Final Inversion Results Research Articles

A petrophysically driven seismic inversion method for the total organic carbon content of source rocks

Organic carbon content is the main index for evaluating organic matter abundance of source rocks, and it is still difficult to quantitatively predict total organic carbon (TOC) in source rocks based on seismic data. The study of seismic fluid identification driven by petrophysics can help to understand the fluid characteristics and distribution patterns of subsurface oil and gas reservoirs. First, this paper clarifies the sweet spot parameters (parameters characterizing hydrocarbon enrichment) and sensitive elastic parameters (a parameter characterizing the nature of an ideal elastic body) of source rocks through theoretical petrophysical modeling. Next, the paper establishes the relationship between sensitive elastic parameters and sweet spot parameters TOC and constructs a statistical petrophysical model that can characterize the relationship between the two on this basis. And then we construct the joint distribution of TOC and elastic impedance through the Bayesian theoretical framework to obtain the maximum posterior probability estimate as the final TOC inversion results of source rocks. Our method successfully predicts the spreading of high-quality source rocks in the Wen4 Section of Lufeng 13 Subsag, and the inversion results are within an uncertainty range of ±14 m for well data, which proves the reliability of the method. The prediction results show that the organic matter abundance of source rocks in the Wen4 Section is high, and the organic carbon content is generally higher than 2%, which provides a reliable basis for the further implementation of the resource scale of the depression and the clarification of the hydrocarbon-rich area, which provides technical support for the evaluation of the source rocks of the new depression in the new area.

Resolution enhancement of 2D controlled-source electromagnetic images by use of point-spread function inversion

The marine controlled-source electromagnetic technique is employed both in large-scale geophysical applications as well as within the exploration of hydrocarbons and gas hydrates. Because of the diffusive character of the EM field, only very low frequencies are used, leading to inversion results with low resolution. In this paper, we calculated the resolution matrix associated with the inversion and derived the corresponding point-spread functions. The PSFs provided information about how much the actual inversion was blurred. Using a space-varying deconvolution can thus further improve the inversion result. The actual deblurring was carried out using the nonnegative flexible conjugate gradient least-squares (NN-FCGLS) algorithm, which is a fast iterative restoration technique. To attain completeness, we also introduced the results obtained using a blind deconvolution algorithm based on the maximum likelihood estimation with unknown PSFs. The potential of the proposed approach has been demonstrated using both complex synthetic data and field data acquired at the Wisting oil field in the Barents Sea. In both cases, the resolution of the final inversion result was improved and showed greater agreement with the known target area.

Comparing Adjoint Waveform Tomography Models of California Using Different Starting Models

AbstractAdjoint waveform tomography (AWT) sits at the cutting edge of seismic tomography on local, regional, and global scales. However, the choice in starting model may have a significant impact on the final inversion results. In this paper, we present 3 AWT models of California that are based on different starting models. We chose three models that were inverted at different scales: SPiRaL, a global travel‐time tomography model (Simmons et al., 2021, 10.1093/gji/ggab277), CSEM_NA, a regional adjoint tomography model of North America and the North Atlantic (Krischer et al., 2018, 10.1029/2017JB015289), and WUS256, a regional adjoint tomography model of the western US (Rodgers et al., 2022, https://doi.org/10.1029/2022JB024549). We then inverted three AWT models using the same source and receiver set. We ran each model over three period bands: 30–100 s, 25–100 s, and 20–80 s. Once the iterations were finalized, we used five methods of testing model similarity in both the model and data space. We conclude that the choice of starting model has a minimal impact on long wavelength models if an appropriate multi‐scale inversion approach is used.

Three-dimensional inversion of semi-airborne electromagnetic data with a second-order finite-element forward solver

SUMMARYThe analysis of controlled-source electromagnetic (EM) data recorded with semi-airborne exploration systems requires advanced simulation and inversion tools that are capable of handling realistic survey geometries. Semi-airborne EM setups with elongated transmitters deployed in mountainous terrain prohibit the exploitation of secondary-field formulations in numerical approximations without producing hardly quantifiable errors. Building upon the open-source software custEM for forward modeling and pyGIMLi for geophysical inversion, we present an inverse modeling procedure based on highly accurate second-order finite-element forward solutions on irregular grids and fast-converging Gauss–Newton minimization. Using the total-field formulation of the electric field approach in combination with a direct solver enables calculating explicit sensitivities with comparatively cheap back-substitutions for thousands of ground and airborne receiver stations in multiple flight areas. Second-order basis functions show general superiority over first-order basis-functions regarding the accuracy and performance of the forward problem. Beyond that, synthetic and real data inversion studies related to semi-airborne geometries indicate that second-order basis functions help particularly to avoid high modeling errors for the weakest field components and artifacts in the vicinity of transmitters or at the surface. This leads generally to a better convergence and final inversion results of higher robustness and quality. The presented tools are freely available such as the underlying software.

Retrieval of 2-D Ocean Total Surface Current From Sentinel-1 Doppler Frequency Shift Using 2-D Kalman Filtering

Synthetic aperture radar (SAR) has all-weather, all-day, large-area observation capability and can measure ocean total surface currents with Doppler frequency shift. However, conventional SAR can only obtain the radial velocity of the ocean total surface current. In this letter, we propose a method for inverting ocean total surface current vectors using a two-dimensional (2D) Kalman filter and a priori information about ocean current fields from Ocean Surface Current Analyses Real-time (OSCAR). We establish a complete filtering process including filter creation, filtering path selection and fusion of filtering results. We construct the Kalman filter according to the motion characteristics of ocean currents and transform the ocean surface current vector inversion problem into a filtering problem. The introduction of two-dimensional filtering can better adapt to the directionality of ocean currents. Furthermore, we design the filtering path to obtain smoother filtering results. In order to synthesize the filtering results of different filtering paths, we use the Covariance Intersection (CI) fusion method in distributed fusion to obtain the final ocean current vector inversion results. The accuracy of the inversion is verified by the measured data. The Root Mean Square Error (RMSE) of the proposed method with the mean Doppler error of 5.43Hz is 0.182 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m/s</i> in eastward speed and 0.141 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m/s</i> in northward speed. The reduction is 0.009 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m/s</i> and 0.029 <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m/s</i> against OSCAR.

Topography effect on ambient noise tomography: a case study for the Longmen Shan area, eastern Tibetan Plateau

SUMMARY Ambient noise tomography (ANT) is a widely used method to obtain shear wave velocity structure in the crust and upper mantle. Usually, the topography is assumed to have negligible effect on the resulting models. This, however, might not be proper in regions with large topographic variation, such as plateau edges, submarine slopes and volcanic islands. In this study, we use synthetics from waveform-based numerical simulation to quantify the topography effect on ANT in the Longmen Shan area, eastern Tibetan Plateau margin. Three kinds of models are used in forward simulation to obtain theoretical waveforms, including Case1: the layered model, Case2: the layered model with topographic variation and Case3: the flattened model of Case2. The final inversion results show that the bias of ANT is negligible in the blocks with relatively flat topography, such as the interior regions of the Tibetan Plateau and the Sichuan Basin. However, for the Longmen Shan boundary zone with significant topographic variation (∼4 km), the shear wave velocity image has an obvious negative bias that can reach up to −4 per cent. The maximum depth of bias is ∼5 km, which is mirrored with the maximum topographic elevation difference of the region, and the average bias disappears as the depth decreases to the surface (0 km) or increases to three times of the maximum influence depth (∼15 km). The horizontal distribution of the tomographic bias is almost linearly related to the topographic elevation difference with a slope of −1.04 and a correlation coefficient of 0.90 at maximum influence depth. According to this first-order correction formula and the decreasing trend of average bias with depth, the topography effect on ANT can be suppressed to a certain extent.

Seismic acoustic full waveform inversion based on the steepest descent method and simple linear regression analysis

Full waveform inversion (FWI) is a high-resolution imaging tool in seismic exploration. The steepest descent (SD) method is the simplest local optimization algorithm to update the P-wave velocity model in acoustic FWI, but it takes more iterations than other algorithms due to its inefficient search direction. In this study, we provide a SDSLR method, which can significantly shorten the convergence process of the SD method by using the simple linear regression (SLR) analysis. The SLR analysis has two important effects in this method: compute a SLR model to approximately estimate the recent variation trend of P-wave velocity model and directly predict the inversion result of the SD method of the next iteration. Based on the prediction of the SLR analysis, the SDSLR method can obtain the final inversion result of the traditional SD method with fewer iterations. Three numerical examples have tested the performance of the SDSLR method. Results show that the SDSLR method has great potential in constructing high-velocity anomalies. The computational efficiency of the SDSLR method is similar to that of the SD and L-BFGS methods, while the convergence rate and accuracy of the SDSLR method are clearly better than those of the SD and L-BFGS methods.

Quantitative Sound Speed Imaging of Cortical Bone and Soft Tissue: Results From Observational Data Sets.

This work presents the first quantitative ultrasonic sound speed images of ex vivo limb cross-sections containing both soft tissue and bone using Full Waveform Inversion (FWI) with level set (LS) and travel time regularization. The estimated bulk sound speed of bone and soft tissue are within 10% and 1%, respectively, of ground truth estimates. The sound speed imagery shows muscle, connective tissue and bone features. Typically, ultrasound tomography (UST) using FWI is applied to imaging breast tissue properties (e.g. sound speed and density) that correlate with cancer. With further development, UST systems have the potential to deliver volumetric operator independent tissue property images of limbs with non-ionizing and portable hardware platforms. This work addresses the algorithmic challenges of imaging the sound speed of bone and soft tissue by combining FWI with LS regularization and travel time methods to recover soft tissue and bone sound speed with improved accuracy and reduced soft tissue artifacts when compared to conventional FWI. The value of leveraging LS and travel time methods is realized by evidence of improved bone geometry estimates as well as promising convergence properties and reduced risk of final model errors due to un-modeled shear wave propagation. Ex vivo bulk measurements of sound speed and MRI cross-sections validates the final inversion results.

Dispersion measurement from ultra-short ambient noise using phase-weighted stacking in urban areas

Passive surface wave methods that utilize ambient noise to investigate underground space have been widely used in densely populated urban areas. As an important step in imaging from ambient noise, dispersion measurement seriously affects the accuracy of the final inversion results. Linear stacking, the most commonly used stacking method in dispersion measurement, usually relies on the long observation time to obtain Green's functions with high signal-to-noise. However, it is sometimes difficult to ensure sufficient observation time for passive surface wave methods for exploration efficiency and environmental restrictions in urban areas, making dispersion measurement from ultra-short noise important and necessary. Considering the limitations of linear stacking, we compared the dispersion images obtained by linear stacking, phase-weighted stacking (PWS), and time-frequency phase-weighted stacking using ultra-short ambient noise to find an appropriate stacking way. Synthetic experiments show that PWS can obtain better cross-correlation functions and dispersion spectra with fewer noise segments. Two field cases further verify the reliability of applying PWS in dispersion measurement from several minutes of the continuous noise record by analyzing the phase velocities error or comparing the inversion results with the drilling data. Both synthetic experiments and field examples illustrate PWS can be used as an efficient and economical method to meet the needs of ultra-short-time imaging and real-time monitoring of urban underground structures.

Three-dimensional inversion for sparse potential data using first-order system least squares with application to gravity anomalies in Western Queensland

SUMMARY We present an inversion algorithm tailored for point gravity data. As the data are from multiple surveys, it is inconsistent with regards to spacing and accuracy. An algorithm design objective is the exact placement of gravity observations to ensure no interpolation of the data is needed prior to any inversion. This is accommodated by discretization using an unstructured tetrahedral finite-element mesh for both gravity and density with mesh nodes located at all observation points and a first-order system least-squares (FOSLS) formulation for the gravity modelling equations. Regularization follows the Bayesian framework where we use a differential operator approximation of an exponential covariance kernel, avoiding the usual requirement of inverting large dense covariance matrices. Rather than using higher order basis functions with continuous derivatives across element faces, regularization is also implemented with a FOSLS formulation using vector-valued property function (density and its gradient). Minimization of the cost function, comprised of data misfit and regularization, is achieved via a Lagrange multiplier method with the minimum of the gravity FOSLS functional as a constraint. The Lagrange variations are combined into a single equation for the property function and solved using an integral form of the pre-conditioned conjugate gradient method (I-PCG). The diagonal entries of the regularization operator are used as the pre-conditioner to minimize computational costs and memory requirements. Discretization of the differential operators with the finite-element method (FEM) results in matrix systems that are solved with smoothed aggregation algebraic multigrid pre-conditioned conjugate gradient (AMG-PCG). After their initial setup, the AMG-PCG operators and coarse grid solvers are reused in each iteration step, further reducing computation time. The algorithm is tested on data from 23 surveys with a total of 6519 observation points in the Mt Isa–Cloncurry region in north–west Queensland, Australia. The mesh had about 2.5 million vertices and 16.5 million cells. A synthetic case was also tested using the same mesh and error measures for localized concentrations of high and low densities. The inversion results for different parameters are compared to each other as well as to lower order smoothing. Final inversion results are shown with and without depth weighting and compared to previous geological studies for the Mt Isa–Cloncurry region.

Seismic inversion via closed-loop fully convolutional residual network and transfer learning

Because deep-learning networks can “learn” the complex mapping function between labeled inputs and outputs, they have shown great potential in seismic inversion. Conventional deep-learning algorithms require a large amount of labeled data for sufficient training. However, in practice, the number of well logs is limited. To address this problem, we have adopted a closed-loop fully convolutional residual network (FCRN) combined with a transfer learning strategy for seismic inversion. This closed-loop FCRN consists of an inverse network and a forward network. The inverse network predicts the inversion target from seismic data, whereas the forward network calculates seismic data from the inversion target. The inverse network is initialized by pretraining on the Marmousi2 model and is fine-tuned with the limited labeled data around the wells through transfer learning, to suit the target seismic data. The forward network is initialized by training with the limited labeled data around the wells. In this way, the closed-loop network is well initialized to ensure relatively good convergence. Then, the misfit of the limited labeled data and the error between the true and the forward seismic data are used to regularize the training of the initialized closed-loop network. The inverse network of the optimized closed-loop network is used to obtain the final inversion results. Our workflow can be used for velocity, density, and impedance inversion from poststack seismic data. We take velocity inversion as an example to illustrate the effectiveness of the method. The experimental results show that closed-loop FCRN with transfer learning is superior to open-loop FCRN with better lateral continuity and velocity details. Closed-loop FCRN can effectively predict velocity with high accuracy on synthetic data, has good antinoise performance, and can also be effectively used for field data with spatial heterogeneity.

3D aquifer characterization of the Hermalle-sous-Argenteau test site using crosshole ground-penetrating radar amplitude analysis and full-waveform inversion

To improve the understanding of flow and transport processes in the critical zone, high-resolution and accurate estimation of the small-scale heterogeneity is essential. Preferential flow paths related to high-porosity layers and clay lenses in gravel aquifers greatly affect flow and transport processes in the subsurface, and their high electrical contrast to their surrounding matrix and limited extent can act as low-velocity electromagnetic waveguides. In the past decade, time-domain full-waveform inversion (FWI) of crosshole ground-penetrating radar (GPR) data has shown to provide 2D decimeter-scale resolution images of relative permittivity and electrical conductivity of the subsurface, which can be related to porosity and soil texture. Most studies using crosshole GPR FWI resolved high-porosity zones that were identified by an amplitude analysis approach. But clay lenses or zones with higher electrical conductivity that act as low-velocity waveguides are hard to distinguish in the measured data and amplitude analysis because of the absence of characteristic wave-propagation features. We have investigated a set of nine crosshole GPR data sets from a test site in Hermalle-sous-Argenteau near the Meuse River in Belgium to characterize the aquifer within a decimeter-scale resolution and to improve the understanding of a previously performed heat tracer experiment. Thereby, we extend the amplitude analysis to identify two different types of low-velocity waveguides either caused by an increased porosity or a higher electrical conductivity (and higher porosity). Combining the GPR amplitude analysis for low-velocity waveguide zones with the standard FWI results provided information on waveguide zones, which modified the starting models and further improved the FWI results. Moreover, an updated effective source wavelet is estimated based on the updated permittivity starting models. In comparison with the traditional FWI results, the updated FWI results present smaller gradient of the medium properties and smaller root-mean-squared error values in the final inversion results. The nine crosshole sections are used to generate a 3D image of the aquifer and allowed a detailed analysis of the porosity distribution along the different sections. Consistent structures of the permittivity and electrical conductivity show the robustness of the updated FWI results. The aquifer structures obtained by the FWI results agree with those results of the heat tracer experiment.

Retrieving Crop Leaf Chlorophyll Content Using an Improved Look-Up-Table Approach by Combining Multiple Canopy Structures and Soil Backgrounds

Leaf chlorophyll content (LCC) is a pivotal parameter in the monitoring of agriculture and carbon cycle modeling at regional and global scales. ENVISAT MERIS and Sentinel-3 OLCI data are suitable for use in the global monitoring of LCC because of their spectral specifications (covering red-edge bands), wide field of view and short revisit times. Generally, remote sensing approaches for LCC retrieval consist of statistically- and physically-based models. The physical approaches for LCC estimation require the use of radiative transfer models (RTMs), which are more robust and transferrable than empirical models. However, the operational retrieval of LCC at large scales is affected by the large variability in canopy structures and soil backgrounds. In this study, we proposed an improved look-up-table (LUT) approach to retrieve LCC by combining multiple canopy structures and soil backgrounds to deal with the ill-posed inversion problem caused by the lack of prior knowledge on canopy structure and soil-background reflectance. Firstly, the PROSAIL-D model was used to simulate canopy spectra with diverse imaging gometrics, canopy structures, soil backgrounds and leaf biochemical contents, and the canopy spectra were resampled according to the spectral response functions of ENVISAT MERIS and Sentinel-3 OLCI instruments. Then, an LUT that included 25 sub-LUTs corresponding to five types of canopy structure and five types of soil background was generated for LCC estimation. The mean of the best eight solutions, rather than the single best solution with the smallest RMSE value, was selected as the retrieval of each sub-LUT. The final inversion result was obtained by calculating the mean value of the 25 sub-LUTs. Finally, the improved LUT approach was tested using simulations, field measurements and ENVISAT MERIS satellite data. A simulation using spectral bands from the MERIS and Sentinel-3 OLCI simulation datasets yielded an R2 value of 0.81 and an RMSE value of 10.1 μg cm−2. Validation performed well with field-measured canopy spectra and MERIS imagery giving RMSE values of 9.9 μg cm−2 for wheat and 9.6 μg cm−2 for soybean using canopy spectra and 8.6 μg cm−2 for soybean using MERIS data. The comparison with traditional chlorophyll-sensitive indices showed that our improved LUT approach gave the best performance for all cases. Therefore, these promising results are directly applicable to the use of ENVISAT MERIS and Sentinel-3 OLCI data for monitoring of crop LCC at a regional or global scale.

Retrieval of Tropospheric Refractivity Profiles Using Slant Tropospheric Delays Derived From a Single Ground‐Based Global Navigation Satellite System Station

AbstractThe Global Navigation Satellite System (GNSS) has proved to be a powerful tool for applications in meteorology. In this study, we propose a novel slant tropospheric delay (STD) model to obtain the vertical distribution of atmospheric refractivity based on a single ground‐based GNSS receiver. The new model is used to convert the STD into a function of the vertical gradient of temperature, and it is divided into two layers (above and below the tropopause) for integration. The optical vertical gradient of temperature can be estimated according to the STD obtained from the GNSS observations from a higher satellite elevation angle. The distribution of atmospheric refractivity can then be derived from the vertical gradient of temperature and the surface atmospheric refractivity. Moreover, to further improve the accuracy of the STD model‐derived atmospheric refractivity, we correct it using a “theoretical retrieval” method based on the STDs obtained at a lower elevation angle. The optical ranges of theoretical retrieval are obtained above and below 5 km. Finally, a search is performed for the value of atmospheric refractivity that best fits the model equations, and this value is taken as the final inversion result. Data collected from eight GNSS stations and nearby radiosonde stations in 2016 were used to verify the new method. Using the radiosonde‐derived values as a reference, the accuracy of the STD model‐derived atmospheric refractivity was improved by 13.4% compared with the traditional technique. In addition, again using the radiosonde‐derived values as a reference, the accuracy of the atmospheric refractivity derived with the optically corrected method was improved by 20.4% compared with the uncorrected STD model.

Passive seismic full waveform inversion using reconstructed body-waves for subsurface velocity construction

ABSTRACTFull waveform inversion (FWI) using passive seismic data can use amplitude, phase and travel time information from the data simultaneously. However, at least three challenges are involved in passive seismic full waveform inversion (PSFWI): a low signal-to-noise ratio (SNR), source location uncertainty and an unknown source wavelet. In this study, we propose a method that combines seismic interferometry and a source-independent inversion algorithm to solve these problems. Using seismic interferometry, the original passive seismic data recorded on the surface can be reconstructed into new virtual source records that have a relatively high SNR and certain source location. The source-independent algorithm eliminates the influence of source wavelet error on the final inversion results. Through numerical tests, we discuss the effects of passive source number and recording time on the inversion results and find that increasing the source number or recording time can improve inversion quality. We extract the background velocity model from the results of PSFWI and use it as the initial model of active source FWI. Least square reverse time migration (LSRTM) is then conducted to verify the accuracy of the inverted velocity models. The final results demonstrate that our PSFWI method can construct accurate long-wavelength velocity structures for subsequent active source FWI. The velocity model constructed using our successive inversion strategy can improve the LSRTM results.

Anisotropic full-waveform inversion of crosshole seismic data: A vertical symmetry axis field data application

Anisotropic waveform tomography (AWT) uses anisotropic traveltime tomography followed by anisotropic full-waveform inversion (FWI). Such an approach is required for FWI in cases in which the geology is likely to exhibit anisotropy. An important anisotropy class is that of transverse isotropy (TI), and the special case of TI media with a vertical symmetry axis (VTI) media is often used to represent elasticity in undeformed sedimentary layering. We have developed an approach for AWT that uses an acoustic approximation to simulate waves in VTI media, and we apply this approach to crosshole data. In our approach, the best-fitting models of seismic velocity and Thomsen VTI anisotropy parameters are initially obtained using anisotropic traveltime tomography, and they are then used as the starting models for VTI FWI within the acoustic approximation. One common problem with the acoustic approach to TI media is the generation of late-arriving (spurious) S-waves as a by-product of the equation system. We used a Laplace-Fourier approach that effectively damps the spurious S-waves to suppress artifacts that might otherwise corrupt the final inversion results. The results of applying AWT to synthetic data illustrate the trade-offs in resolution between the two parameter classes of velocity and anisotropy, and they also verify anisotropic traveltime tomography as a valid method for generating starting models for FWI. The synthetic study further indicates the importance of smoothing the anisotropy parameters before proceeding to FWI inversions of the velocity parameter. The AWT technique is applied to real crosshole field gathers from a sedimentary environment in Western Canada, and the results are compared with the results from a simpler (elliptical) anisotropy model. The transversely isotropic approach yields an FWI image of the vertical velocity that (1) exhibits a superior resolution and (2) better predicts the field data than does the elliptical approach.

Dynamic Convolution-based Misfit Function for Time Domain Full Waveform Inversion

Under the same propagation operator, the precision of the seismic wavelet determines whether synthetic data can match field data accurately. By constructing the convolution wavefield objective function, the source difference between simulated and observed data is ignored, thus avoiding the source wavelet estimation. Theoretically, this process has no restriction on the accuracy of the wavelet, and a multi-scale inversion strategy can be implemented by using a source wavelet with different dominant frequencies. When the propagation operator used does not conform with reality, even if both the wavelet and the parameter mode are accurate, it is impossible to simulate the full waveforms of the observed data. Meanwhile, the difference in the Green function brings new discrepancy to the convolution wavefield objective function and affects the final inversion results. The method presented in this paper is based on the convolution wavefield objective function. On the basis of an original single reference trace, we discuss the performance of the convolution wavefield-type objective function under multiple reference traces selected from different offsets. After introducing the changed wavefield information, the objective function has the ability to adapt to different types of data. The analysis shows that nonlinearity is significantly increased after introducing the different wavefield information and also increases with inversion frequency. Even for anisotropic data, it is still possible to give a relatively accurate structure at the low-frequency stage, which shows that the wavefield information from different offsets can help to weaken the artifacts introduced by operator mismatch, thus providing more possibilities for the application of acoustic wave equation inversion.

Characterization of full tensor properties of single-domain tetragonal 0.63Pb(Mg1/3Nb2/3)O3–0.37PbTiO3 single crystal using only one sample

Complete sets of piezoelectric, dielectric and elastic material constants are of great importance for both theoretical study and device design during applications. Usually several samples are needed to get the complete matrix properties. Property variation between different samples makes the obtained data difficult to achieve self-consistency. In this work, the combined pulse-echo ultrasound and inverse impedance spectroscopy method was adopted to determine the full tensor properties of [001]C–poled single domain 0.63Pb(Mg1/3Nb2/3)O3–0.37PbTiO3 single crystals. By using this method, only one small sample was needed, therefore self-consistency was easily achieved. The final inversion results were proved to be stable by changing the initial values. In addition, the obtained full matrix data were compared to those measured by combined resonance and ultrasonic method, which showed that our method exhibited high accuracy. This unique method provides a powerful tool for the accurate characterization of piezoelectric materials, especially those are highly segregated or difficult to grow.

Multi-model method for solving nonlinear transient inverse heat conduction problems

The multi-model inverse method for nonlinear inverse problems is established based on the multi-model control theory. First the model switching variable is chosen and several typical operating balance points in the workspace of the balance variable are selected. Then for each operating balance point the linear local model is established, and the local controller is designed for each linear local model. Finally, according to the instantaneous matching degree between the actual model and the local models, the inversion results of each local controller are weighted and synthesized to obtain the final inversion result. Numerical tests are implemented to solve the one-dimensional nonlinear inverse heat conduction problem by the multi-model inverse method associated with the dynamic matrix control (DMC) and DMC filter, respectively. Numerical results by the multi-model inverse method based on DMC demonstrate that the multi-model inverse method is a highly computationally efficient and accurate algorithm for inverse problems with complicated direct problems. Numerical results by the multi-model inverse method based on DMC filter show that the presented method can extend the applied field of the complicated linear inverse algorithms such as digital filter to the nonlinear inverse problems and it can obtain satisfactory inversion results.

Adaptive multi-step Full Waveform Inversion based on Waveform Mode Decomposition

Full Waveform Inversion (FWI) can be used to build high resolution velocity models, but there are still many challenges in seismic field data processing. The most difficult problem is about how to recover long-wavelength components of subsurface velocity models when seismic data is lacking of low frequency information and without long-offsets. To solve this problem, we propose to use Waveform Mode Decomposition (WMD) method to reconstruct low frequency information for FWI to obtain a smooth model, so that the initial model dependence of FWI can be reduced. In this paper, we use adjoint-state method to calculate the gradient for Waveform Mode Decomposition Full Waveform Inversion (WMDFWI). Through the illustrative numerical examples, we proved that the low frequency which is reconstructed by WMD method is very reliable. WMDFWI in combination with the adaptive multi-step inversion strategy can obtain more faithful and accurate final inversion results. Numerical examples show that even if the initial velocity model is far from the true model and lacking of low frequency information, we still can obtain good inversion results with WMD method. From numerical examples of anti-noise test, we see that the adaptive multi-step inversion strategy for WMDFWI has strong ability to resist Gaussian noise. WMD method is promising to be able to implement for the land seismic FWI, because it can reconstruct the low frequency information, lower the dominant frequency in the adjoint source, and has a strong ability to resist noise.