noise ratios (SNRs) on inversion results in various fluid models are studied. The numerical simulations show that the hybrid method and optimized observation parameters are applicable to fluid typing of gas-water and oil-water models.