alternative waveform inversion for surface wave analysis in 2 d media 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 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 x domain for each window the amplitude of the f 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

structure of the california coast ranges and san andreas fault at safod from seismic waveform inversion and reflection imaging 1 a seismic reflection and refraction survey across the san andreas fault saf near parkfield provides a detailed characterization of crustal structure across the location of the san andreas fault observatory at depth safod steep dip prestack migration and frequency domain acoustic waveform tomography were applied to obtain highly resolved images of the upper 5 km of the crust for 15 km on either side of the saf the resulting velocity model constrains the top of the salinian granite with great detail steep dip reflection seismic images show several strong amplitude vertical reflectors in the uppermost crust near safod that define an 2 km wide zone comprising the main saf and two or more local faults another prominent subvertical reflector at 2 4 km depth 9 km to the northeast of the saf marks the boundary between the franciscan terrane and the great valley sequence a deep seismic section of low resolution shows several reflectors in the salinian crust west of the saf two horizontal reflectors around 10 km depth correlate with strains of seismicity observed along strike of the saf they represent midcrustal shear zones partially decoupling the ductile lower crust from the brittle upper crust the deepest reflections from 25 km depth are interpreted as crust mantle boundary

elastic full waveform inversion of multi component obc seismic data elastic full waveform inversion of seismic reflection data represents a data driven form of analysis leading to quantification of sub surface parameters in depth in previous studies attention has been given to p wave data recorded in the marine environment using either acoustic or elastic inversion schemes in this paper we exploit both p waves and mode converted s waves in the marine environment in the inversion for both p and s wave velocities by using wide angle multi component ocean bottom cable seismic data an elastic waveform inversion scheme operating in the time domain was used allowing accurate modelling of the full wavefield including the elastic amplitude variation with offset response of reflected arrivals and mode converted events a series of one and two dimensional synthetic examples are presented demonstrating the ability to invert for and thereby to quantify both p and s wave velocities for different velocity models in particular for more realistic low velocity models including a typically soft seabed an effective strategy for inversion is proposed to exploit both p and mode converted ps waves whilst p wave events are exploited for inversion for p wave velocity examples show the contribution of both p and ps waves to the successful recovery of s wave velocity

two dimensional waveform inversion of multi component data in acoustic elastic coupled media 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

global adjoint tomography first generation model we present the first generation global tomographic model constructed based on adjoint tomography an iterative full waveform inversion technique synthetic seismograms were calculated using gpu accelerated spectral element simulations of global seismic wave propagation accommodating effects due to 3d anelastic crust mantle structure topography bathymetry the ocean load ellipticity rotation and self gravitation frechet derivatives were calculated in 3d anelastic models based on an adjoint state method the simulations were performed on the cray xk7 named titan a computer with 18 688 gpu accelerators housed at oak ridge national laboratory the transversely isotropic global model is the result of 15 tomographic iterations which systematically reduced differences between observed and simulated three component seismograms our starting model combined 3d mantle model s362ani kustowski et al 2008 with 3d crustal model crust2 0 bassin et al 2000 we simultaneously inverted for structure in the crust and mantle thereby eliminating the need for widely used crustal corrections we used data from 253 earthquakes in the magnitude range 5 8 mw 7 0 for the first 12 iterations we combined 30 s body wave data with 60 s surface wave data the shortest period of the surface waves was gradually decreased and in the last three iterations we combined 17 s body waves with 45 s surface waves we started using 180 min long seismograms after the 12th iteration and assimilated minor and major arc body and surface waves the 15th iteration model features enhancements of well known slabs an enhanced image of the samoa tahiti plume as well as various other plumes and hotspots such as caroline galapagos yellowstone and erebus furthermore we see clear improvements in slab resolution along the hellenic and japan arcs as well as subduction along the east of scotia plate which does not exist in the starting model point spread function tests demonstrate that we are approaching the resolution of continental scale studies in some areas for example underneath yellowstone this is a consequence of our multi scale smoothing strategy in which we define our smoothing operator as a function of the approximate hessian kernel thereby smoothing gradients less wherever we have good ray coverage such as underneath north america

an alternative strategy for non linear inversion of seismic waveforms1 a common example of a large scale non linear inverse problem is the inversion of seismic waveforms techniques used to solve this type of problem usually involve finding the minimum of some misfit function between observations and theoretical predictions as the size of the problem increases techniques requiring the inversion of large matrices become very cumbersome considerable storage and computational effort are required to perform the inversion and to avoid stability problems consequently methods which do not require any large scale matrix inversion have proved to be very popular currently descent type algorithms are in widespread use usually at each iteration a descent direction is derived from the gradient of the misfit function and an improvement is made to an existing model based on this and perhaps previous descent directions a common feature in nearly all geophysically relevant problems is the existence of separate parameter types in the inversion i e unknowns of different dimension and character however this fundamental difference in parameter types is not reflected in the inversion algorithms used usually gradient methods either mix parameter types together and take little notice of the individual character or assume some knowledge of their relative importance within the inversion process we propose a new strategy for the non linear inversion of multi offset reflection data the paper is entirely theoretical and its aim is to show how a technique which has been applied in reflection tomography and to the inversion of arrival times for 3d structure may be used in the waveform case specifically we show how to extend the algorithm presented by tarantola to incorporate the subspace scheme the proposed strategy involves no large scale matrix inversion but pays particular attention to different parameter types in the inversion we use the formulae of tarantola to state the problem as one of optimization and derive the same descent vectors the new technique splits the descent vector so that each part depends on a different parameter type and proceeds to minimize the misfit function within the sub space defined by these individual descent vectors in this way optimal use is made of the descent vector components i e one finds the combination which produces the greatest reduction in the misfit function based on a local linearization of the problem within the subspace this is not the case with other gradient methods by solving a linearized problem in the chosen subspace at each iteration one need only invert a small well conditioned matrix the projection of the full hessian on to the subspace the method is a hybrid between gradient and matrix inversion methods the proposed algorithm requires the same gradient vectors to be determined as in the algorithm of tarantola although its primary aim is to make better use of those calculations in minimizing the objective function

seismic imaging of complex onshore structures by 2d elastic frequency domain full waveform inversion quantitative imaging of the elastic properties of the subsurface at depth is essential for civil engineering applications and oil and gas reservoir characterization a realistic synthetic example provides for an assessment of the potential and limits of 2d elastic full waveform inversionfwiof wide aperture seismic data for recovering high resolution p and s wave velocity models of complex onshore structures fwi of land data is challengingbecauseoftheincreasednonlinearityintroducedbyfreesurface effects such as the propagation of surface waves in the heterogeneous near surface moreover the short wavelengths of the shear wavefield require an accurate s wave velocity starting modeliflowfrequenciesareunavailableinthedata weevaluated different multiscale strategies with the aim of mitigating the nonlinearities massively parallel full waveform inversion was implemented in the frequency domain the numerical optimization relies on a limited memory quasi newton algorithm that outperforms the more classic preconditioned conjugate gradient algorithm the forward problem is based upon a discontinuous galerkin dg method on triangular mesh which allows accuratemodelingoffree surfaceeffects sequentialinversionsofincreasingfrequenciesdefinethemostnaturallevelofhierarchyin multiscale imaging in the case of land data involving surface waves the regularization introduced by hierarchical frequency inversions is not enough for adequate convergence of the inversion a second level of hierarchy implemented with complexvalued frequencies is necessary and provides convergence of the inversion toward acceptable p and s wave velocity models amongthepossiblestrategiesforsamplingfrequenciesintheinversion successive inversions of slightly overlapping frequency groups is the most reliable when compared to the more standard sequential inversion of single frequencies this suggests that simultaneous inversion of multiple frequencies is critical when consideringcomplexwavephenomena

shallow structure characterization by 2d elastic full waveform inversion assessing the effectiveness of elastic full waveform inversion fwi algorithms when applied to shallow 2d structures in the presence of a complex topography is critically important by using fwi we overcome inherent limitations of conventional seismic methods used for near surface prospecting acoustic tomography and multichannel spectral analysis of surface waves the elastic forward problem formulated in the frequency domain is based on a mixed finite element p0p1 discontinuous galerkin method to ensure accurate modeling of complex topography effects at a reasonable computing cost the inversion problem uses an fwi algorithm to minimize the misfit between observed and calculated data based on results from a numerical experiment performed on a realistic landslide model inspired from the morphostructure of the super sauze earthflow we analyzed the effect of using a hierarchical preconditioning strategy based on a simultaneous multifrequency inversion of damped data to mitigate the strong nonlinearities coming from the surface waves this strategy is a key point in alleviating the strong near surface effects and avoiding convergence toward a local minimum using a limited memory quasi newton method improved the convergence level these findings are analogous to recent applications on large scale domains although limited sourcereceiver offset ranges low frequency content of the source and domination of surface waves on the signal led to some difficulties regarding the impact of data decimation on the inversion results we have learned that an inversion restricted to the vertical data component can be successful without significant loss in terms of parameter imagery resolution in our investigations of the effect of increased source spacing we found that a sampling of 4 m less than three times the theoretical maximum of one half wavelength led to severe aliasing

reflection waveform inversion using local descent methods estimating attenuation and velocity over a gas sand deposit prestack seismic reflection data contain amplitudes traveltimes and moveout information waveform inversion of such data has the potential to estimate attenuation levels reflector depths and geometry and background velocities however when inverting reflection data strong nonlinearities can cause reflectors to be incorrectly imaged and can prevent background velocities from being updated to successfully recover background velocities previous authors have resorted to nonlinear global search inversion techniques we propose a two step inversion procedure using local descent methods in which we perform alternate inversions for the reflectors and the background velocities for our reflector inversion we exploit the efficiency of the back propagation method when inverting for a large parameter set for our background velocity inversion we use newton inverse methods during the background velocity inversions it is crucial to adaptively depth stretch the model to preserve the vertical traveltimes this reduces nonlinearity by largely decoupling the effects of the background velocities and reflectors on the data nonlinearity is further reduced by choosing to invert for slownesses and by inverting for a sparse parameter set which is partially defined using geological reflector picks applying our approach to shallow seismic data from the north sea collected over a gas sand deposit we demonstrate that the proposed method is able to estimate both the geometry and internal velocity of a significant velocity structure not present in the initial model over successive iterations the use of adaptive depth stretching corrects the pull down of the base of the gas sand vertical background velocity gradients are also resolved for an insignificant extra cost the acoustic attenuation parameter q is included in the inversion scheme the final attenuation tomogram contains realistic values of q for the expected lithologies and for the effect of partial fluid saturation associated with a shallow bright spot the attenuation image may also indicate the presence of fracturing

full waveform inversion and the truncated newton method quantitative imaging of complex subsurface structures full waveform inversion fwi is a powerful tool for quantitative seismic imaging from wide azimuth seismic data the method is based on the minimization of the misfit between observed and simulated data this amounts to the resolution of a large scale nonlinear minimization problem the inverse hessian operator plays a crucial role in this reconstruction process accounting accurately for the effect of this operator within the minimization scheme should correct for illumination deficits restore the amplitude of the subsurface parameters and help to remove artifacts generated by energetic multiple reflections conventional preconditioned gradient based minimization methods only roughly approximate the effect of this operator we are interested in this study to another class of minimization methods named as truncated newton methods these methods are based on the computation of the model update through a matrix free conjugate gradient resolution of the newton linear system the aim of this study is to present a feasible implementation of this method for the fwi problem based on a second order adjoint state formulation for the computation of hessian vector products we compare this method with the nonlinear conjugate gradient and the l bfgs method within the context of 2d acoustic frequency fwi for the reconstruction of p wave velocity models two test cases are investigated the first is the synthetic bp 2004 model representative of the gulf of mexico geology with high velocity contrasts associated with the presence of salt structures the second is a 2d real data set from the valhall oil field in north sea these tests emphasize the interesting properties of the truncated newton method regarding conventional optimization methods within the context of fwi

efficient 3 d frequency domain mono parameter full waveform inversion of ocean bottom cable data application to valhall in the visco acoustic vertical transverse isotropic approximation computationally efficient 3 d frequency domain full waveform inversion fwi is applied to ocean bottom cable data from the valhall oil field in the visco acoustic vertical transverse isotropic vti approximation frequency domain seismic modelling is performed with a parallel sparse direct solver on a limited number of computer nodes a multiscale imaging is performed by successive inversions of single frequencies in the 3 5 10 hz frequency band the vertical wave speed is updated during fwi while density quality factor qp and anisotropic thomsen s parameters and are kept fixed to their initial values the final fwi model shows the resolution improvement that was achieved compared to the initial model that was built by reflection traveltime tomography this fwi model shows a glacial channel system at 175 m depth the footprint of drifting icebergs on the palaeo seafloor at 500 m depth a detailed view of a gas cloud at 1 km depth and the base cretaceous reflector at 3 5 km depth the relevance of the fwi model is assessed by frequency domain and time domain seismic modelling and source wavelet estimation the agreement between the modelled and recorded data in the frequency domain is excellent up to 10 hz although amplitudes of modelled wavefields propagating across the gas cloud are overestimated this might highlight the footprint of attenuation whose absorption effects are underestimated by the homogeneous background qp model qp 200 the match between recorded and modelled time domain seismograms suggests that the inversion was not significantly hampered by cycle skipping however late arrivals in the synthetic seismograms computed without attenuation and with a source wavelet estimated from short offset early arrivals arrive 40 ms earlier than the recorded seismograms this might result from dispersion effects related to attenuation the repeatability of the source wavelets inferred from data that are weighted by a linear gain with offset is dramatically improved when they are estimated in the fwi model rather than in the smooth initial model the two source wavelets estimated in the fwi model from data with and without offset gain show a 40 ms time shift which is consistent with the previous analysis of the time domain seismograms the computational efficiency of our frequency domain approach is assessed against a recent time domain fwi case study performed in a similar geological environment this analysis highlights the efficiency of the frequency domain approach to process a large number of sources and receivers with limited computational resources thanks to the efficiency of the substitution step performed by the direct solver this efficiency can be further improved by using a block low rank version of the multifrontal solver and by exploiting the sparsity of the source vectors during the substitution step future work will aim to update attenuation and density at the same time of the vertical wave speed

crustal seismic imaging from multifold ocean bottom seismometer data by frequency domain full waveform tomography application to the eastern nankai trough 1 in offshore surveys the deep crust is generally investigated by traveltime tomography applied to sparse ocean bottom seismometer data the inferred velocity models are of limited resolution precluding a quantitative analysis of deep tectonic discontinuities if dense arrays of ocean bottom seismometers can be deployed the resulting data sets become amenable to full waveform processing which should lead to a significant improvement in the resolution of structures such acquisition and processing were achieved on the eastern nankai subduction zone full waveform inversion is entirely implemented in the frequency domain enabling efficient finite difference wave modeling and allowing to limit the inversion to a few discrete frequencies of increasing value such a hierarchical procedure defines a multiresolution approach to seismic imaging the data set was recorded by 93 instruments deployed along a 105 km long profile thirteen frequencies ranging from 3 to 15 hz were inverted sequentially wavelengths imaged by the full waveform inversion typically range between 0 5 and 8 km full waveform tomography reveals an intense compression in the upper prism and underlying backstop as evidenced by several thrusts the frontal ones still active corresponding to negative velocity anomalies the subducting paleo zenisu ridge is also reconstructed above which stands the decollement velocities in the upper mantle beneath the ridge are rather low 7 5 km s 1 suggesting partially serpentinized mantle beneath the ridge this paper demonstrates the feasibility of full waveform tomography based on dense ocean bottom seismometer data sets and its ability to quantitatively image the entire crust with a significantly improved resolution compared to what is usually achieved through traveltime tomography

3d elastic full waveform inversion of surface waves in the presence of irregular topography using an envelope based misfit function full waveform inversion fwi is a powerful method for estimating the earth s material properties we demonstrate that surface wave driven fwi is well suited to recovering near surface structures and effective at providing shear wavespeed starting models for use in conventional body wave fwi we illustrate the method with a synthetic example based on the seam phase ii foothills model to accurately model surface waves in the presence of complex tomography we used a spectral element wave propagation solver we started first with an envelope based objective function to invert for shallow large scale heterogeneities then using the recovered model of the subsurface we applied a waveform difference inversion to obtain higher resolution models envelope misfit functions were found to be effective in minimizing cycle skipping issues for surface wave inversions which are useful for constraining complex near surface features

waveform tomography imaging of a megasplay fault system in the seismogenic nankai subduction zone abstract we apply frequency domain waveform tomography to form quantitative high resolution p wave velocity images of a megasplay fault system within the central nankai subduction zone offshore of southwest japan using controlled source ocean bottom seismometer obs data originally acquired in 2004 the waveform tomography method exploits recorded seismic waveforms beyond their first arrivals and thus achieves a much higher resolution of the order of a wavelength than that of conventional traveltime tomography methods frequency domain waveform tomography facilitates a multi scale approach to stabilize the inversion in which initial traveltime tomography results are sequentially improved on by first fitting low frequency components of the seismic records starting at 2 25 hz higher frequency components up to 8 5 hz are then introduced progressively our final waveform tomography image allows velocity anomalies as small as 700 m horizontally and 350 m vertically to be discerned and interpreted as confirmed by checkerboard modeling tests the improved explanatory power of the final images is verified by observing that synthetic waveforms calculated from the final results yield much better fit to the observed waveforms than those estimated from the original traveltime tomography image apparent lithological boundaries from waveform tomography agree well with corresponding reflections on seismic migration images providing further confidence in the validity of the results the megasplay fault is evident on the final waveform tomography image as a sharp velocity discontinuity delineating the upper surface of a velocity reduction of nearly 1 km s with respect to the regional 1d velocity trend the megasplay fault can be traced continuously throughout the entire image from a nearly horizontal section at the landward extent moving seaward through to a steeper angle penetrating the old accretionary prisms with several additional splays appearing to branch in the shallow subsurface the location of the low velocity zones imaged by our waveform tomography method coincides with two previously identified low velocity zones the image reveals a low velocity zone that is continuous from deeper to shallower portions of the subsurface suggesting that pore fluids may be transported from the inner wedge to the transition zone and to the surface through fluid conduits associated with the megasplay fault system

exploring some issues in acoustic full waveform inversion the least squares error measures the difference between observed and modelled seismic data because it suffers from local minima a good initial velocity model is required to avoid convergence to the wrong model when using a gradient based minimization method if a data set mainly contains reflection events it is difficult to update the velocity model with the least squares error because the minimization method easily ends up in the nearest local minimum without ever reaching the global minimum several authors observed that the model could be updated by diving waves requiring a wide angle or large offset data set this full waveform tomography is limited to a maximum depth here we use a linear velocity model to obtain estimates for the maximum depth in addition we investigate how frequencies should be selected if the seismic data are modelled in the frequency domain in the presence of noise the condition to avoid local minima requires more frequencies than needed for sufficient spectral coverage we also considered acoustic inversion of a synthetic marine data set created by an elastic time domain finite difference code this allowed us to validate the estimates made for the linear velocity model the acoustic approximation leads to a number of problems when using long offset data nevertheless we obtained reasonable results the use of a variable density in the acoustic inversion helped to match the data at the expense of accuracy in the inversion result for the density

toward a robust workflow for deep crustal imaging by fwi of obs data the eastern nankai trough revisited crustal scale imaging by the full waveform inversion fwi of long offset seismic data is inherently difficult because the large number of wavelengths propagating through the crust makes the inversion prone to cycle skipping therefore efficient crustal scale fwi requires an accurate starting model and a stable workflow minimizing the nonlinearity of the inversion here we attempt to reprocess a challenging 2d ocean bottom seismometer obs dataset from the eastern nankai trough the starting model is built by first arrival traveltime tomography fat which is fwi assisted for tracking cycle skipping we iteratively refine the picked traveltimes and then reiterate the fat until the traveltime residuals remain below the cycle skipping limit subsequently we apply laplace fourier fwi in which progressive relaxation of time damping is nested within frequency continuation to hierarchically inject more data into the inversion these two multiscale levels are complemented by a layer stripping approach implemented through offset continuation the reliability of the fwi velocity model is assessed by means of source wavelet estimation synthetic seismogram modeling ray tracing modeling dynamic warping and checkerboard tests although the visco acoustic approximation is used for wave modeling the synthetic seismograms reproduce most of the complexity of the data with a high traveltime accuracy the revised fwi scheme produces a high resolution velocity model of the entire crust that can be jointly interpreted with migrated images derived from multichannel seismic data this study opens a new perspective on the design of obs crustal scale experiments amenable to fwi however a further assessment of the optimal obs spacing is required for reliable fwi

shear wave velocity and density estimation from ps wave avo analysis application to an obs dataset from the north sea s wave velocity and density information is crucial for hydrocarbon detection because they help in the discrimination of pore filling fluids unfortunately these two parameters cannot be accurately resolved from conventional p wave marine data recent developments in ocean bottom seismic obs technology make it possible to acquire high quality s wave data in marine environments the use of s waves for amplitude variation with offset avo analysis can give better estimates of s wave velocity and density contrasts like p wave avo s wave avo is sensitive to various types of noise we investigate numerically and analytically the sensitivity of avo inversion to random noise and errors in angles of incidence synthetic examples show that random noise and angle errors can strongly bias the parameter estimation the use of singular value decomposition offers a simple stabilization scheme to solve for the elastic parameters the avo inversion is applied to an obs data set from the north sea special prestac

timelapse ultrasonic tomography for measuring damage localization in geomechanics laboratory tests variation of mechanical properties in materials can be detected non destructively using ultrasonic measurements in particular changes in elastic wave velocity can occur due to damage i e micro cracking and particles debonding here the challenge of characterizing damage in geomaterials i e rocks and soils is addressed geomaterials are naturally heterogeneous media in which the deformation can localize so that few measurements of acoustic velocity across the sample are not sufficient to capture the heterogeneities therefore an ultrasonic tomography procedure has been implemented to map the spatial and temporal variations in propagation velocity which provides information on the damage process moreover double beamforming has been successfully applied to identify and isolate multiple arrivals that are caused by strong heterogeneities natural or induced by the deformation process the applicability of the developed experimental technique to laboratory geomechanics testing is illustrated using data acquired on a sample of natural rock before and after being deformed under triaxial compression the approach is then validated and extended to time lapse monitoring using data acquired during plane strain compression of a sample including a well defined layer with different mechanical properties than the matrix

high resolution seismic attenuation imaging from wide aperture onshore data by visco acoustic frequency domain full waveform inversion summary here we assess the potential of the visco acoustic frequency domain full waveform inversion fwi to reconstruct p wave velocity vp and p wave attenuation factor q from surface onshore seismic data first we perform a sensitivity analysis of the fwi based upon a grid search analysis of the misfit function and several synthetic fwi examples using velocity and q models of increasing complexity subsequently we applied both the acoustic and viscoacousticfwitorealsurfacewide apertureonshoreseismicdatafromthepolishbasin wherea strongattenuationoftheseismicdataisobserved thesensitivityanalysisofthevisco acoustic fwi suggests that the fwi can jointly reconstruct the velocity and the attenuation factor if the signatureoftheattenuationissufficientlystronginthedata asyntheticexamplecorresponding to a homogeneous background model with an inclusion shows a reliable reconstruction of vp and q in the inclusion when q is as small as 90 and 50 in the background model and in the inclusion respectively a first application of acoustic fwi to real data shows that a heuristic normalization of the data with offset allows us to compensate for the effect of the attenuation in the data and reconstruct a reliable velocity model alternatively we show that visco acoustic fwi allows us to reconstruct jointly both a reliable velocity model and a q model from the true amplitude data we propose a pragmatical approach based upon seismic modelling and source wavelet estimation to infer the best starting homogeneous q model for visco acoustic fwi we find the source wavelet estimation quite sensitive to the quality of the velocity and attenuation models used for the estimation for example source to source wavelets are significantly more consistent when computed in the final fwi model than in the initial one a good kinematic and amplitude match between the early arriving phases of the real and time domain synthetic seismograms computed in the final fwi model provides an additional evidence of the reliability of the final fwi model we find the recovered velocity and attenuation models consistent with the expected lithology and stratigraphy in the study area we link high attenuation zones with the increased clay content and the presence of the mineralized fluids

resolving the fine scale velocity structure of continental hyperextension at the deep galicia margin using full waveform inversion continental hyperextension during magma poor rifting at the deep galicia margin is characterised by a complex pattern of faulting thin continental fault blocks and the serpentinisation with local exhumation of mantle peridotites along the s reflector interpreted as a detachment surface in order to understand fully the evolution of these features it is important to image seismically the structure and to model the velocity structure to the greatest resolution possible travel time tomography models have revealed the long wavelength velocity structure of this hyperextended domain but are often insufficient to match accurately the short wavelength structure observed in reflection seismic imaging here we demonstrate the application of two dimensional 2d time domain acoustic full waveform inversion to deep water seismic data collected at the deep galicia margin in order to attain a high resolution velocity model of continental hyperextension we have used several quality assurance procedures to assess the velocity model including comparison of the observed and modelled waveforms checkerboard tests testing of parameter and inversion strategy and comparison with the migrated reflection image our final model exhibits an increase in the resolution of subsurface velocities with particular improvement observed in the westernmost continental fault blocks with a clear rotation of the velocity field to match steeply dipping reflectors across the s reflector there is a sharpening in the velocity contrast with lower velocities beneath s indicative of preferential mantle serpentinisation this study supports the hypothesis that normal faulting acts to hydrate the upper mantle peridotite observed as a systematic decrease in seismic velocities consistent with increased serpentinisation our results confirm the feasibility of applying the full waveform inversion method to sparse deep water crustal datasets

time lapse seismic imaging using regularized full waveform inversion with a prior model which strategy full waveform inversion is an appealing technique for time lapse imaging especially when prior model information is included into the inversion workflow once the baseline reconstruction is achieved several strategies can be used to assess the physical parameter changes such as parallel difference two separate inversions of baseline and monitor data sets sequential difference inversion of the monitor data set starting from the recovered baseline model and double difference inversion of the difference data starting from the recovered baseline model strategies using syntheticmarmousi data sets we investigate which strategy should be adopted to obtain more robust and more accurate time lapse velocity changes in noise free and noisy environments this synthetic application demonstrates that the double difference strategy provides the more robust time lapse result in addition we propose a target oriented time lapse imaging using regularized full waveform inversion including a prior model and model weighting if the prior information exists on the location of expected variations this scheme applies strong prior model constraints outside of the expected areas of timelapse changes and relatively less prior constraints in the time lapse target zones in application of this process to the marmousi model data set the local resolution analysis performed with spike tests shows that the target oriented inversion prevents the occurrence of artefacts outside the target areas which could contaminate and compromise the reconstruction of the effective time lapse changes especially when using the sequential difference strategy in a strongly noisy case the target oriented prior model weighting ensures the same behaviour for both time lapse strategies the double difference and the sequential difference strategies and leads to a more robust reconstruction of the weak time lapse changes the double difference strategy can deliver more accurate time lapse variation since it can focus to invert the difference data however the double difference strategy requires a preprocessing step on data sets such as time lapse binning to have a similar source receiver location between two surveys while the sequential difference needs less this requirement if we have prior information about the area of changes the target oriented sequential difference strategy can be an alternative and can provide the same robust result as the doubledifference strategy

nonlinear elastic waveform inversion of land seismic reflection data data from 53 shot records collected in a conventional land seismic reflection survey are inverted to obtain subsurface maps of short wavelength variations in elastic parameters impedance the inversion method employs a robust nonlinear iterative gradient algorithm which inverts waveform data thus there is no picking of travel times or amplitudes the algorithm is also computationnally expensive as it relies heavily upon elastic finite difference modeling in addition because a gradient search is employed to minimize the misfit between observed and modeled data we attempt to solve only the weakly nonlinear problem associated with the short wavelenghts of imedance information on the short wavelengths of impedance is mainly derived from amplitude variations of the data resolving the long wavelengths of velocity background is thought to be a highly nonlinear problem at least for waveform inversion and is not attempted herein for the inversion of this data set long wavelenghts have been derived from well logs located along the seismic reflection profile although the data set is dominated by unconverted p wave arrivals we obtain maps of the short wavelenghts of both p impedance and s impedance three well logs in the survey area confirm the validity of the p impedance map however no s velocity well log are available from this area there are channel sands of economic interest which have a thickness of approximately 10 m in one well and are very thin or absent in the other two wells the 10 m occurrence of channel sands is quite visible in both impedance maps we note that because inversion in three dimensions of a realistically sized data set is simply not possible on present day computers all modeling was performed in two dimensions and a rather crude conversion from spherical to cylindrical energy spreading was applied to the original field data before inversion other seismic reflection data in the survey area suggest that there is little lateral variation in the subsurface except for the channel sands thus we feel that a two dimensional inversion with energy compensation is justified

early basic magmatism in the evolution of the northern marginal zone of the archean limpopo belt abstract basaltic rocks enclosed in quartzo feldspathic gneisses and metamorphosed to granulite grade at 2 9 ga from the north marginal zone of the limpopo belt are subdivided into three types group a basalts are tholeiitic and have flat rare earth element ree patterns field and chemical evidence suggest that these metabasic rocks may have originated as basaltic lavas prior to the 2 9 ga metamorphism group b basalts are enriched in trace elements relative to group a particularly in the lree this group merges into a smaller group of basalts group c which are highly enriched in trace elements group b and possibly group c basalts are tentatively identified as dykes which cut the quartzo feldspathic gneisses but predate the metamorphism the cause of the trace element enrichment in groups b and c cannot be uniquely identified for whilst some evidence suggests crustal contamination it is impossible to unambiguously choose between crustal contamination a small percentage of melting and source region heterogeneity trace element patterns for the group b basalts show a striking similarity to those for phanerozoic basalts from this region and which are thought to have been derived from an enriched mantle source

multiscale imaging of complex structures from multifold wide aperture seismic data by frequency domain full waveform tomography application to a thrust belt summary an application of full waveform tomography to dense onshore wide aperture seismic data recorded in a complex geological setting thrust belt is presented the waveform modelling and tomography are implemented in the frequency domain the modelling part is solved with a finite difference method applied to the visco acoustic wave equation the inversion is based on a local gradient method only the p wave velocity is involved in the inversion the inversion is applied iteratively to discrete frequency components by proceeding from low to high frequencies this defines a multiscale imaging in the sense that high wavenumbers are progressively incorporated in images the linearized waveform tomography requires an accurate starting velocity model that has been developed by first arrival traveltime tomography after specific pre processing of the data 16 frequency components ranging between 5 4 and 20 hz were inverted ten iterations were computed per frequency component leading to 160 tomographic models the waveform tomography has successfully imaged southwest dipping structures previously identified from other geophysical data as being associated with high resistivity bodies the relevance of the tomographic images is locally demonstrated by comparison of a velocity depth function extracted from the waveform tomography models with a coincident vertical seismic profiling vsp log available on the profile moreover comparison between observed and synthetic seismograms computed in the starting traveltime and waveform tomography models demonstrates unambiguously that the waveform tomography successfully predicts for wide angle reflections from southwest dipping geological structures this study demonstrates that the combination of first arrival traveltime and frequency domain full waveform tomographies applied to dense wide aperture seismic data is a promising approach to quantitative imaging of complex geological structures indeed wide aperture acquisition geometries offer the opportunity to develop an accurate background velocity model for the subsequent waveform tomography this is critical because the building of the macromodel remains an open question when only near vertical reflection data are considered

waveform tomography at a groundwater contamination site vsp surface data set application of 2d frequency domain waveform tomography to a data set from a high resolution vertical seismic profiling vsp experiment at a groundwater contamination site in hill air force base hafb utah reveals a surprisingly complicated shallow substructure with a resolution of approximately 1 5 m variance in the waveform misfit function is reduced 69 4 by using an initial velocity model from first arrival traveltime tomography the waveform tomography model suggests 1 a low velocity layer at 1 to 4 m depth 2 a high vertical velocity gradient of 80 m s m on average and 3 severe lateral variations velocity contrasts as large as about 200 m s occur in a distance as short as 1 5 m the model is well correlated with lithologic logs and is interpreted geologically a q value of 20 is estimated for the target area the extreme lateral and vertical variations of the subsurface compromise many standard seismic processing methods

3d prestack plane wave full waveform inversion prestack depth migration has been used for decades to derive velocity distributions in depth numerous tools and methodologies have been developed to reach this goal exploration in geologically more complex areas exceeds the abilities of existing methods new data acquisition and data processing methods are required to answer these new challenges effectively the recently introduced wide azimuth data acquisition method offers better illumination and noise attenuation as well as an opportunity to more accurately determine velocities for imaging one of the most advanced tools for depth imaging is full waveform inversion prestack seismic full waveform inversion is very challenging because of the nonlinearity and nonuniqueness of the solution combined with multiple iterations of forward modeling and residual wavefield back propagation the method is computer intensive especially for 3d projects we studied a time domain plane wave implementation of 3d waveform inversion we found that plane wave gathers

disturbance effects in pressuremeter tests in clay this paper analyzes the effect of borehole disturbance caused by installation of pressuremeter probes in clays on the derived stress strain curves both overpushing and overcutting induced distu

efficient waveform tomography for lithospheric imaging implications for realistic two dimensional acquisition geometries and low frequency data summary we provide a series of numerical experiments designed to test waveform tomography under i a reduction in the number of input data frequency components efficient waveform tomography ii sparse spatial subsampling of the input data and iii an increase in the minimum data frequency used these results extend the waveform tomography results of a companion paper using the same third party 2 d wide angle synthetic viscoelastic seismic data computed in a crustal geology model 250 km long and 40 km deep with heterogeneous p velocity s velocity density and q factor structure accurate velocity models were obtained using efficient waveform tomography and only four carefully selected frequency components of the input data 0 8 1 7 3 6 and 7 0 hz this strategy avoids the spectral redundancy present in full waveform tomography and yields results that are comparable with those in the companion paper for an 88 per cent decrease in total computational cost because we use acoustic waveform tomography the results further justify the use of the acoustic wave equation in calculating p wave velocity models from viscoelastic data the effect of using sparse survey geometries with efficient waveform tomography were investigated for both increased receiver spacing and increased source spacing sampling theory formally requires spatial sampling at maximum interval of one half wavelength 2 5 km at 0 8 hz for data with receivers every 0 9 km conforming to this criterion artefacts in the tomographic images were still minimal when the source spacing was as large as 7 6 km three times the theoretical maximum larger source spacings led to an unacceptable degradation of the results when increasing the starting frequency image quality was progressively degraded acceptable image quality within the central portion of the model was nevertheless achieved using starting frequencies up to 3 0 hz at 3 0 hz the maximum theoretical sample interval is reduced to 0 67 km due to the decreased wavelengths the available sources were spaced every 5 0 km more than seven times the theoretical maximum and receivers were spaced every 0 9 km 1 3 times the theoretical maximum higher starting frequencies than 3 0 hz again led to unacceptable degradation of the results

comparison of acoustic and elastic full waveform inversion of 2d towed streamer data in the presence of salt abstract over the last years full waveform inversion has become an important tool in the list of processing and imaging technologies available to the industry for marine towed streamer data full waveform inversion is typically applied using an acoustic approximation because s waves do not propagate in water and elastic effects in recorded data are generally assumed to be small we compare acoustic and elastic modelling and full waveform inversion for a field data set acquired offshore angola over sediments containing a salt body with significant topology forward modelling tests reveal that such geological structures lead to significant mode conversions at interfaces and consequently to significant relative amplitude differences when elastically and acoustically modelled traces are compared using an acoustic approach for modelling in full waveform inversion therefore leads to problems matching the synthetic data with the field data even for recorded pressure data and with trace normalization applied full waveform inversion is unable to find consistent model updates applying elastic full waveform inversion leads to more consistent and reliable model updates with less artefacts at the expense of additional computation cost although two dimensional marine towed streamer data are least favourable for the application of full waveform inversion compared to three dimensional data or ocean bottom data it is recommended to check on the existence of elastic effects before deciding on the final processing and imaging approach

acoustic full waveform inversion of surface seismic data using the gauss newton method with active constraint balancing we propose a full waveform inversion algorithm using the gauss newton inversion method with active constraint balancing that uses the spatially variant damping factor and source normalized wavefield approach for surface seismic data in the frequency domain the active constraint balancing technique automatically determines the optimum distribution of damping factors that control the stability and resolution in gauss newton inversion by using a parameter resolution matrix and spread function analysis through numerical experiments we present that the active constraint balancing scheme provides stable inversion results without a severe loss of resolution compared with the conventional gauss newton method the reconstructed image using the active constraint balancing method more closely resembles the true image for the region with low sensitivity also the estimated value converges faster to the smaller rms error level than those estimated by the conventional gauss newton method we also implement the normalized wavefield method to overcome the lack of precise knowledge on the source the source normalized wavefield approach effectively removes the potential inversion errors from source estimation because the source spectrum is eliminated during the normalization procedure our inversion algorithm using the source normalization scheme provides excellent inversion results even though the data are generated by two slightly different source wavelets we present that the frequency selection scheme proposed by sirgue and pratt which is based on the average amplitude of the whole received data provides a useful guideline for selecting the proper frequencies for our inversion our novel inversion algorithm successfully reconstructs the velocity model within 10 30 iterations despite its starting from a homogeneous or linearly increasing velocity model in addition for testing the performance of our inversion algorithm on a more complicated structure we apply the algorithm to the seg eage overthrust model successful inversion is achieved as the reconstructed image approaches the true model with the consistently converging rms error even though insufficient data are used

inverse theory applied to multi source cross hole tomography part 1 acoustic wave equation method1 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

full waveform inversion and distance separated simultaneous sweeping a study with a land seismic data set abstract dense wide aperture and broad frequency band acquisition improves seismic imaging and potentially allows the use of full waveform inversion for velocity model building the cost of dense acquisitions however limits its applicability blended or simultaneous shooting could lead to a good compromise between cost and dense acquisition although the cross talk between simultaneous sweeps may reduce imaging capabilities onshore a compromise is achieved with distance separated simultaneous sweeping acquisition because the shots are easily separated when the processing focuses on pre critical reflected events full waveform inversion for velocity model building however relies on post critical reflected refracted and diving events these events can interfere in a distance separated simultaneous sweeping acquisition by using a single vibrator single receiver data set recorded in inner mongolia china a distance separated simultaneous sweeping data set is created to study the robustness of full waveform inversion in this acquisition context this data set is well suited for full waveform inversion since it contains frequencies down to 1 5 hz and offsets up to 25 km full waveform inversion after a crude deblending of the distance separated simultaneous sweeping data set leads to a result very similar to the one obtained from the single vibrator single receiver data set the inversion of the blended data set gives a slightly less good result because of the cross talk but it is still quite satisfactory

building starting models for full waveform inversion from wide aperture data by stereotomography building an accurate initial velocity model for full waveform inversion fwi is a key issue to guarantee convergence of full waveform inversion towards the global minimum of a misfit function in this study we assess joint refraction and reflection stereotomography as a tool to build a reliable starting model for frequency domain full waveform inversion from long offset i e wide aperture data stereotomography is a slope tomographic method that is based on the inversion of traveltimes and slopes of locally coherent events in a data cube one advantage of stereotomography compare to conventional traveltime reflection tomography is the semi automatic picking procedure of locally coherent events which is easier than the picking of continuous events and can lead to a higher density of picks while conventional applications of stereotomography only consider short offset reflected waves we assess the benefits provided by the joint inversion of reflected and refracted arrivals introduction of the refracted waves allows the construction of a starting model that kinematically fits the first arrivals a necessary requirement for full waveform inversion in a similar way to frequency domain full waveform inversion we design a multiscale approach of stereotomography which proceeds hierarchically from the wide aperture to the short aperture components of the data to reduce the non linearity of the stereotomographic inversion of long offset data this workflow which combines stereotomography and full waveform inversion is applied to synthetic and real data case studies for the valhall oil field target the synthetic results show that the joint refraction and reflection stereotomography for a 24 km maximum offset data set provides a more reliable initial model for full waveform inversion than reflection stereotomography performed for a 4 km maximum offset data set in particular in low velocity gas layers and in the deep part of a structure below a reservoir application of joint stereotomography full waveform inversion and reverse time migration to real data reveals that the fwi models and the reverse time migration images computed from the stereotomography model shares several features with fwi velocity models and migrated images computed from an anisotropic reflection traveltime tomography model although stereotomography was performed in the isotropic approximation implementation of anisotropy in joint refraction and reflection stereotomography of long offset data is a key issue to further improve the accuracy of the method

seismic waveform inversion in the frequency domain part 2 fault delineation in sediments using crosshole data a crosshole experiment was carried out in a layered sedimentary environment in which a normal fault is known to cut through the section initial traveltime inversions produced stable but low resolution images from which the fault could be only vaguely inferred to image the fault wavefield inversion was used to produce a velocity model consistent with the detailed phase and amplitude of the data at a number of frequencies our wavefield inversion scheme uses a classical descent type algorithm for decreasing the data misfit by iteratively computing the gradient of this misfit by repeated forward and backward propagations our propagator is a full wave equation frequency domain acoustic finite difference method the use of the frequency space domain yields computational advantages for multisource data and allows an easy incorporation of viscous effects by running wavefield inversion on the field data a quantitative velocity image was produced that yielded a significantly improved image of the fault when compared with the original traveltime inversions because the original field data were noisy and contained a high degree of multiple scattering from the layering of the sediments the transmitted arrivals were selectively windowed to enhance the image the sediments at the site were strongly attenuating we therefore used a viscoacoustic model during the modeling and the inversion that correctly simulated the observed decrease in amplitude with increasing frequency and source receiver offset furthermore since the traveltime inversion indicated a high degree of anisotropy at the site a fixed homogeneous level of anisotropy was used during the inversion tests at varying levels of anisotropy confirmed the improvement in image quality and in data fit when anisotropy was incorporated the final image was verified by examining the distribution of the residuals in the frequency domain by comparing time domain modeled wavefields with the observed data and by direct comparison with borehole logs

two dimensional full wavefield inversion of wide aperture marine seismic streamer data summary 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

waveform tomography of two dimensional three component seismic data for hti anisotropic media reservoirs with vertically aligned fractures can be represented equivalently by horizontal transverse isotropy hti media but inverting for the anisotropic parameters of hti media is a challenging inverse problem because of difficulties inherent in a multiple parameter inversion in this paper when we invert for the anisotropic parameters we consider for the first time the azimuthal rotation of a two dimensional seismic survey line from the symmetry of hti the established wave equations for the hti media with azimuthal rotation consist of nine elastic coefficients expressed in terms of five modified thomsen parameters the latter are parallel to the thomsen parameters for describing velocity characteristics of weak vertical transverse isotropy media we analyze the sensitivity differences of the five modified thomsen parameters from their radiation patterns and attempt to balance the magnitude and sensitivity differences between the parameters through normalization and tuning factors which help to update the model parameters properly we demonstrate an effective inversion strategy by inverting velocity parameters in the first stage and updates the five modified thomsen parameters simultaneously in the second stage for generating reliably reconstructed models

joint acoustic full waveform inversion of crosshole seismic and ground penetrating radar data in the frequency domain abstractintegrating crosshole ground penetrating radar gpr with seismic methods is an efficient way to reduce the uncertainty and ambiguity of data interpretation in shallow geophysical investigations we have developed a new approach for joint full waveform inversion fwi of crosshole seismic and gpr data in the frequency domain to improve the inversion results of both fwi methods in a joint objective function three geophysical parameters p wave velocity permittivity and conductivity are effectively connected by three weighted cross gradient terms that enforce the structural similarity between parameter models simulation of acoustic seismic and scalar electromagnetic problems is implemented using 2d finite difference frequency domain methods and the inverse problems of seismic fwi and gpr fwi are solved using a matrix free truncated newton algorithm the joint inversion procedure is performed in several hierarchical frequencies and the three parameter models are sequentially inverted at each

sensitivity analysis and application of time lapse full waveform inversion synthetic testing and field data example from the north sea norway time lapse refraction can provide complementary seismic solutions for monitoring subtle subsurface changes that are challenging for conventional p wave reflection methods the utilization of refraction time lapse has lagged behind in the past partly due to the lack of robust techniques that allow extracting easy to interpret reservoir information however with the recent emergence of the full waveform inversion technique as a more standard tool we find it to be a promising platform for incorporating head waves and diving waves into the time lapse framework here we investigate the sensitivity of 2d acoustic time domain full waveform inversion for monitoring a shallow weak velocity change 30 m s or 1 6 the sensitivity tests are designed to address questions related to the feasibility and accuracy of full waveform inversion results for monitoring the field case of an underground gas blowout that occurred in the north sea the blowout caused the gas to migrate both vertically and horizontally into several shallow sand layers some of the shallow gas anomalies were not clearly detected by conventional 4d reflection methods i e time shifts and amplitude difference due to low 4d signal to noise ratio and weak velocity change on the other hand full waveform inversion sensitivity analysis showed that it is possible to detect the weak velocity change with the non optimal seismic input detectability was qualitative with variable degrees of accuracy depending on different inversion parameters we inverted the real 2d seismic data from the north sea with a greater emphasis on refracted and diving waves energy i e most of the reflected energy was removed for the shallow zone of interest after removing traces with offset less than 300 m the full waveform inversion results provided more superior detectability compared with the conventional 4d stacked reflection difference method for a weak shallow gas anomaly 320 m deep

full waveform tomography for lithospheric imaging results from a blind test in a realistic crustal model summary a comprehensive validation of 2 d frequency domain acoustic wave equation tomography was undertaken in a blind test using third party realistic elastic wave equation data the synthetic 2 d wide angle seismic data were provided prior to a recent workshop on the methods of controlled source seismology the true model was not revealed to the authors until after the presentation of our waveform tomography results the original model was specified on a detailed grid with variable p wave velocity s wave velocity density and viscoelastic q factor structure designed to simulate a section of continental crust 250 km long and 40 km deep synthetic vertical and horizontal component data were available for 51 shot locations spaced every 5 km recorded at 2779 receivers spaced every 90 m evenly spread along the surface of the model the data contained energy from 0 2 to 15 hz waveform tomography a combination of traveltime tomography and 2 d waveform inversion of the early arrivals of the seismic waveforms was used to recover crustal p velocity structure from the vertical component data using data from 51 sources 1390 receivers and frequencies between 0 8 and 7 0 hz the waveform tomography result contained apparent structure at wavelength scale resolution that was not evident on the traveltime tomography result the predicted acoustic waveforms in the final result matched the original elastic data to a high degree of accuracy during the workshop the exact model was revealed over much of the model the waveform tomography results provided a good correspondence with the true model from large to intermediate wavelength scales with a resolution limit on the order of 1 km a significant near surface low velocity zone invisible to traveltime methods was correctly recovered the results also provided a high resolution image of the complex structure of the entire crust and the depth and nature of the crust mantle transition some inaccuracies were observed near the edges of the images due to the limited ray coverage inherent to the footprint of the survey geometry several aspects of the waveform tomography strategy were critical to the success of the acoustic method with realistic synthetic viscoelastic data i the accuracy of the starting model from traveltime tomography ii implementation in the frequency domain iii the use of complex valued frequencies to effect time damping of the data residuals iv the selection of a suitable subset of data and data frequencies v progressive inversion of low to high frequency components of the data vi initial pre inversion matching of the amplitudes between observed and modelled data and vii sufficient preconditioning of both the data and the update images combined these strategies were effectively equivalent to a multiscale approach that mitigated the non linearity of the seismic inverse problem during the inversion we carried out repeated forward modelling to ensure our modelled waveforms matched the observed data as closely as possible in both frequency and time domains the synthetic data set used in this paper provides a benchmark for future testing of modelling inversion and imaging algorithms for wide angle lithospheric imaging

cross well seismic waveform tomography for monitoring co2 injection a case study from the ketzin site germany seismic full waveform inversion waveform tomography is a method to reconstruct the underground velocity field in high resolution using seismic data the method was first introduced during the 1980 s and became computationally feasible during the late 1990 s when the method was implemented in the frequency domain this work presents three case studies and one synthetic benchmark of full waveform inversion applications two of the case studies are focused on time lapse cross well and 2d reflection seismic data sets acquired at the ketzin co2 geological storage site these studies are parts of the co2sink and co2man projects the results show that waveform tomography is more effective than traveltime tomography for the co2 injection monitoring at the ketzin site for the cross well geometry for the surface data sets we find it is difficult to recover the true value of the velocity anomaly due to the injection using the waveform inversion method but it is possible to qualitatively locate the distribution of the injected co2 the results agree well with expectations based upon conventional 2d cdp processing methods and more extensive 3d cdp processing methods in the area a further investigation was done to study the feasibility and efficiency of seismic full waveform inversion for time lapse monitoring of onshore co2 geological storage sites using a reflection seismic geometry with synthetic data sets the results show that waveform inversion may be a good complement to standard cdp processing when monitoring co2 injection the choice of method and strategy for waveform inversion is quite dependent on the goals of the time lapse monitoring of the co2 injection the last case study is an application of the full waveform inversion method to two crooked profiles at the forsmark site in eastern central sweden the main goal of this study was to help determine if the observed reflections are mainly due to fluid filled fracture zones or mafic sills one main difficulty here is that the profiles have a crooked line geometry which corresponds to 3d seismic geometry but a 2d based inversion method is being used this is partly handled by a 3d to 2d coordinate projection method from traveltime inversion the results show that these reflections are primarily due to zones of lower velocity consistent with them being generated at water filled fracture zones

diffraction tomography and multisource holography applied to seismic imaging seismic tomography is emerging as an imaging method for determining subsurface structure when the view angle coverage is limited and the scale of the medium inhomogeneities is comparable with the wavelength as is often true in geophysical applications the performance of ordinary ray tomography becomes poor other tomographic methods are needed to improve the imaging process here we study diffraction tomography and multisource holography and evaluate their performances for surface reflection profiling srp vertical seismic profiling vsp and cross hole measurements theoretical formulations are derived for two dimensional geometry in terms of line sources along a source line and line receivers along a receiver line the theory for diffraction tomography is based on the born or rytov approximation the performances of diffraction tomography and multisource holography are evaluated by examining the information coverage in the spatial frequency domain and by numerical examples multisource holography

improved amplitude preservation for prestack depth migration by inverse scattering theory a prestack reverse time migration image is not properly scaled with increasing depth the main reason for the image being unscaled is the geometric spreading of the wavefield arising during the back propagation of the measured data and the generation of the forward modelled wavefields this unscaled image can be enhanced by multiplying the inverse of the approximate hessian appearing in the gauss newton optimization technique however since the approximate hessian is usually too expensive to compute for the general geological model it can be used only for the simple background velocity model we show that the pseudo hessian matrix can be used as a substitute for the approximate hessian to enhance the faint images appearing at a later time in the 2d prestack reverse time migration sections we can construct the pseudo hessian matrix using the forward modelled wavefields which are used as virtual sources in the reverse time migration by exploiting the uncorrelated structure of the forward modelled wavefields and the impulse response function for the estimated diagonal of the approximate hessian although it is also impossible to calculate directly the inverse of the pseudo hessian when using the reciprocal of the pseudo hessian we can easily obtain the inverse of the pseudo hessian as examples supporting our assertion we present the results obtained by applying our method to 2d synthetic and real data collected on the korean continental shelf

early arrival waveform tomography on near surface refraction data we develop a waveform tomography method for estimating the velocity distribution that minimizes the waveform misfit between the predicted and observed early arrivals in space time seismograms by fitting the waveforms of early arrivals early arrival waveform tomographyewt naturally takes into account more general wave propagation effects compared to the high frequency method of traveltime tomography meaning that ewt can estimate a wider range of slowness wavenumbers another benefit of ewt is more reliable convergence compared to full waveform tomography because an early arrival misfit function contains fewer local minima synthetic test results verify that the waveform tomogram is much more accurate than the traveltime tomogram and that this algorithm has good convergence properties for marine data from the gulf of mexico the statics problem caused by shallow gassy muds was attacked by using ewt to obtain a more accurate velocity model using the waveform tomogram to correct for statics the stacked section was significantly improved compared to using the normal moveout nmo velocity and moderately improved compared to using the traveltime tomogram inverting high resolution land data from mapleton utah showed an ewt velocity tomogram that was more consistent with the ground truth trench log than the traveltime tomogram our results suggest that ewt can provide supplemental shorter wavelength information compared to the traveltime tomogram for both shallow and moderately deep seismic data

individual and joint 2 d elastic full waveform inversion of rayleigh and love waves we investigate the performance of the individual 2 d elastic full waveform inversion fwi of rayleigh and love waves as well as the feasibility of a simultaneous joint fwi of both wave types the fwi of surface waves can provide a valuable contribution to near surface investigations since they are mainly sensitive to the s wave velocity and hold a high signal to noise ratio in synthetic reconstruction tests we compare the performance of the individual wave type inversions and explore the benefits of a simultaneous joint inversion in these tests both individual wave type inversions perform similarly well given that the initial p wave velocity model is accurate enough in this case the joint fwi further improves the result for an inaccurate initial p wave velocity model we observe artifacts in the results of the rayleigh wave fwi and the joint fwi subsequently we recorded a near surface field dataset to verify the results by a realistic example in the field data application the love wave fwi is superior to the rayleigh wave fwi possibly due to the initial p wave velocity model also in this case the joint fwi further improves the inversion result