Abstract Nitric oxide (NO) regulates renal O2 consumption, but the source of NO mediating this effect is unclear. We explored the effects of renal NO production on O2 consumption using renal cortex from mice deficient (-/-) in endothelial (e) nitric oxide synthase (NOS). O2 consumption was determined polarographically in slices of cortex from control and eNOS-/- mice. NO production was stimulated by bradykinin (BK) or ramiprilat (Ram) in the presence or absence of an NOS inhibitor. Basal O2 consumption was higher in eNOS-/- mice than in heterozygous controls (919 +/- 46 vs. 1,211 +/- 133 nmol O(2). min(-1). g(-1); P < 0.05). BK and Ram decreased O2 consumption significantly less in eNOS-/- mice [eNOS-/-: BK -19.0 +/- 2.8%, Ram -20.5 +/- 3.3% at 10(-4) M; control: BK -29.5 +/- 2.5%, Ram -34 +/- 1.6% at 10(-4) M]. The NO synthesis inhibitor nitro-L-arginine methyl ester (L-NAME) attenuated this decrease in control but not eNOS-/- mice. An NO donor inhibited O2 consumption similarly in both groups independent of the presence of L-NAME. These results demonstrate that NO production by eNOS is responsible for regulation of renal O2 consumption in mouse kidney.

A least-squares curve-fitting program in which calculations of surface wave dispersion are used has been developed in order to compute an interpretation of empirical dispersion data in terms of a layered model of the earth. Input may consist of dispersion data (phase velocity versus wave period) for both Love and Rayleigh waves in any modes of propagation. Output consists of successive approximations of the values of parameters such as layer thicknesses, shear velocities, and densities which minimize the mean square of residuals of the empirical data with respect to theoretical dispersion curves calculated from the parameters. Tests made by applying the method to precisely computed theoretical dispersion curves demonstrate the validity of the method. In these, as many as six parameters of the original theoretical models are calculated under a wide variety of conditions from the dispersion data only. In other cases, the amount of information obtainable may be greater or smaller, depending on the quality of the input data.The New York-Pennsylvania dispersion data of Oliver et al. [1961] can be successfully interpreted by using additional information from seismic refraction and studies of nearby earthquakes in the area. A solution including the important effect of the mantle low-velocity channel gives a crustal thickness of 38.6 km, a crustal shear velocity of 3.64 km/sec, a shear velocity of 4.685 km/sec below the M discontinuity, and a ratio of 2.86/3.30 between crustal and subcrustal density values. The density measurement is a new result. The shear velocity structure derived here is consistent with results obtained by Katz from seismic refraction profiles in the same area. Additional data are needed in order to derive more detailed information on crustal structure.

Recent field tests illustrate the accuracy and consistency of calculating near-surface shear (S)-wave velocities using multichannel analysis of surface waves (MASW). S-wave velocity profiles (S-wave velocity vs. depth) derived from MASW compared favorably to direct borehole measurements at sites in Kansas, British Columbia, and Wyoming. Effects of changing the total number of recording channels, sampling interval, source offset, and receiver spacing on the inverted S-wave velocity were studied at a test site in Lawrence, Kansas. On the average, the difference between MASW calculated V s and borehole measured V s in eight wells along the Fraser River in Vancouver, Canada was less than 15%. One of the eight wells was a blind test well with the calculated overall difference between MASW and borehole measurements less than 9%. No systematic differences were observed in derived V s values from any of the eight test sites. Surface wave analysis performed on surface data from Wyoming provided S-wave velocities in near-surface materials. Velocity profiles from MASW were confirmed by measurements based on suspension log analysis.

This study evaluated the potential of using Multi-channel Spectral Analysis of Surface Wave (MASW) seismic techniques to image steeply dipping cavities in laterally inhomogeneous geological terrain. The primary test site was the Montague District, a historical gold mining area in Nova Scotia, Canada with numerous narrow steeply dipping mine workings, actively subsiding or collapsed crown pillars, and laterally inhomogeneous bedrock. Seismic surveys were conducted at two test sites using portable components and an effective geophone spacing of 1 m. A complimentary gravity survey was also conducted at one of the sites. Pre-processing focused on techniques which highlighted and then isolated the direct Rayleigh Waves for each waveform. Two MASW techniques were applied to the resulting pre-processed seismic sections; time delay mapping and shear velocity imaging. Both techniques showed the presence of time-delay or velocity anomalies where mine workings were mapped or inferred from surface subsidence patterns. Time-delay mapping was effective at determining the lateral position of the cavities, however, velocity imaging was able to generate images in both lateral distance and depth and thus has the greater potential to image both the shape and position of the cavities. Reduced velocity regions on the shear velocity images were consistent with the relative thickness of overburden at both test sites and the weakening of crown pillars at one site. Gravity surveying agreed with both the time-delay and velocity images and highlighted the use complimentary geophysical techniques to image near-surface cavities. Recommended future work includes additional field trials with rigorous ground truthing, improvements in the waveform processing methodology to reduce the processing time and the accuracy of depth resolution, and continued work in a related research program to quantify the relationships between seismic attributes and rock mass quality, subsidence potential, etc

High-frequency ( 2 Hz) Rayleigh wave phase velocities can be inverted to shear (S)-wave velocities for a layered earth model up to 30 m below the ground surface in many settings. Given S-wave velocity ( V S), compressional (P)-wave velocity ( V P), and Rayleigh wave phase velocities, it is feasible to solve for P-wave quality factor Q P and S-wave quality factor Q S in a layered earth model by inverting Rayleigh wave attenuation coefficients. Model results demonstrate the plausibility of inverting Q S from Rayleigh wave attenuation coefficients. Contributions to the Rayleigh wave attenuation coefficients from Q P cannot be ignored when Vs/ V P reaches 0.45, which is not uncommon in near-surface settings. It is possible to invert Q P from Rayleigh wave attenuation coefficients in some geological setting, a concept that differs from the common perception that Rayleigh wave attenuation coefficients are always far less sensitive to Q P than to Q S. Sixty-channel surface wave data were acquired in an Arizona desert. For a 10-layer model with a thickness of over 20 m, the data were first inverted to obtain S-wave velocities by the multichannel analysis of surface waves (MASW) method and then quality factors were determined by inverting attenuation coefficients.

A Gibson half-space model (a non-layered Earth model) has the shear modulus varying linearly with depth in an inhomogeneous elastic half-space. In a half-space of sedimentary granular soil under a geostatic state of initial stress, the density and the Poisson's ratio do not vary considerably with depth. In such an Earth body, the dynamic shear modulus is the parameter that mainly affects the dispersion of propagating waves. We have estimated shear-wave velocities in the compressible Gibson half-space by inverting Rayleigh-wave phase velocities. An analytical dispersion law of Rayleigh-type waves in a compressible Gibson half-space is given in an algebraic form, which makes our inversion process extremely simple and fast. The convergence of the weighted damping solution is guaranteed through selection of the damping factor using the Levenberg-Marquardt method. Calculation efficiency is achieved by reconstructing a weighted damping solution using singular value decomposition techniques. The main advantage of this algorithm is that only three parameters define the compressible Gibson half-space model. Theoretically, to determine the model by the inversion, only three Rayleigh-wave phase velocities at different frequencies are required. This is useful in practice where Rayleigh-wave energy is only developed in a limited frequency range or at certain frequencies as data acquired at manmade structures such as dams and levees. Two real examples are presented and verified by borehole S-wave velocity measurements. The results of these real examples are also compared with the results of the layered-Earth model. ?? Springer 2006.

The surface wave (S-wave) method has gained popularity in engineering practice for determining S-wave velocity depth profiles. A growing trend is towards the application of S-wave testing for spatially 2-D S-wave velocity tomography, ignoring the assumption of horizontally layered medium. A fourth-order velocity-stress finite difference method is used to perform numerical simulations of S-wave testing in earth models with lateral variation. Results show that the lateral heterogeneity induces a non-stationary property in the space domain, resulting in false depth-related dispersion or higher modes if conventional approach based on stationary assumption is used for the dispersion analysis. Artifacts maybe introduced in spatially 2-D S-wave velocity imaging if the effect of lateral heterogeneity is not accounted for. As a potential countermeasure, a high-lateral-resolution S-wave method is proposed to reduce the effect of lateral heterogeneity while maintaining the resolution and depth range of dispersion analysis. It consists of a walk-away survey and a phase-seaming procedure when synthesizing seismograms with different nearest source-to-receiver offset, allowing wide-wavelength dispersion analysis within a small spatial range. The proof of concept is given with several numerical examples. They show that the high-resolution S-wave method can greatly alleviate the effect of lateral heterogeneity and increase spatial resolution.

A 2-D full wavefield inversion method is presented for the processing of wide-aperture data. The diversity of information contained within such datasets may be handled in a complete manner by first matching the traveltimes of the main events and then progressing to waveform fitting of the data through explicit full wavefield modelling. Our wavefield inversion scheme is based upon a finite difference solution of the 2-D elastic wave equation in the time distance domain. The strength of adopting such an approach is the ability to generate all possible wave types within a given 2-D model (multiples, converted waves, etc.) and thus to simulate and accurately model complex seismic wavefields. The aim of the inversion is to find the 2-D P -wave velocity model that minimizes the least squared difference between the observed and synthetic data across the full range of offsets. Following extensive testing on synthetic data, the wavefield inversion scheme has been applied to wide-aperture real marine seismic streamer datasets. We present results from the synthetic testing and the wavefield inversion of wide-aperture real data out to 12 km offset that was recorded on a single streamer. Even though current computational restrictions allow only a small subsection of the data to be analysed, these examples demonstrate the potential value of wide-aperture 2-D full wavefield inversion.

Elastic Full Waveform Tomography (FWT) aims to reduce the misfit between recorded and modelled data, to deduce a very detailed model of elastic material parameters in the underground. The choice of the elastic model parameters to be inverted affects the convergence and quality of the reconstructed subsurface model. Using the Cross-Triangle-Squares (CTS) model three elastic parametrizations, Lam0108 parameters m1 = [0203, 0204, 0301], seismic velocities m2 = [Vp, Vs, 0301] and seismic impedances m3 = [Ip, Is, 0301] for far-offset reflection seismic acquisition geometries with explosive point sources and free-surface condition are studied. In each CTS model the three elastic parameters are assigned to three different geometrical objects that are spatially separated. The results of the CTS model study reveal a strong requirement of a sequential frequency inversion from low to high frequencies to reconstruct the density model. Using only high-frequency data, cross-talk artefacts have an influence on the quantitative reconstruction of the material parameters, while for a sequential frequency inversion only structural artefacts, representing the boundaries of different model parameters, are present. During the inversion, the Lam0108 parameters, seismic velocities and impedances could be reconstructed well. However, using the Lam0108 parametrization -artefacts are present in the 0203 model, while similar artefacts are suppressed when using seismic velocities or impedances. The density inversion shows the largest ambiguity for all parametrizations. However, the artefacts are again more dominant, when using the Lam0108 parameters and suppressed for seismic velocity and impedance parametrization. The afore mentioned results are confirmed for a geologically more realistic modified Marmousi-II model. Using a conventional streamer acquisition geometry the P-velocity, S-velocity and density models of the subsurface were reconstructed successfully and are compared with the results of the Lam0108 parameter inversion.

Time-lapse seismic data are widely used to monitor reservoir changes. Qualitative comparisons between baseline and monitor data sets or image volumes provide information about fluid and pressure effects within the reservoir during production. However, to perform real quantitative analysis of such reservoir changes, quantitative estimates of the elastic parameters are required as input parameters to rock-physics-based reservoir models. Full-waveform inversion has been proposed as a potential tool for retrieving subsurface properties, such as P- and S-wave velocities and density by fitting simulated waveforms to seismic data. An extension of this method to time-lapse applications seems straightforward, but, in fact, it requires more tailored processes such as double-difference waveform inversion (DDWI). We used realistic 2D synthetic pressure data examples to compare the performance of DDWI with that of two other inversion schemes: one using the same starting model for both inversions and the other starting the monitor inversion with the final baseline inversion model. The data simulation and inversion were based on acoustic theory. Although P-wave velocity changes were reliably recovered by each inversion method, DDWI was found to deliver the best results when perfectly repeated surveys were used. However, differencing the baseline and monitor data sets, as required by DDWI, could be found to be sensitive to the presence of survey nonrepeatability. To investigate the feasibility of using DDWI in practice, the dependence of DDWI on the quality of the baseline models and its robustness to survey nonrepeatability were studied with numerical tests. Various types of nonrepeatability were considered separately in the synthetic tests, including random noise, acquisition geometry mismatch, source wavelet discrepancy, and overburden velocity changes. A study of the correlation between the levels and types of nonrepeatability and the resulting contamination of the inversion results found that, for pressure data, DDWI was capable of inverting reliably for P-wave velocity changes under realistic survey nonrepeatability conditions.

The gradient of standard full waveform inversion attempts to map the data residuals to perturbations in the model. Such perturbations may include smooth background updates from the transmission components or high wavenumber updates from the reflection components. However, if we fix the reflection components using imaging, the gradient of what is referred to as reflection FWI (RFWI) admits mainly transmission background-type updates to the velocity model. The drawback of existing RFWI methods is that they lack an optimal image capable of producing reflections within the convex region of the optimization. Since the influence of velocity on the data is given mainly by its propagator(background) and perturbed (reflectivity) components, we optimize both components simultaneously using a modified objective function. Specifically, we invert for the velocity and image simultaneously with an objective function that fits the summation of the modeled data from the source and the image to the observed data. Since the objective function is quadratic with respect to the image, the inversion for the image is fast which meant to absorb mainly the amplitude residual. An application to Marmousi model shows that this method converges starting with a linearly increasing velocity, and with data free of frequencies below 4 Hz.

Abstract We have proposed a misfit function based on adaptive matching filtering (AMF) to tackle challenges associated with cycle skipping and local minima in full-waveform inversion (FWI). This AMF is designed to measure time-varying phase differences between observations and predictions. Compared with classical least-squares waveform differences, our misfit function behaves as a smooth, quadratic function with a broad basin of attraction. These characters are important because local gradient-based optimization approaches used in most FWI schemes cannot guarantee convergence toward true models if misfit functions include local minima or if the starting model is far away from the global minimum. The 1D and 2D synthetic experiments illustrate the advantages of the proposed misfit function compared with the classical least-squares waveform misfit. Furthermore, we have derived adjoint sources associated with the proposed misfit function and applied them in several 2D time-domain acoustic FWI experiments. Numerical results found that the proposed misfit function can provide good starting models for FWI, particularly when low-frequency signals are absent in recorded data.

Frequency-domain methods are well suited to the imaging of wide-aperture cross-hole data. However, although the combination of the frequency domain with the wavenumber domain has facilitated the development of rapid algorithms, such as diffraction tomography, this has also required linearization with respect to homogeneous reference media. This restriction, and association restrictions on source-receiver geometries, are overcome by applying inverse techniques that operate in the frequency-space domain. In order to incorporate the rigorous modelling technique of finite differences into the inverse procedure a nonlinear approach is used. To reduce computational costs the method of finite differences is applied directly to the frequency-domain wave equation. The use of high speed, high capacity vector computers allow the resultant finite-difference equations to be factored in-place. In this way wavefields can be computed for additional source positions at minimal extra cost, allowing inversions to be generated using data from a very large number of source positions. Synthetic studies show that where weak scatter approximations are valid, diffraction tomography performs slightly better than a single iteration of non-linear inversion. However, if the background velocities increase systematically with depth, diffraction tomography is ineffective whereas non-linear inversion yields useful images from one frequency component of the data after a single iteration. Further synthetic studies indicate the efficacy of the method in the time-lapse monitoring of injection fluids in tertiary hydrocarbon recovery projects.

Frequency-domain methods are well suited to the imaging of wide-aperture cross-hole data. However, although the combination of the frequency domain with the wavenumber domain has facilitated the development of rapid algorithms, such as diffraction tomography, this has also required linearization with respect to homogeneous reference media. This restriction, and association restrictions on source-receiver geometries, are overcome by applying inverse techniques that operate in the frequency-space domain. In order to incorporate the rigorous modelling technique of finite differences into the inverse procedure a nonlinear approach is used. To reduce computational costs the method of finite differences is applied directly to the frequency-domain wave equation. The use of high speed, high capacity vector computers allow the resultant finite-difference equations to be factored in-place. In this way wavefields can be computed for additional source positions at minimal extra cost, allowing inversions to be generated using data from a very large number of source positions. Synthetic studies show that where weak scatter approximations are valid, diffraction tomography performs slightly better than a single iteration of non-linear inversion. However, if the background velocities increase systematically with depth, diffraction tomography is ineffective whereas non-linear inversion yields useful images from one frequency component of the data after a single iteration. Further synthetic studies indicate the efficacy of the method in the time-lapse monitoring of injection fluids in tertiary hydrocarbon recovery projects.

Summary By specifying a discrete matrix formulation for the frequency090009space modelling problem for linear partial differential equations ('FDM' methods), it is possible to derive a matrix formalism for standard iterative non-linear inverse methods, such as the gradient (steepest descent) method, the Gauss090009Newton method and the full Newton method. We obtain expressions for each of these methods directly from the discrete FDM method, and we refer to this approach as frequency-domain inversion (FDI). The FDI methods are based on simple notions of matrix algebra, but are nevertheless very general. The FDI methods only require that the original partial differential equations can be expressed as a discrete boundary-value problem (that is as a matrix problem). Simple algebraic manipulation of the FDI expressions allows us to compute the gradient of the misfit function using only three forward modelling steps (one to compute the residuals, one to backpropagate the residuals, and a final computation to compute a step length). This result is exactly analogous to earlier backpropagation methods derived using methods of functional analysis for continuous problems. Following from the simplicity of this result, we give FDI expressions for the approximate Hessian matrix used in the Gauss090009Newton method, and the full Hessian matrix used in the full Newton method. In a new development, we show that the additional term in the exact Hessian, ignored in the Gauss090009Newton method, can be efficiently computed using a backpropagation approach similar to that used to compute the gradient vector. The additional term in the Hessian predicts the degradation of linearized inversions due to the presence of first-order multiples (such as free-surface multiples in seismic data). Another interpretation is that this term predicts changes in the gradient vector due to second-order non-linear effects. In a numerical test, the Gauss090009Newton and full Newton methods prove effective in helping to solve the difficult non-linear problem of extracting a smooth background velocity model from surface seismic-reflection data.

We present a discontinuous Galerkin finite-element method (DG-FEM) formulation with Convolutional Perfectly Matched Layer (CPML) absorbing boundary condition for 3-D elastic seismic wave modelling. This method makes use of unstructured tetrahedral meshes locally refined according to the medium properties (h-adaptivity), and of approximation orders that can change from one element to another according to an adequate criterion (p-adaptivity). These two features allow us to significantly reduce the computational cost of the simulations. Moreover, we have designed an efficient CPML absorbing boundary condition, both in terms of absorption and computational cost, by combining approximation orders in the numerical domain. A quadratic interpolation is typically used in the medium to obtain the required accuracy, while lower approximation orders are used in the CPMLs to reduce the total computational cost and to obtain a well-balanced workload over the processors. While the efficiency of DG-FEMs have been largely demonstrated for high approximation orders, we favour the use of low approximation orders as they are more appropriate to the applications we are interested in. In particular, we address the issues of seismic modelling and seismic imaging in cases of complex geological structures that require a fine discretization of the medium. We illustrate the efficiency of our approach within the framework of the EUROSEISTEST verification and validation project, which is designed to compare high-frequency (up to 4 Hz) numerical predictions of ground motion in the Volvi basin (Greece). Through the tetrahedral meshing, we have achieved fine discretization of the basin, which appears to be a sine qua non condition for accurate computation of surface waves diffracted at the basin edges. We compare our results with predictions computed with the spectral element method (SEM), and demonstrate that our method yields the same level of accuracy with computation times of the same order of magnitude.

In this paper,we investigate several source-independent methods of nonlinear full-waveform inversion of multicomponent elastic-wave data.This includes iterative estimation of source signature IES,standard trace normalization STN,and average trace normalization ATN inversion methods.All are based on the finite-element method in the frequency domain.One synthetic elastic crosshole model is used to compare the recovered images with all these methods as well as the known source signature KSS inversion method.The numerical experiments show that the IES method is superior to both STN and ATN methods in two-component,elastic-wave inversion in the frequency domain when the source signature is unknown.The STN and ATN methods have limitations associated with near-zero amplitudes or polarity reversals_ in traces from one of the components,which destroy the energy balance in the normalized traces and cause a loss of frequency information.But the ATN method is somewhat superior to the STN method in suppressing random noise and improving stability,as the developed formulas and the numerical experiments show.We suggest the IES method as a practical procedure for multicomponent seismic inversion.

We perform the full elastic waveform inversion in the frequency domain in a 2-D geometry. This method allows imaging of two physical seismic parameters, using vertical and horizontal field components. The forward problem is discretized using finite difference, allowing to simulate the full elastic wavefield propagation. Moreover, it is solved in the frequency domain, a fast approach for multisource and multireceiver acquisition. The non-linear inversion is based on a pre-conditioned gradient method, where Born and Rytov formulations are used to compute Fr chet derivatives. Parameter perturbations linearly depend on fields perturbations in the Born kernel, and on the generalized complex phases of fields in the Rytov kernel, giving different Fr chet derivatives. The gradient is pre-conditioned with the diagonal part of the inverse Hessian matrix, allowing to better estimate the stepping in the optimization direction. Non-linearity is taken into account by updating parameters at each iteration and proceeding from low to high frequencies. The latter allows as well to progressively introduce smaller wavelengths in parameter images. On a very simple synthetic example, we examine the way the inversion determines the V p ( P -wave velocity) and V s ( S -wave velocity) images. We highlight that, with a transmission acquisition, final parameter images weakly depend on the chosen formulation to compute Fr chet derivatives and on the inverted parameters choice. Of course, convergence strongly depends on the medium wavenumber illumination which is related somehow to the acquisition geometry. With a reflection acquisition, the Born formulation allows to better recover scatterers. Moreover, the medium anomalies are not well reconstructed when surface waves propagate in the medium. This may be due to the evanescent nature of surface waves. By selecting first body waves and then surface waves, we improve the convergence and properly reconstruct anomalies. This shows us that preparation of the seismic data before the inversion is as critical as the initial model selection.

In order to account for the effects of elastic wave propagation in marine seismic data, we develop a waveform inversion algorithm for acoustic-elastic media based on a frequency-domain finite-element modelling technique. In our algorithm we minimize residuals using the conjugate gradient method, which back-propagates the errors using reverse time migration without directly computing the partial derivative wavefields. Unlike a purely acoustic or purely elastic inversion algorithm, the Green's function matrix for our acoustic-elastic algorithm is asymmetric. We are nonetheless able to achieve computational efficiency using modern numerical methods. Numerical examples show that our coupled inversion algorithm produces better velocity models than a purely acoustic inversion algorithm in a wide variety of cases, including both single- and multi-component data and low-cut filtered data. We also show that our algorithm performs at least equally well on real field data gathered in the Korean continental shelf.

We present a regularized Gauss090009Newton (GN) inversion method for solving the elastic full-waveform inversion problem in the frequency domain. The main bottleneck of this method is the Jacobian matrix storage and the computational cost of calculating the GN step (the inner-loop calculation). In this work, we managed to reduce the memory usage by calculating the Jacobian matrix on the fly in each inner-loop iteration. By doing so the computational cost of calculating the GN step increases; however, this overhead is mitigated by compressing the field matrices using the adaptive cross approximation scheme. For some cases, this compressed implicit Jacobian scheme may even speed-up the GN step calculation and further regularizes the GN method. As examples, we present inversion results of cross-well seismic and surface seismic data.

To interpret subsurface structures properly, elastic wave propagation must be considered. Because elastic media are described by more parameters than acoustic media, elastic waveform inversion is more likely to be affected by local minima than acoustic waveform inversion. In a conventional elastic waveform inversion, P- and S-wave velocities are properly recovered, whereas density is difficult to reconstruct. For this reason, most elastic full-waveform inversion studies assume that density is fixed. Although several algorithms have been developed that attempt to describe density properly, their results are still not satisfactory.In this study, we propose a two-stage elastic waveform inversion strategy to recover density properly. The Lam0108 constants are first recovered while holding density fixed. While the Lam0108 constants and density are not correct under this assumption, the velocities obtained using these incorrect Lam0108 constants and constant density may be reliable. In the second stage, we simultaneously update density and Lam0108 constants using the wave equations expressed through velocities and density. While density is updated following the conventional method, the Lam0108 constants are updated using the gradient obtained by applying the chain rule. Among several parameter-selection strategies tested, only this strategy gives reliable solutions for both velocities and density. Our elastic full waveform inversion algorithm is based on the finite-element method and the backpropagation technique in the frequency domain. We demonstrate our inversion strategy for the modified Marmousi-2 model and the SEG/EAGE salt model. Numerical examples show that this new inversion strategy enhances density inversion results.

全波形反演技术是当前勘探地球物理领域的研究热点之一。新一轮的全波形反演研究触及了波场模拟、梯度估计、数据预处理、目标泛函的选择等诸多深层次的内容,逐渐将全波形反演对实际观测系统、地震数据等要求的局限性以及其具备的潜力揭示出来。通过对全波形反演理论和技术研究进展及应用现状的全面调研,介绍了全波形反演算法研究从时间域到频率域、再到混合域和拉普拉斯域的发展进程;阐明了全波形反演技术已实现海上地震资料应用但对陆上地震资料还没有真正成功实例的应用现状;着重分析了陆上资料全波形反演应用的瓶颈主要在于观测系统的限制、低频数据的缺失、数据预处理面临的挑战以及近地表条件和激发-接收的影响等;指出了发展分步骤、分尺度的反演方法和反演策略以及多种手段的有效联合是实现陆上资料全波形反演的有效途径。

Since the pioneering work of Tarantola, waveform inversion has emerged as a tool for estimating velocity models of the subsurface using pre-stack seismic data. The waveform inversions have usually been performed in the time or frequency domain, but this can make it difficult to recover long-wavelength components of the velocity model due to the high non-linearity of the objective function and the lack of low-frequency components in the field data. Instead, it has been recently suggested that Laplace-domain waveform inversion can circumvent these limitations. By using the zero-frequency component of the damped wavefield, the Laplace-domain waveform inversion can recover long-wavelength structures of the velocity model even if low-frequency components less than 5 Hz are unreliable or would be unusable in conventional inversions. The main drawback is that the penetration depth of the Laplace-domain inversion depends on the offset distance and the choice of Laplace damping constants. In this paper, we propose an improved Laplace Fourier-domain waveform inversion to compensate for these weak points. This is accomplished by exploiting low frequency components (less than 5 Hz) of the damped wavefield. The success of this technique arises from the 'mirage-like' resurrection of low-frequency components less than 5 Hz and the unique characteristics of the complex logarithmic wavefield. The latter is capable of separating the wavefield into amplitude and phase components, allowing us to simultaneously generate both long-wavelength and medium-short-wavelength velocity models. We successfully applied the Laplace Fourier-domain waveform inversion to a synthetic data set of the BP model calculated using the time-domain finite difference method. This not only produced a more refined velocity model when compared to Laplace-domain inversion results, but it also improved the penetration depth of the inversion. Furthermore, when the velocity model produced by the Laplace Fourier-domain waveform inversion was then used as an initial velocity model of a conventional frequency-domain inversion, we obtained an inverted velocity model containing almost every feature of the true BP model. We applied our two-step, Laplace-domain waveform inversion to field data and obtained a refined velocity model containing short- and long-wavelength components. To convince ourselves of the accuracy of the inversion results, we computed a synthetic model using the estimated source wavelet and our velocity model from the inversion, and we obtained a migrated image and angle-domain common-image gathers at several points by a reverse-time pre-stack depth migration in the frequency domain. The reconstructed synthetic data were in good agreement with the field data and most parts of the reflections in the image gathers were flattened.

When full waveform inversion (FWI) is performed in the Laplace-Fourier domain, Laplace-Fourier-domain wave modeling, using finite-difference or finite-element methods, is performed to compute the gradient direction. In this case, a complex impedance matrix is composed and factored by direct matrix solvers. Alternatively, iterative matrix solvers may be used. However, solving 3D problems with such methods requires excessive computer memory or computing time, which causes problems in the application of the Laplace-Fourier-domain FWI. To avoid computational overburden in 3D problems, we propose a time-Laplace-Fourier hybrid FWI, in which forward and backward modeling are performed in the time domain and other procedures are conducted in the Laplace-Fourier domain. Our hybrid FWI is applied to two groups of frequencies. Inversions for the first and second groups of frequencies correspond to the Laplace-domain FWI and the Laplace-Fourier-domain FWI, respectively. The graphic processing unit is used to speed up the hybrid inversion algorithm. To verify the feasibility of this technique, the 3D hybrid FWI is applied to the data recorded along the A1 line of the synthetic SEG/EAGE 3D salt model and 3D wide-azimuth real exploration data. Numerical examples show that the hybrid FWI yields reasonable subsurface velocity structures that contribute to the enhancement of reverse-time migration images.

Laplace-domain waveform inversion (WI) is generally used to generate smooth initial velocity models for frequency- or time-domain full-waveform inversion. However, in the inver- sion results of Laplace-domain WI, anomalies such as salt domes are sometimes shifted. We evaluate the "gradient-distor- tion effect" that causes undesirable changes in parameter up- dates and found that this is caused by the relationship between the partial derivatives of Laplace wavefields with re- spect to two different parameters. By analyzing the gradient of the Laplace-domain misfit function, we found that the gra- dient distortion effect increases as the Laplace constants used in the Laplace-domain WI decrease. The velocity model in- verted in the Laplace domain is generally blurred from shal- lower parameters to deeper parameters because the partial derivatives of the Laplace wavefields with respect to shallower

<p>全波形反演方法利用叠前地震波场的运动学和动力学信息重建地下速度结构,具有揭示复杂地质背景下构造与岩性细节信息的潜力.根据研究需要,全波形反演既可在时间域也可在频率域实现.频率域相对于时间域反演具有计算高效、数据选择灵活等优势.近十几年来频率域全波形反演理论在波场模拟方法、反演频率选择策略、目标函数设置方式、震源子波处理方式、梯度预处理方法等方面取得了进展.目标函数存在大量局部极值的特性是影响反射地震全波形反演效果的重要内在因素之一.如果将Laplace域波形反演、频率域阻尼波场反演、频率域波形反演三种方法有机结合,可以降低反演的非线性程度.</p>

近年来,随着计算机硬件水平的提高,地震全波形反演技术研究快速发展,并有效的推进了油气勘探.本综述主要对当前地震全波形反演主要存在反演非唯一性、噪声敏感性、初始模型强依赖、易陷入局部极值、计算量大等问题进行调研,重点介绍了地震全波形反演方法在时间域,频率域和Laplace域内的各种改进和优化的策略,为全波形反演方法研究提供参考.

<p>本文首先对20世纪80年代发展起来的全波形反演应用及其在勘探地球物理领域的发展进行了分析；其次，面对定量化、精细化的地震勘探要求，提出了将地震勘探全波形反演与其他数据处理环节或处理技术相结合的研究设想，并展望了全波形反演的发展趋势；最后，论述了全波形反演研究中地震波场数值模拟、反演初始速度模型获取、目标函数形式选择、寻优算法启用及各向异性介质中的应用等关键问题，并总结了通过Laplace域的全波形反演获取反演初始速度模型、结合射线追踪并充分发挥并行计算之于波动方程方法来模拟地震波场的巨大优势，及灵活选用反演目标函数形式和寻优算法更新速度模型参数来加快全波形反演方法的实用化进程。</p>

建立了天然气水合物似海底反射层(BSR)研究的全波形反演方法. 这是一种将 水平层状弹性介质的反射共中心点道集转换为截距时间-水平慢度域的反演方法. 反演过程 中采用了全局搜索方法与非线性局部搜索方法. 分两步进行. 第一步是根据走时数据应用非 常快速模拟算法求得速度结构的长波长分量. 第二步，利用波形资料用共轭梯度法求得速度 的短波长扰动分量. 这样，最后反演得到的速度结构模型包含了长波长与短波长分量. 反演 中利用了多网格参数化技术. 日本东南海海槽双BSR的速度结构的反演表明，全波形反演是 天然气水合物BSR研究的重要手段之一.

在频率域弹性波有限元正演方程的基础上,依据匹配函数(也就是观测数据和正演数据残差的二次范数)最小的准则,用矩阵压缩存储与LU分解技术来存储和求解频率域正演方程中的大型稀疏复系数矩阵、用可调阻尼因子的Levenberg-Marquard方法求解反演方程组,直接求取地下介质的弹性波速度,导出了频率域弹性波有限元最小二乘反演算法.为了利用地下地质体的分布规律,减少反演所求的未知数个数,本文又提出了规则地质块体建模方法引入到反演中来.经数值模型验证,在噪声干扰很大(噪声达到50%)或初始模型与真实模型相差很大的情况下,反演也能取得很满意的效果,证明本方法具有很好的抗噪性与"强壮性".

本文从VTI介质弹性波波动方程出发,借助VTI介质弹性参数和Thomsen参数,结合Kelvin-Christoffel方程,推导了VTI介质中准P波波动方程,并对VTI介质准P波进行了正演模拟。在正演模拟中,为了克服常规差分算子的数值频散,采用了25点优化差分算子;再依据最优化理论求取的优化系数建立了频率-空间域中准P波波动方程的差分格式;为了消除人为边界反射,根据特征分析方法并利用Kelvin-Christoffel方程,构建了VTI介质中准P波方程在不同边界和角点处的边界条件;再由准P波波动方程和边界条件,通过频率-空间域有限差分法,对准P波在均匀VTI介质、层状VTI介质和凹陷模型中的传播过程进行了数值正演模拟。通过正演模拟,得到了单频波波场、时间切片和共炮点记录,为研究地震成像及反演等提供了依据。

讨论了VTI介质中准P波频率空间域的边界条件。首先给出了VTI介质准P波波动方程,阐述了特征分析方法的基本原理,讨论了边界上的反射系数与入射角和度量准纵、横波各向异性强度因子的关系;然后利用特征分析法结合Kelvin-Christoffel方程,构造了准P波波动方程在不同边界和角点的频率域吸收边界条件,利用最佳匹配层法构造了衰减边界条件;最后利用数值模拟对构造的边界条件进行了验证。为了得到好的吸收效果,将吸收边界条件和衰减边界条件有机地结合起来,即先用最佳匹配层法衰减传播到边界的入射波能量,然后再用吸收边界条件吸收边界反射,最终使边界反射降低到可以忽略不计。数值模拟的共炮点记录说明了组合边界条件的良好效果。

波动方程有限差分方法能够较精确地模拟任意非均匀介质中的地震波场，但它本身存在着数值频散问题。在具有倾斜对称轴的横向各向同性介质(TTI介质)地震波正演模拟中，为了解决常规有限差分算子的数值频散问题，本文构造了频率—空间域qP波方程加权平均有限差分算子，求取了归一化相速度，并根据最优化理论中的高斯—牛顿法确定了加权平均差分算子的最优加权系数。利用常规差分算子和加权平均差分算子对归一化相速度进行了频散分析，并对均匀TTI介质(包括各向同性介质和椭圆各向异性介质)中的qP波地震波场进行了有限差分数值模拟。结果表明：加权平均有限差分算子具有较高的数值精度，能有效地压制常规有限差分算子的数值频散，为TTI介质频率—空间域qP波正演模拟奠定了基础。

有限差分方法是波场数值模拟的一个重要方法,但常规的有限差分法本身存在着数值频散问题，会降低波场模拟的精度与分辨率，为了克服常规差分算子的数值频散，本文采用25点优化差分算子，再根据最优化理论求取的优化系数，建立了频率空间域中弹性波波动方程的差分格式；为了消除边界反射，引入最佳匹配层，构造了各向同性介质中弹性波方程在不同边界和角点处的边界条件. 最后由弹性波波动方程和边界条件，通过频率域有限差分法，分别利用不同震源对弹性波在均匀各向同性介质、层状介质及凹陷模型中的传播过程进行了数值正演模拟，得到了单频波波场、时间切片和共炮点道集，为下一步的研究工作（如成像、反演）提供了研究基础.

<FONT face=Verdana>WTW(Wave equation traveltime+Waveform inversion)反演是基于波动方程的走时反演（WT反演）和波形反演的联合反演方法.WT反演利用波动方程计算走时和走时关于速度的导数，和传统以射线为基础的走时反演相比，具有不必射线追踪、不必拾取初至、不必高频假设以及初始模型和实际模型差别较大时也能较好收敛等优点，但WT反演与波形反演相比其结果分辨率低.与之互补的是，波形反演的反演结果分辨率高，但是当所给初始模型和实际模型相差太大时，波形反演迭代算法容易陷入局部极小点.可见结合两种方法的WTW反演是一种比较好的联合反演方法.常规WTW迭代算法是首先以WT反演为主反演得到地质模型的整体特征，然后再以波形反演为主反演模型细节，该算法耗时和占用计算机存储空间接近WT反演或波形反演的两倍.为了节省运算耗时和计算机存储空间，往往采取首先单独利用WT反演然后再单独利用波形反演的算法.这样做的缺点是不能紧密结合两种反演方法，使得它们的优缺点在每一次迭代中无法得到互补，从而影响了最终的反演结果.针对以上事实，本文提出一种新的方法实现WTW，使得WTW运算速度和存储空间在任何情况下等同于WT反演或波形反演.模型计算表明新的算法具有更好的收敛性.</FONT>

在用稀疏矩阵的LU分解技术对频率域粘弹性声波方程进行直接求解的基础上,根据失配函数二范数最小准则,用预条件梯度类方法对粘弹性声波介质的速度结构进行了逐频反演.局部非均匀介质模型和层状介质模型速度结构反演的实验结果表明,不同频率能够反映地下介质的多尺度物性结构(低频数据对应与介质物性的大尺度结构),用低频反演结果作为高频反演的初值逼近这一顺序模式,能大大改善反演过程中解的非唯一性.而且,在反演过程中用Hess矩阵的对角线元素来做梯度类方法的预条件算子,能够吸收了高斯牛顿法的二次收敛优势,使得本文算法具有较快的收敛速度.

<FONT face=Verdana>提出一种利用零偏移距VSP资料初至下行波(即直达波)反演介质品质因子<EM>Q</EM>及层速度<EM>V</EM>等参数的方法, 称为自适应时域波形反演法(ATWI). 为了充分地利用有效信息, 该方法根据实际VSP资料的信噪比及直达波与上行波干涉的程度,自适应最大限度地选取未受干扰的初至波片段，并用该片段构造目标函数; 通过恰当地构造数据加权矩阵提高目标函数对<EM>Q</EM>值变化的敏感性；为克服非线性反演的病态问题，采用近来发展的乘性正则化方法，并通过约束条件限制待求参数的取值范围；文中推导出了雅可比矩阵各元素的解析表达式，从而减小了反问题的计算量.合成数据反演结果表明，与谱比值法和子波包络峰值瞬时频率法相比较，ATWI法受上行波影响相对较小、抗噪性能更强.实际资料算例进一步证明了ATWI方法的有效性.</FONT>

<FONT face=Verdana>地层密度直接与孔隙度、孔隙流体类型、饱和度和骨架矿物成分有关.本文通过理论分析和计算，讨论了油气藏储层物性参数变化引起的密度变化及密度变化对地震波速度、阻抗和振幅的影响，提出了基于完全纵波方程的全波形地震密度反演和孔隙度估计方法，克服了常规地震密度反演对地震数据更多处理引起的信号畸变，提高了地震密度反演和地层孔隙度估计的精度.该方法采用波场导数的时间积分和多炮求和，对地震数据中的噪声具有比较强的压制作用.理论模型研究表明该方法是可行的.通过对我国西部某气田实际数据处理、分析和反演，获得了地层密度和孔隙度，结果与测井基本吻合，证明了预测结果的准确性和方法的有效性，从而为后续的有效储层预测和储量计算提供了可靠的数据.</FONT>

似海底反射层的速度异常是识别天然气水合物的重要标志，这里提出了一种针对天然气水合物似海 底反射层的全波形反演方法。这种方法分为全局搜索与局部搜索二部份：首先使用遗传算法进行旅行时，反演得到背景速度模型；然后用其作为初始模型，使用共轭 梯度算法进行全波形反演。通过对含噪数据的数值试验，算法表现出了较高的稳定性，并确定了进行全波形反演的遗传算子。将这种波形反演方法应用于我国南海北 部海域的天然气水合物研究，反演得到了分辨率高于常规速度分析的似海底反射层速度结构，并识别出似海底反射层的速度异常。利用纵波速度反演的结果，计算出 沉积物中游离气的含量，认为BSR下方的低速层可以解释为含至少1％游离气的薄层。并分析了研究区内甲烷气的来源，认为该区域游离气兼有生物气和热解气。

波动方程深度偏移是解决复杂地质体成像的关键技术,基于波动方程的速度建模为其提供更为精确的速度模型.频率域波形反演是目前研究最为广泛的波动方程速度建模方法之一,它推动了波形反演在勘探尺度下的应用.本文通过对频率域波形反演的实现,分析对比了其有效执行过程中与频率相关的影响因素.介绍了时间域的多尺度反演方法在频率域的一种实现方式,对比分析了输入数据的频点带宽和应用的子波频带范围不同时对反演结果的影响.本文通过设计的山地地质模型对频率域波形反演进行了测试和对比,得到的结论为频率域波形反演的有效计算提供了依据和参考.

地震波传播的复杂性所引起的地震反演中强烈的非线性问题是目前全波形反演在技术上遇到的最大难题,了解全波形反演中不同的目标函数随不同物性参数的不同摄动尺度的变化性态,对选择合理的反演方法和反演策略具有重要意义.本文参照Jannane等对波形反演目标函数性态的分析方法,通过变密度声波方程,分析了多种地震数据子集的不同目标函数随物性参数的摄动尺度的变化关系,重点分析了它们的非线性程度,为进行分步骤、分尺度全波形反演方法和反演策略的选择提供了理论指导.

全波形反演是地震资料处理中速度建模的有力工具，相比层析成像等速度建模方法它能够得到速度场的更高频成分.本文给出了基于声波方程格子法正演的时间域全波形反演方法，该方法用非规则、非结构化的三角网格来离散计算区域及模型参数，能实现网格粒度与反演分辨率在空间上的自动匹配，内存需求少，计算效率高；采用L-BFGS优化方法，以分频段变网格的方式实施多尺度反演.以二维Overthrust模型进行了速度反演数值测试，显示了该方法的高效性和潜力.

<p>为了提高表层速度反演精度，本文提出了一种新的波形反演方法.该方法只利用初至波波形信息以减少波形反演对初始模型的依赖性，降低反演多解性与稳定性.由于只利用初至波波形信息，所以该方法利用高斯束计算格林函数和正演波场，以减少正演计算量.为了避免庞大核函数的存储，该方法基于Born波路径，利用矩阵分解算法实现方向与步长的累加计算.将此基于Born波路径的初至波波形反演方法应用于理论模型实验，并与声波方程全波形反演和初至波射线走时层析方法相对比，发现该方法的反演效果略低于全波形反演方法，但明显优于传统初至波射线走时层析方法，而计算效率却与射线走时层析相当.同时，相对于全波形反演，本文方法对初始模型的依赖性也有所降低.</p>

Laplace-Fourier域全波形反演可以利用简单的初始模型，从缺失低频信息的地震数据中得到长波长速度模型.Laplace-Fourier域全波形反演等价于本文的复频率全波形反演，但二者的实现方式不同，因此研究复频率全波形反演，可以为二者的对比研究并发展更有效的方法奠定重要基础.本文首先比较用线性增加模型作为初始模型时几个包含不同高低频成分的频率组的反演效果，再比较结合复频率之后各个频率组的反演效果，从简单模型和复杂模型的测试中都可以看出这种复频率+频率反演的方式对反演效果有明显改善.

全波形反演利用了波形的整体特征，是一种高分辨率的成像方法。目前广泛使用的最小二乘法全波形反演隐含了地震数据处理中噪声服从正态分布，限制了实际应用的效果。本文在假设地震数据噪声误差服从柯西分布的前提下，提出了一种基于柯西分布的频率域目标函数构造方法，推导出了相应的梯度表达式，通过对理论模型的数值合成记录加入随机脉冲噪声、高斯噪声和线性噪声，验证本方法的正确性。反演过程中采用拟牛顿法从低频到高频进行了多尺度的全波形反演，并将低频反演结果作为高频反演的初始模型以便减少解的非唯一性。研究结果表明：该方法相对于最小二乘全波形反演方法，在噪声存在且不满足高斯正态分布的情况下，仍然能够得到较好的反演结果。

Abstract Because modeling for full-waveform inversion (FWI) cannot produce reflections unless the velocity model has the scattering potential (high wavenumbers), using a migration/demigration process to generate modeling data, which is a key step in what is now known as reflection FWI (RFWI), is a credible alternative to tackle the reflection nonlinearity associated with FWI. However, because RFWI depends on a conventional data residual or zero-lag correlation objective function, high nonlinearity can still exist when the true amplitude migration is not used, as well as at far offsets due to cycle skipping. To avoid the cycle skipping and the need for a true amplitude migration, we have developed a correlation-based reflection full-waveform inversion method to update the low-wavenumber components of the velocity model. The success of this method relies on a sensitivity kernel decomposition and a correlation-based objective function. The sensitivity kernel decomposition makes it possible to separate out the contributions of different subkernels and to smear the reflected wave residuals along the "rabbit-ear" wavepath to obtain middle and deep background model estimates. The correlation-based objective function measures differences in kinematic information and behaves in a more linear way than the traditional waveform residual misfit. Moreover, our approach is less sensitive to the frequency content and amplitude information of the seismic data, enabling reliable background velocity estimates to be obtained without the need for low frequencies and full-physics modeling. Because the kinematic features of reflected waves are described correctly, the inversion result of the proposed method can be used as a migration model or an initial model for conventional FWI to achieve a correct high-wavenumber model update.

Full waveform inversion (FWI) is an efficient way to solve parameter reconstruction problems, such as velocity, density, and viscosity coefficient. In this study, we apply a memoryless quasi-Newton (MLQN) method in FWI to invert velocity from surface seismic data for the first time. This method can attain acceptable results with low computational cost and small memory storage requirements. To ensure that the inverted velocity is maintained between the lower and upper boundaries of the velocity model, a nonlinear transformation is added to velocity as a priori information. To test the efficiency of the MLQN method in FWI, two synthetic models, a modified Marmousi model and a modified overthrust model, are examined from the surface seismic data with and without white Gaussian noise. For comparison, the conjugate gradient (CG) method is carried out for the same velocity models with the same parameters. We compare the inverted velocities by the two methods based on the aspects of memory storage requirements, computation time for each iteration, and error. By keeping the memory storage requirements and computation time in each iteration similar, the reconstructed velocity models obtained using the MLQN method are closer to the true velocity models than those obtained using the CG method. Our numerical tests show that the MLQN method is feasible and reliable in FWI.

How to obtain a correct source wavelet is not easy for practical seismic explorations. We define the convolution-based hybrid-norm objective function for the time-domain elastic FWI. We use the synthetic data of Marmousi2 model with Gaussian and spike noise to verify the correctness and feasibility of our method. The inversion results show that our method can not only eliminate the artifacts caused by the incorrect source wavelet, but also improve the anti-noise ability. In addition, due to the filter role of the objective function, we adopt the multi-scale strategy to reduce the sensitivity of FWI to the initial models and to improve the quality of the inversion results.

Summary. We present a technique for the inversion of fundamental and higher-mode waveform data for regional Earth structure. Seismograms are represented as a sum of travelling modes, and an adaptive quadrature scheme based on Filon's method is developed to evaluate the wavenumber integrals efficiently. The difference between an observed and synthetic seismogram is approximated as a linear functional of the residual dispersion which, in turn, is parameterized by perturbations to the Earth structure. The data functionals used by the inversion are branch cross-correlation functions (bccfs) between a particular single-mode synthetic and the observed seismogram. To reduce the effects of ambient noise and the interference by spurious signals and other modes, the bccfs are windowed and tapered about zero lag. The sensitivity of the bccfs to amplitude differences between the synthetic and observed seismograms is reduced by an orthogonalization procedure which strips from the linearized system of equations any information that can otherwise be explained by adjusting the scalar amplitudes of the mode branches. The bccfs are inverted for Earth structure using an iterative, generalized least-squares algorithm. Numerical experiments with synthetic data show that, if the starting model is far enough from the true solution and the path lengths are long enough, the bccfs can be sufficiently dephased to lock the inversion into a spurious local minimum. However, this situation can usually be spotted by a direct comparison of the model synthetics with data and corrected by initializing the inversion with a perturbation to the starting model designed to roughly align the fundamental and first-higher mode groups; interactive software has been developed for this purpose. We have applied these methods to vertical-component data from two well-studied paths, one crossing Eurasia from sources in the Kurils-Japan area to a receiver array centred on the Baltic Shield, and the other crossing the Pacific from the New Hebrides to the western United States. Structures derived from dispersion data by Cara and Cara, Nercessian &amp; Nolet were used as starting models, and bccfs up to the fourth-higher mode were inverted. Although the starting models produced synthetics in reasonably good agreement with the data, a variance reduction on the order of 70 per cent was achieved for both paths. The final models show substantial differences in the two shear-velocity profiles below 200 km depth, in agreement with the results of Cara et al. and inferences based on the study of multiple-ScS travel times by Sipkin &amp; Jordan. Synthetics generated from these models are in excellent agreement with the complex higher-mode waveforms observed for the entire range of receiver distances and source depths.

Rayleigh wave phase velocities at periods 30-80 s in the Pacific Ocean are calculated by inverting phase and amplitude anomaly data using the paraxial ray approximation and the Gaussian beam method. The region is divided into 500°0103 500° blocks, and approximately 200 source090009receiver pairs from 18 well-studied events around the Pacific Ocean are used. First, we assume phase anomalies for the lithospheric age-dependent model. Next, conventional phase data inversions are conducted assuming great circle paths so that the phase discrepancies are reduced to less than 0300. This procedure is essential for later inversions using amplitude data. We then determine the residuals of both amplitude and phase terms by calculating ray-synthetic seismograms. Using the Born approximation for a 2-D wave equation, a non-linear iterative inversion for phase velocities is performed with both residuals. Fr0108chet derivatives for the inversion consist primarily of two wavefields: (1) the wavefield at the model point from the source, and (2) the Green's function from the model point to the receiver. These wavefields are also calculated by the paraxial ray approximation and Gaussian beam methods. In the inverse formulations, the simple use of the conventional Backus090009Gilbert approach yields undesirable results in the non-linear iterative case and an extra term is necessary to control the model perturbations in order to minimize departures from the a priori model. The use of this additional term guarantees that we are able to obtain a fairly reliable phase velocity model even in the present non-linear problem. In most cases residual variances are significantly reduced after two or three iterations as far as the starting model is fairly correct. Compared with the phase data inversions, this inverse scheme gives more reliable resolution and most of the inverted features in phase velocities are significantly larger than the uncertainty level while some features obtained by the great circle phase data inversions are suspicious. The resulting model displays some interesting deviations from the lithospheric age-dependent model. For example, low velocity regions are correlated with the Hawaii, Samoa, French Polynesia and Gilbert Islands hotspots.

Surface wave scattering theory is presented as a new method for analyzing teleseismic surface wave data. Using surface wave scattering integrals the effect of lateral heterogeneity both on the surface wave coda generation and on the direct surface wave is described. Since the employed scattering theory for the forward problem is linear, the inverse problem can conveniently be solved in the least squares sense using an iterative matrix solver. For waveform inversions of the direct surface wave, only near forward scattering contributes. For this case the isotropic approximation is introduced, which makes it possible to retrieve phase velocity information from scattering theory. It is shown that for practical waveform inversions the resulting system of linear equations is extremely large and how row action methods can be used conveniently for carrying out the inversion on moderate size computers. The performance of the inversions is illustrated with two numerical examples. In the first example the surface wave coda generated by one point scatterer is inverted. It is shown that the reconstruction in this case is similar to Kirchhoff migration methods as used in exploration seismics. In the second example, ray geometrical effects (focusing and phase shifting) are obtained from the linear inversion with scattering theory. It follows from this example that linear waveform inversion can simultaneously fit the amplitude and the phase of surface wave data.

We propose a waveform inversion scheme that can be used to invert strong structural heterogeneities. The method is based on a ray approximation for surface waves. Strong structural lateral variations are modelled by vertical discontinuities. Therefore, a geologically heterogeneous region is partitioned into a number of lateral homogeneous subregions. Synthetic seismograms are calculated by modal summation over incident and transmitted modes. With this method the complete waveforms of surface waves, including mode cross-branch coupling, multipathing and scattering, are considered in the inversion. We test the method with several geophysically realistic structural models. An example of waveform inversion for real data090000a wave path across the Iberian peninsula and the oceanic structure off the French coast owing to the Gibraltar earthquake ( M s = 5.7)090000is presented. The method allows us to obtain the information represented by different set of structures along the same source090009receiver minor arc through which the waves have propagated. The method is applicable to different models of lateral heterogeneity. In its present development, it is most appropriate for inverting structures around tectonic scenarios such as continental margins, grabens and discontinuities between major plates.

78 Proposed a waveform inversion scheme for surface wave analysis. 78 Extended the conventional surface wave analysis from 1D to 2D. 78 Improved the accuracy of handling lateral heterogeneity in surface wave method. 78 Several typical near-surface models containing strong lateral heterogeneity are demonstrated.

78 Present a technique to invert full seismic waveforms. 78 Apply the technique to both synthetic and real experimental data. 78 Verify inverted results of the real experimental data by independent invasive tests (SPT).

Full-waveform inversion (FWI) of Rayleigh waves is attractive for shallow geotechnical investigations due to the high sensitivity of Rayleigh waves to the S-wave velocity structure of the subsurface. In shallow-seismic field data, the effects of anelastic damping are significant. Dissipation results in a low-pass effect as well as frequency-dependent decay with offset. We found this by comparing recorded waveforms with elastic and viscoelastic wave simulation. The effects of anelastic damping must be considered in FWI of shallow-seismic Rayleigh waves. FWI using elastic simulation of wave propagation failed in synthetic inversion tests in which we tried to reconstruct the S-wave velocity in a viscoelastic model. To overcome this, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">Q-values can be estimated from the recordings to quantify viscoelasticity. Waveform simulation in the FWI then uses these a priori values when inferring seismic velocities and density. A source-wavelet correction, which is inevitable in FWI of field data, can compensate a significant fraction of the residuals between elastically and viscoelastically simulated data by narrowing the signals bandwidth. This way, elastic simulation becomes applicable in FWI of data from anelastic media. This approach, however, was not able to produce a frequency-dependent amplitude decay with offset. Reconstruction, therefore, was more accurate when using appropriate viscoelastic modeling in FWI of shallow-seismic Rayleigh waves. We found this by synthetic inversion tests using elastic forward simulation as well as viscoelastic simulation with different a priori values for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline">Q.

In the context of near surface seismic imaging (a few hundreds of metres), we propose an alternative approach for inversion of surface waves in 2-D media with laterally varying velocities. It is based on Full Waveform Inversion (FWI) but using an alternative objective function formulated in the frequency–wavenumber f 61 k domain. The classical FWI objective function suffers from severe local minima problems in the presence of surface waves. It thus requires a very accurate initial model. The proposed objective function is similar to the one used in classical surface wave analysis. In this approach, the data are first split using sliding windows in the time–space t 61 x domain. For each window, the amplitude of the f 61 k spectrum is computed. The objective function measures the least-squares misfit between the amplitude of observed and modelled 2-D Fourier transformed data sets. We call this formulation the windowed-amplitude waveform inversion (w-AWI). The w-AWI objective function reduces some local minima problems as shown here through numerical examples. The global minimum basin is wider in the w-AWI approach than in FWI. Synthetic examples show that w-AWI may achieve convergence if the lowest data frequency content is twice higher than the one needed by FWI. For elastic inversion, w-AWI can be used to reconstruct a velocity model explaining surface waves. This surface wave inversion procedure can be used to retrieve near-surface model parameters in lateral-varying media