reverse time migration a prospect of seismic imaging methodology abstract reverse time migration rtm is a seismic imaging method to map the subsurface reflectivity using recorded seismic waveforms the practice in exploration seismology has long established a two fold approach of seismic imaging using velocity modeling building to establish the long wavelength reference velocity models and using seismic migration to map the short wavelength reflectivity structures among various seismic migration methods for different situations rtm is the only method that is capable to use all seismic wave types that can be computed numerically being initiated in early 1980 s rtm seeks an image of the subsurface reflectivity as the best match in an image space between the extrapolation of time reversed waveform data and the prediction based on estimated velocity model and source parameters judging the image quality in the same space of forming the images is more advantageous than the approaches of modeling and inversion which seek the solution in the model space but judge its fitness in data space considering that most seismic migration applications today still use primary reflection as the only signal the capability of rtm to use all computable wave types is unique and helpful reducing the imaging artifacts due to mistaking non primary waves as primary reflections hence we refer to those rtm algorithms using only primary reflections as the first generation rtm methods and the rtm algorithms making a full use of primary reflections multiple reflections and other non primary waveform data as the second generation rtm methods this paper reviews the development history of the rtm along with its major challenges current solutions and future perspectives

wavefield tomography using reverse time migration backscattering abstractreverse time migration backscattering contains kinematic information that can be used to constrain velocity models the backscattering results from the correlation between forward scattered and backscattered wavefields from sharp interfaces i e sediment salt interfaces the synchronization between these wavefields depends on the velocity of the sediment section and the correct interpretation of the sharp boundary we have developed an optimization workflow in which the sediment velocity and the sharp boundary are updated iteratively the presence of sharp boundaries in the model lead to high and low wavenumber components in the objective function gradient the high wavenumber components correspond to the correlation of wavefields traveling in opposite directions whereas the low wavenumber components correspond to the correlation of wavefields traveling in the same direction this behavior is similar to reverse time migration in which the high wavenumber components represent the reflectors th

understanding the reverse time migration backscattering noise or signal reverse time migration backscattered events are produced by the cross correlation between waves reflected from sharp interfaces e g salt bodies these events along with head waves and diving waves produce the so called reverse time migration artefacts which are visible as low wavenumber energy on migrated images commonly these events are seen as a drawback for the reverse time migration method because they obstruct the image of the geologic structure which is the real objective for the process in this paper we perform numeric and theoretical analysis to understand the reverse time migration backscattering energy in conventional and extended images we show that the reverse time migration backscattering contains a measure of the synchronization and focusing information between the source and receiver wavefields we show that this synchronization and focusing information is sensitive to velocity errors this implies that a correct velocity model produces reverse time migration backscattering with maximum energy therefore before filtering the reverse time migration backscattered energy we should try to obtain a model that maximizes it

imaging passive seismic data imaging passive seismic data is the process of synthesizing the wealth of subsurface information available from reflection seismic experiments by recording ambient sound using an array of geophones distributed at the surface crosscorrelating the traces of such a passive experiment can synthesize data that are identical to actively collected reflection seismic data with a correlation based imaging condition wave equation shot profile depth migration can use raw transmission wavefields as input for producing a subsurface image migration is even more important for passively acquired data than for active data because with passive data the source wavefields are likely to be weak compared with background and instrument noise a condition that leads to a low signal to noise ratio fourier analysis of correlating long field records shows that aliasing of the wavefields from distinct shots is unavoidable although this reduces the order of computations for correlation by the length of the original trace the

analysis of the traveltime sensitivity kernels for an acoustic transversely isotropic medium with a vertical axis of symmetry in anisotropic media several parameters govern the propagation of the compressional waves to correctly invert surface recorded seismic data in anisotropic media a multi parameter inversion is required however a tradeoff between parameters exists because several models can explain the same dataset to understand these tradeoffs diffraction reflection and transmission type sensitivity kernels analyses are carried out such analyses can help us to choose the appropriate parameterization for inversion in tomography the sensitivity kernels represent the effect of a parameter along the wave path between a source and a receiver at a given illumination angle similarities between sensitivity kernels highlight the tradeoff between the parameters to discuss the parameterization choice in the context of finite frequency tomography we compute the sensitivity kernels of the instantaneous traveltimes derived from the seismic data traces we consider the transmission case with no encounter of an interface between a source and a receiver with surface seismic data this corresponds to a diving wave path we also consider the diffraction reflection case when the wave path is formed by two parts one from the source to a sub surface point and the other from the sub surface point to the receiver we illustrate the different parameter sensitivities for an acoustic transversely isotropic medium with a vertical axis of symmetry the sensitivity kernels depend on the parameterization choice by comparing different parameterizations we explain why the parameterization with the normal moveout velocity the anellipitic parameter and the parameter is attractive when we invert diving and reflected events recorded in an active surface seismic experiment

ocean surface wave evolvement in the arctic basin 1 recent basin scale changes to the compactness and thickness of arctic sea ice foreshadow that encroaching swells and locally generated waves will exert more influence there in the future indeed it is conceivable that waves may have already hastened the adjustments observed by breaking up ice floes yet waves advancing in sea ice attenuate due to being scattered from ice thickness variations and damped by ice inelasticity turbulence and friction while past research focuses on scattering by unnaturally perfect features in the ice the model reported herein assimilates realistic basin scale swathes of heterogeneous ice and parameterizes damping by way of example we show how an ocean wave train evolves during its passage in an 1670 km long arctic sea ice profile obtained from submarine

interferometric imaging condition for wave equation migration the fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wavefield reconstruction models can be decomposed in two components corresponding to large scale and small scale variations in practice the large scale velocity model component can be estimated with high accuracy using repeated migration tomography cycles but the small scale component cannot when the earth has significant small scale velocity components wavefield reconstruction does not completely describe the recorded data and migrated images are perturbed by artifacts there are two possible ways to address this problem 1 improve wavefield reconstruction by estimating more accurate velocity models and image using conventional techniques e g wavefield crosscorrelation or 2 reconstruct wavefields with conventional methods using the known background velocity model but improve the imaging condition to alleviate the artifacts caused by the imprecise reconstruction wedescribe the unknown component o

anisotropy signature in reverse time migration extended images reverse time migration can accurately image complex geologic structures in anisotropicmedia extended images at selected locations in the earth i e at commonimage point gathers carry rich information to characterize the angle dependent illumination and to provide measurements for migration velocity analysis however characterizing the anisotropy influence on such extended images is a challenge extended common image point gathers are cheap to evaluate since they sample the image at sparse locations indicated by the presence of strong reflectors such gathers are also sensitive to velocity error that manifests itself through moveout as a function of space and time lags furthermore inaccurate anisotropy leaves a distinctive signature in common image point gathers which can be used to evaluate anisotropy through techniques similar to the ones used in conventional wavefield tomography it specifically admits a v shaped residual moveout with the slope of the v flanks depending on the anisotropic parameter regardless of the complexity of the velocity model it reflects the fourth order nature of the anisotropy influence on moveout as it manifests itself in this distinct signature in extended images after handling the velocity properly in the imaging process synthetic and real data observations support this assertion

angle dependent reflectivity by means of prestack migration most present day seismic migration schemes determine only the zero offset reflection coefficient for each grid point depth point in the subsurface in matrix notation the zero offset reflection coefficient is found on the diagonal of a reflectivity matrix operator that transforms the illuminating source wave field into a reflected wave field however angle dependent reflectivity information is contained in the full reflectivity matrix our objective is to obtain angle dependent reflection coefficients from seismic data by means of prestack migration multisource multioffset after downward extrapolation of source and reflected wave fields to one depth level the rows of the reflectivity matrix representing angle dependent reflectivity information for each grid point at that depth level are recovered by deconvolving the reflected wave fields with the related source wave fields this process is carried out in the space frequency domain in order to preserve the angle dependent reflectivity in the im

regularization in slope tomography seismic imaging in depth is limited by the accuracy of velocity model estimation slope tomography uses the slowness components and traveltimes of picked reflection or diffraction events for velocity model building the unavoidable data incompleteness requires additional information to assure stability to inversion one natural constraint for ray based tomography is a smooth velocity model we propose a new reflection angle based kind of smoothness constraint as regularization in slope tomography and have compared its effects to three other more conventional constraints the effects of these constraints were evaluated through angle domain common image gathers computed with wave equation migration using the estimated velocity model we found that the smoothness constraints have a distinct effect on the velocity model but a weaker effect on the migrated data in numerical tests on synthetic data the new constraint leads to geologically more consistent models

enabling affordable omnidirectional subsurface extended image volumes via probing image gathers as a function of subsurface offset are an important tool for the inference of rock properties and velocity analysis in areas of complex geology traditionally these gathers are thought of as multidimensional correlations of the source and receiver wavefields the bottleneck in computing these gathers lies in the fact that one needs to store compute and correlate these wavefields for all shots in order to obtain the desired image gathers therefore the image gathers are typically only computed for a limited number of subsurface points and for a limited range of subsurface offsets which may cause problems in complex geological areas with large geologic dips we overcome increasing computational and storage costs of extended image volumes by introducing a formulation that avoids explicit storage and removes the customary and expensive loop over shots found in conventional extended imaging as a result we end up with a matrix vector formulation from which different image gathers can be formed and with which amplitude versus angle and wave equation migration velocity analysis can be performed without requiring prior information on the geologic dips aside from demonstrating the formation of two way extended image gathers for different purposes and at greatly reduced costs we also present a new approach to conduct automatic wave equation based migration velocity analysis instead of focusing in particular offset directions and preselected subsets of subsurface points our method focuses every subsurface point for all subsurface offset directions using a randomized probing technique as a consequence we obtain good velocity models at low cost for complex models without the need to provide information on the geologic dips

split step fourier migration the split step fourier method is developed and applied to migrating stacked seismic data in two and three dimensions this migration method which is implemented in both the frequency wavenumber and frequency space domains takes into account laterally varying velocity by defining a reference slowness reciprocal of velocity as the mean slowness in the migration interval and a perturbation term that is spatially varying the mean slowness defines a reference vertical wavenumber which is used in the frequency wavenumber domain to downward continue the data across a depth interval as in constant velocity phase shift migration the perturbation term is used to define a source contribution that is taken into account by the application of a second phase shift in the frequency space domain since the method does not include the effects of second and higher order spatial derivatives of the slowness field the method theoretically is accurate only when there are no rapid lateral slowness variations combined wi

stacking angle domain common image gathers for normalization of illumination unequal illumination of the subsurface highly impacts the quality of seismic imaging different image points receive different folds of reflection angle illumination which can be caused by irregular acquisition or by wave propagation in complex media illumination problems can deteriorate amplitudes in migrated images to address this problem we present a method of stacking angle domain common image gathers in which we use local similarity with soft thresholding to determine the folds of local illumination normalization by local similarity regularizes local illumination of reflection angles for each image point of the subsurface model this approach compensates for irregular illumination by selective stacking in the image space regardless of the cause of acquisition or propagation irregularities additional migration is not required because the methodology is implemented in the reflection angle domain after migration we use two synthetic examples to demonstrate that our method can normalize migration amplitudes and effectively suppress migration artefacts

3d angle decomposition for elastic reverse time migration abstractwe have developed three approaches for 3d angle decomposition using elastic reverse time migration the first approach uses time and space lag common image point gathers computed from elastic wavefields this method facilitates computing angle gathers at sparse and possibly irregularly distributed points in the image the second approach transforms extended time lag images to the angle domain using slant stacks along 4d surfaces instead of using slant stacks along 2d straight lines the third approach transforms space lag common image gathers to the angle domain the three proposed methods solve a system of equations that handles dipping reflectors and they yield angle gathers that are more accurate compared with those obtained via alternative existing methods we have developed our methods using 2d and 3d synthetic and field data examples and found that they provide accurate opening and azimuth angles and they can handle steeply dipping reflectors and converted wave modes

equivalence of source receiver migration and shot profile migration at first glance shot profile migration jacobs 1982 and source receiver survey sinking migration claerbout 1985 seem to be substantially different algorithms the basic principles used by the two schemes are different shot profile migration is performed by independently propagating the source wavefield and the receiver wavefield the image is obtained by crosscorrelating the two wavefields possibly normalized by the amplitude of the source wavefield source receiver migration is based on the concept of survey sinking by which we recursively synthesize equivalent data sets at increasing depth at each depth step imaging is performed by extracting the wavefield at zero time recently the issue of the relation between shot profile migration and source receiver migration has become more relevant because of two important developments 1 the increase in the practical applications of 3d prestack migration by wavefield continuation for imaging complex structures and 2 the introduction of methods for computing angle domain common image gathers adcig both for velocity estimation biondi and sava 1999 prucha et al 1999 clapp and biondi 2000 and for amplitude variation with angle ava analysis de bruin et al 1990 wapenaar et al 1999 sava et al 2001

image domain wavefield tomography with extended common image point gathers waveform inversion is a velocity model building technique based on full waveforms as the input and seismic wavefields as the information carrier conventional waveform inversion is implemented in the data domain however similar techniques referred to as image domain wavefield tomography can be formulated in the image domain and use a seismic image as the input and seismic wavefields as the information carrier the objective function for the image domain approach is designed to optimize the coherency of reflections in extended common image gathers the function applies a penalty operator to the gathers thus highlighting image inaccuracies arising from the velocity model error minimizing the objective function optimizes the model and improves the image quality the gradient of the objective function is computed using the adjoint state method in a way similar to that in the analogous data domain implementation we propose an image domain velocity model building method using extended common image point space and time lag gathers constructed sparsely at reflections in the image the gathers are effective in reconstructing the velocity model in complex geologic environments and can be used as an economical replacement for conventional common image gathers in wave equation tomography a test on the marmousi model illustrates successful updating of the velocity model using commonimage point gathers and resulting improved image quality

the impact of migration on avo amplitude variation with offset avo analysis is often limited to areas where multidimensional propagation effects such as reflector dip and diffractions from faults can be ignored migration inversion provides a framework for extending the use of seismic amplitudes to areas where structural or stratigraphic effects are important in this procedure sources and receivers are downward continued into the earth using uncollapsed prestack migration instead of stacking the data as in normal migration the prestack migrated data are used in avo analysis or other inversion techniques to infer local earth properties the prestack migration can take many forms in particular prestack time migration of common angle sections provides a convenient tool for improving the lateral resolution and spatial positioning of avo anomalies in this approach a plane wave decomposition is first applied in the offset direction separating the wavefield into different propagating angles the data are then gathered into common angle sections and migrated one angle at a time the common angle migrations have a simple form and are shown to adequately preserve amplitude as a function of angle normal avo analysis is then applied to the prestack migrated data examples using seismic lines from the gulf of mexico show how migration improves avo analysis in the first set of examples migration is shown to improve imaging of subtle spatial variations in bright spots subsequent avo analysis reveals dim spots associated with dry hole locations that were not resolvable using traditional processing techniques including both conventional avo and poststack migration a second set of examples shows improvements in avo response after migration is used to reduce interference from coherent noise and diffractions a final example shows the impact of migration on the spatial location of dipping avo anomalies in all cases migration improves both the signal to noise ratio and spatial resolution of avo anomalies

polarization based wave equation migration velocity analysis in acoustic media abstractthe source extrapolation step in wave equation prestack reverse time migration gives wavefield polarization information which can be used to generate angle domain common image gathers adcigs from seismic reflection data from acoustic media concatenation of p wave polarization segments gives wavefield propagation paths wavepaths which are similar to the raypaths in ray based velocity tomography the adcigs provide residual depth moveout rmo information from which a system of linear equations is constructed for tomography to solve for the velocity ratio used for velocity updating an empirical relation between the rmo data and the velocity ratio updates reduces the amount of computation and is stabilized by the feedback provided by the iterative loop through prestack migration to rmo to velocity update to prestack migration correcting the rmos to flatten the adgigs is the convergence condition synthetic data for a layered model with a fault successfully illustrates the method

vector acoustic reverse time migration of volve ocean bottom cable data set without up down decomposed wavefields abstractmethods for wavefield injection are commonly used to extrapolate seismic data in reverse time migration rtm injecting a single component of the acoustic field for example pressure leads to ambiguity in the direction of propagation each recorded wavefront is propagated both upward and downward and spurious or ghost reflectors are created alongside real reflectors in the subsurface image thus wavefield separation based on the combination of pressure and particle velocity data is generally performed prior to imaging to extract only the upgoing field from multicomponent seabed or towed marine seismic recordings by instead combining vector acoustic va data with monopole and dipole type propagators in the extrapolation of shot or receiver gathers we show that wavefield separation or deghosting can instead be performed on the fly at limited additional cost this strategy was successfully applied to a line of a north sea ocean bottom cable data set acquired over the volve field we t

an overview of depth imaging in exploration geophysics prestack depth migration is the most glamorous step of seismic processing because it transforms mere data into an image and that image is considered to be an accurate structuraldescriptionoftheearth thus ourexpectationsofitsaccuracy robustness and reliability are high amazingly seismic migration usually delivers the past few decades have seen migration move from its heuristic roots to mathematically sound techniques that using relatively few assumptions render accurate pictures of the interior of the earth interestingly theearthandthesubjectswewanttoimageinside itarevariedenoughthat sofar nosinglemigrationtechnique has dominated practical application all techniques continually improve and borrow from each other so one technique mayneverdominate despitetheprogressinstructuralimaging wehavenotreachedthepointwhereseismicimagesprovide quantitatively accurate descriptions of rocks and fluids nor have we attained the goal of using migration as part of a purelycomputationalprocesstodeterminesubsurfacevelocity in areas where images have the highest quality we might be nearing those goals collectively called inversion where data are more challenging the goals seem elusive we describe the progress made in depth migration to the present and the most significant barriers to attaining its inversion goalsinthefuture wealsoconjectureonprogresslikelytobe made in the years ahead and on challenges that migration mightnotbeabletomeet

sensitivity kernel based tomographic migration velocity analysis using reverse time migration angle image gathers abstractsensitivity kernel based tomographic migration velocity analysis tmva provides a means to better update the migration velocity model in complex media for actual seismic data with finite frequency bandwidth migration velocity updated from wave equation based tomography is more suitable and robust than ray based tomography for images obtained from reverse time migration rtm depth residuals in the rtm extracted angle image gathers offer a reliable source of velocity information we have developed cost effective means of calculating the angle domain sensitivity kernel and incorporated it into the tmva approach using rtm angle image gathers the angle domain sensitivity kernels are used to convert the depth residuals from rtm angle image gathers into velocity perturbations which were then used to refine the velocity model we derived an approximate analytical residual moveout function for measuring depth residuals of the rtm angle image gather in isotropic media and also devised a workflow for

improving the gradient of the image domain objective function using quantitative migration for a more robust migration velocity analysis migration velocity analysis aims at determining the background velocity model classical artefacts such as migration smiles are observed on subsurface offset common image gathers due to spatial and frequency data limitations we analyse their impact on the differential semblance functional and on its gradient with respect to the model in particular the differential semblance functional is not necessarily minimum at the expected value tapers are classically applied on common image gathers to partly reduce these artefacts here we first observe that the migrated image can be defined as the first gradient of an objective function formulated in the data domain for an automatic and more robust formulation we introduce a weight in the original data domain objective function the weight is determined such that the hessian resembles a dirac function in that way we extend quantitative migration to the subsurface offset domain this is an automatic way to compensate for illumination we analyse the modified scheme on a very simple 2d case and on a more complex velocity model to show how migration velocity analysis becomes more robust

offset and angle domain common image point gathers for shot profile migration prestack depth migration of shot profiles by downward continuation is a practical imaging algorithm that is especially cost effective for sparse shot wide azimuth geometries the interpretation of offset as the displacement between the downward propagating shot wavefield and upward propagating receiver wavefield enables us to extract offset domain common image point cip gathers during shot profile migration the offset domain gathers can then be transformed to the angle domain with a radial trace mapping originally introduced for shot geophone migration the computational implications of this procedure include both the additional cost of multioffset imaging and an implicit transformation from shot geophone to midpoint offset coordinates although this algorithm provides a mechanism for imaging angle dependent reflectivity via shot profile migration for sparse shot geometries the fundamental problem of shot aliasing may severely impact the quality of cip gathers

scattering and dip angle decomposition based on subsurface offset extended wave equation migration abstractan angle dependent reflection coefficient is recovered by seismic migration in the angle domain we have developed a postmigration technique for computing scattering and dip angle common image gathers cigs from seismic images extended by the subsurface offset based on wave equation migration methods our methodology suggests a system of radon transform operators by introducing local transform relations between the subsurface offset image and the angle domain components in addition to the commonly used decomposition of the scattering angle the methodology associates the wave equation migration with dip domain images as well the same postmigration subsurface offset image is used to decompose scattering and dip angle cigs individually or to decompose a multiangle cig by showing simultaneously both angles on the gather s axis we show that the dip angle response of seismic reflections is a spot like signature focused at the specular dip of the subsurface reflector it differs from the well stu

image enhancement by multi parameter characterization of common image gathers we present an innovative approach for seismic image enhancement using multiparameter angle domain characterization of common image gathers a special subsurface angle domain imaging system is used to generate the multi parameter common image gathers in a summation free image space the imaged data associated with each common image gathers depth point contain direction dependent opening angle image contributions from all the available incident and scattered wave pairs at this point each direction dependent opening angle data can be differently weighted according to its coherency measure once the optimal migration velocity is used it is assumed that in the actual specular direction the coherency measure semblance along reflection events from all available opening angles and opening azimuths is larger than that along non specular directions the computed direction dependent semblance attribute is designed to operate as an imaging filter which enhances specular migration contributions and suppresses all others in the final migration image the ability to analyse the structural properties of the image points by the multi parameter common image gather allows us to better handle cases of complicated wave propagation and to improve the image quality at poorly illuminated regions or near complex structures the proposed method and some of its practical benefits are demonstrated through detailed analysis of synthetic and real data examples

angle domain common image gathers for migration velocity analysis by wavefield continuation imaging we analyze the kinematic properties of offset domain common image gathers cigs and angle domain cigs adcigs computed by wavefield continuation migration our results are valid regardless of whether the cigs were obtained by using the correct migration velocity they thus can be used as a theoretical basis for developing migration velocity analysis mva methods that exploit the velocity information contained in adcigs we demonstrate that in an adcig cube the image point lies on the normal to the apparent reflector dip that passes through the point where the source ray intersects the receiver ray the image point position on the normal depends on the velocity error when the velocity is correct the image point coincides with the point where the source ray intersects the receiver ray starting from this geometric result we derive an analytical expression for the expected movements of the image points in adcigs as functions of the traveltime perturbation caused by velocity errors by applying this ana

true amplitude prestack depth migration most current true amplitude migrations correct only for geometric spreading we present a new prestack depth migration method that uses the framework of reverse time migration to compensate for geometric spreading intrinsic q losses and transmission losses geometric spreading is implicitly compensated by full two way wave propagation intrinsic q losses are handled by including a q dependent term in the wave equation transmission losses are compensated based on an estimation of angle dependent reflectivity using a two pass recursive reverse time prestack migration the image condition used is the ratio of receiver source wavefield amplitudes two dimensional tests using synthetic data for a dipping layer model and a salt model show that loss compensating prestack depth migration can produce reliable angle dependent reflection coefficients at the target the reflection coefficient curves are fitted to give least squares estimates of the velocity ratio at the target the main new result is a procedure

true amplitude recovery in reverse time extrapolation of plane and spherical waves one of the challenging outstanding problems in reverse time extrapolation is recovering accurate amplitudes at reflectors from the receiver wavefield various migrations have been developed to produce accurate image locations rather than correct amplitude information because of inadequate compensation of attenuation dispersion and transmission losses we first evaluated the requirements and demonstrated the theoretical feasibility of true amplitude recovery of 2d acoustic and elastic seismic data by using the analytic zoeppritz equations for plane wave reflection and transmission coefficients then we used synthetic acoustic and elastic wavefield data generated by elastodynamic finite differences to verify the recovery in the reverse time propagation of spherical waves and illustrated the salient differences between the incident wavefields reconstructed from reflection data only and from the combination of reflection and transmission data these examples quantitatively verified that recovering an

minor and trace elements as indicators of solute provenance and flow routing in a subglacial hydrological system mitchell a c brown g h fuge r 2006 minor and trace elements as indicators of solute provenance and flow routing in a subglacial hydrological system hydrological processes 20 4 877 897 sponsorship university of wales aberystwyth studentship am university of wales aberystwyth research grants 56 95 and 36 96 ghb and rf and nerc grant no gr3 11216

true amplitude angle domain common image gathers from one way wave equation migrations true amplitude wave equation migration provides a quality migrated image of the earth s interior in addition the amplitude of the output provides an estimate of the angular dependent reflection coefficient similar to the output of kirchhoff inversion recently true amplitude wave equation migration for common shot data has been proposed to generate amplitude reliable shot domain common image gathers in heterogeneous media we present a method to directly produce angle domain common image gathers from both common shot and shot receiver wave equation migration generating true amplitude shot domain common image gathers requires a deconvolution type imaging condition using the ratio of the upgoing and downgoing wavefield each downward projected to the image point producing true amplitude angle domain common image gathers requires instead the product of the upgoing wavefield and the complexconjugate of the downgoing wavefield in the imaging condition since multiplication is a more stable comput

image domain velocity inversion and event location for microseismic monitoring abstractmicroseismic event locations obtained from seismic monitoring data sets are often a primary means of determining the success of fluid injection programs such as hydraulic fracturing for oil and gas extraction geothermal projects and wastewater injection event locations help the decision makers to evaluate whether operations conform to expectations or parameters need to be changed and may be used to help assess and reduce the risk of induced seismicity however obtaining accurate event location estimates requires an accurate velocity model which is not available at most injection sites common velocity updating techniques require picking arrivals on individual seismograms this can be problematic in microseismic monitoring particularly for surface acquisition due to the low signal to noise ratio of the arrivals we have developed a full wavefield adjoint state method for locating seismic events while inverting for p and s wave velocity models that optimally focus multiple complementary ima

wide azimuth angle gathers for wave equation migration extended common image point cip gathers contain all of the necessary information for decomposition of reflectivity as a function of the reflection and azimuth angles at selected locations in the subsurface this decomposition operates after the imaging condition applied to wavefields reconstructed by any type of wide azimuth migration method e g using downward continuation or time reversal the reflection and azimuth angles are derived from the extended images using analytic relations between the space lag and time lag extensions the transformation amounts to a linear radon transform applied to the cips obtained after applying the extended imaging condition if information about the reflector dip is available at the cip locations then only two components of the space lag vectors are required thus reducing computational cost and increasing the affordability of the method applications of this method include the study of subsurface illumination in areas of complex geology where ray based methods are

3d angle domain common image gathers for migration velocity analysis angle domain common image gathers adcigs are an essential tool for migration velocity analysis mva we present a method for computing adcigs in 3d from the results of wavefield continuation migration the proposed methodology can be applied before or after the imaging step in a migration procedure when computed before imaging 3d adcigs are functions of the offset ray parameters we derive the geometric relationship that links the offset ray parameters to the aperture angle and the reflection azimuth when computed after imaging 3d adcigs are directly produced as functions of and the mapping of the offset ray parameters into the angles depends on both the local dips and the local interval velocity therefore the transformation of adcigs computed before imaging into adcigs that are functions of the actual angles is difficult in complex structure by contrast the computation of adcigs after imaging is efficient and accurate even in the presence of complex structure and a heterogeneous velocity function on the other hand the estimation of the offset ray parameters is less sensitive to velocity errors than the estimation of the angles when adcigs that are functions of the offset ray parameters are adequate for the application of interest e g ray based tomography the computation of adcigs before imaging might be preferable errors in the migration velocity cause the image point in the angle domain to shift along the normal to the apparent geological dip by assuming stationary rays i e small velocity errors we derive a quantitative relationship between this normal shift and the traveltime perturbation caused by velocity errors this relationship can be directly used in an mva procedure to invert depth errors measured from adcigs into migration velocity updates in this paper we use it to derive an approximate 3d residual moveout rmo function for measuring inconsistencies between the migrated images at different and we tested the accuracy of our kinematic analysis on a 3d synthetic data set with steeply dipping reflectors and a vertically varying propagation velocity the tests confirm the accuracy of our analysis and illustrate the limitations of the straight ray approximation underlying our derivation of the 3d rmo function

full azimuth subsurface angle domain wavefield decomposition and imaging part i directional and reflection image gathers we present a new subsurface angle domain seismic imaging systemforgeneratingandextractinghigh resolutioninformation about subsurface angle dependent reflectivity the system enables geophysicists to use all recorded seismic data in a continuousfashiondirectlyinthesubsurfacelocalangledomainlad resulting in two complementary full azimuth common imageangle gather systems directional and reflection the complete setofinformationfrombothtypesofanglegathersleadstoaccurate high resolution reliable velocity model determination and reservoir characterization the directional angle decomposition enables the implementation of specular and diffraction imaging in real 3d isotropic anisotropic geological models leading to simultaneous emphasis on continuous structural surfaces and discontinuous objects such as faults and small scale fractures structural attributes at each subsurface point e g dip azimuth andcontinuity canbederiveddirectlyfromthedirectionalangle gathers the reflection angle gathers display reflectivity as a function of the opening angle and opening azimuth these gathers are most meaningful in the vicinity of actual local reflecting surfaces wherethereflectionanglesaremeasuredwithrespectto the derived background specular direction the reflection angle gathers are used for automatic picking of full azimuth angle domainresidualmoveoutsrmowhich togetherwiththederived background orientations of the subsurface reflection horizons provide a complete set of input data to isotropic anisotropic tomography the full azimuth angle dependent amplitude variations are used for reliable and accurate amplitude versus angle andazimuthavazanalysisandreservoircharacterization the proposed system is most effective for imaging and analysis below complex structures such as subsalt and subbasalt high velocity carbonate rocks shallow low velocity gas pockets and others in addition it enables accurate azimuthal anisotropic imaging and analysis providing optimal solutions for fracture detectionandreservoircharacterization

geochemical weathering at the bed of haut glacier d arolla switzerland a new model waters were sampled from 17 boreholes at haut glacier d arolla during the 1993 and 1994 ablation seasons three types of concentrated subglacial water were identified based on the relative proportions of ca 2c h co 3 and so4 2 to si type a waters are the most solute rich and have the lowest relative proportion of si they are believed to form in hydrologically inefficient areas of a distributed drainage system most solute is obtained from coupled sulphide oxidation and carbonate dissolution so cd it is possible that there is a subglacial source of o2 perhaps from gas bubbles released during regelation because the high so4 2 levels found up to 1200 eq l are greater than could be achieved if sulphides are oxidized by oxygen in saturated water at 0 c c 414 eq l a more likely alternative is that sulphide is oxidized by fe 3c in anoxic environments if this is the case exchange reactions involving fe iii and fe ii from silicates are possible these have the potential to generate relatively high concentrations of hco3 with respect to so4 2 formation of secondary weathering products such as clays may explain the low si concentrations of type a waters type b waters were the most frequently sampled subglacial water they are believed to be representative of waters flowing in more efficient parts of a distributed drainage system residence time and reaction kinetics help determine the solute composition of these waters the initial water rock reactions are carbonate and silicate hydrolysis and there is exchange of divalent cations from solution for monovalent cations held on surface exchange sites hydrolysis is followed by so cd the so4 2 concentrations usually are 414 eq l although some range up to 580 eq l which suggests that elements of the distributed drainage system may become anoxic type c waters were the most dilute yet they were very turbid their chemical composition is characterized by low so4 2 h co3 ratios and high ph type c waters were usually artefacts of the borehole chemical weathering environment true type c waters are believed to flow through sulphide poor basal debris particularly in the channel marginal zone the composition of bulk runoff was most similar to diluted type b waters at high discharge and was similar to a mixture of type b and c waters at lower discharge these observations suggest that some supraglacial meltwaters input to the bed are stored temporarily in the channel marginal zone during rising discharge and are released during declining flow little of the subglacial chemical weathering we infer is associated with the sequestration of atmospheric co2 t he progression of reactions is from carbonate and silicate hydrolysis through sulphide oxidation by first oxygen and then fe iii which drives further carbonate and silicate weathering a crude estimate of the ratio of carbonate to silicate weathering following hydrolysis is 4 1 we speculate that microbial oxidation of organic carbon also may occur both sulphide oxidation and microbial oxidation of organic carbon are likely to drive the bed towards suboxic conditions hence we believe that subglacial chemical weathering does not sequester significant quantities of atmospheric co2 and that one of the key controls on the rate and magnitude of solute acquisition is microbial activity which catalyses the reduction of fe iii and the oxidation of fes2 copyright 2002 john wiley sons ltd

extended wave equation imaging conditions for passive seismic data abstractthe information obtained from seismic monitoring at injection sites is often limited to seismic event properties e g location origin time moment tensor the accuracy of which greatly depends on the assumed or estimated elastic velocity models current traveltime based methods to calibrate velocity models rely on having distinct arrivals in surface seismic monitoring however the signal to noise ratio of arrivals is often too poor for pick based methods and migration techniques are needed wave equation migration can image microseismic sources without the need for picking or knowledge of the onset time by reconstructing the wavefield through the model space and applying an imaging condition we have devised extended imaging conditions for passive seismic wave equation imaging algorithms and we have found that they represent a key step toward verifying and updating elastic velocity models by extending imaging conditions away from zero lag in time and space we can better evaluate the focu

vertical seismic profile migration velocity analysis via residual moveout in receiver domain common image gathers abstractthe success of imaging vertical seismic profile vsp data critically depends upon obtaining and using an accurate subsurface velocity model first arrival time tomography can be used to derive velocities above the receivers reflection time tomography can be used to derive velocities below the receivers but it requires reflection time picking and association with appropriate horizons we described an alternative faster way to perform velocity analysis by assessing the residual moveout after migrating walk away vsp data we have derived residual moveout equations for migrated common receiver gathers assuming a constant velocity model with a single horizontal reflector the observed residual moveout in common image gathers in the receiver domain will be aligned and flat if the migration velocity is correct if the residual moveout is not flat by digitizing the extreme point on the unstacked migrated traces in each common receiver gather we could invert for the velocity of the target layer usin

3 d shallow water seismic survey evaluation and design using the focal beam method a case study offshore abu dhabi for 3 d shallow water seismic surveys offshore abu dhabi imaging the target reflectors requires high resolution characterization and monitoring of hydrocarbon reservoirs by seismic amplitude versus offset techniques demands high pre stack amplitude fidelity in this region however it still was not clear how the survey parameters should be chosen to satisfy the required data quality to answer this question we applied the focal beam method to survey evaluation and design this subsurfaceand target oriented approach enables quantitative analysis of attributes such as the best achievable resolution and pre stack amplitude fidelity at a fixed grid point in the subsurface for a given acquisition geometry at the surface this method offers an efficient way to optimize the acquisition geometry for maximum resolution and minimum amplitude versus offset imprint we applied it to several acquisition geometries in order to understand the effects of survey parameters such as the four spatial sampling intervals and apertures of the template geometry the results led to a good understanding of the relationship between the survey parameters and the resulting data quality and identification of the survey parameters for reflection imaging and amplitude versus offset applications

subglacial drilling at black rapids glacier alaska u s a drilling method and sample descriptions we employed a commercial wireline drill rig to investigate the subglacial conditions of black rapids glacier a well studied surge type glacier in the central alaska range the four main goals were to assess the capabilities of the commercial drilling industry for sampling subglacial material to investigate the basal morphology to determine the subglacial geology and to emplace borehole instruments the drilling was done in an area where seasonal and secular variations in speed are large and where seismic studies suggested the presence of a till layer four holes were drilled at three locations to a maximum depth of 620 m three holes yielded samples of basal ice and till although recovery of the latter was generally poor bedrock was sampled in one or possibly two of the holes in the area sampled the glacier is underlain by a till layer some 4 7 m thick confirming the seismic interpretation it consists ofa sandy matrix at least 20 30 of which comprises larger clasts limited samples ofthe matrix indicate that near the top ofthe till the porosity is 40 and that some of the pore water is frozen geologic studies suggest that the drilling area lies to the north of the denali fault a major tectonic boundary followed by the glacier and that most of the till is locally derived with transport distances of 2 km

black box modeling of the subglacial water system measurements of water pressure beneath trapridge glacier yukon territory canada yield the following generalizations about subglacial conditions in the studied region 1 even over short distances the subglacial water system is highly heterogeneous 2 the subglacial water system consists of at least two distinct components which we refer to as the connected and unconnected water systems 3 regions of the glacier bed can switch back and forth from being part of the connected or part of the unconnected water system 4 large spatial pressure gradients can exist within the unconnected water system and between the connected and unconnected systems 5 rapid pressure variations can occur in the unconnected water system 6 pressure variations in the unconnected water system do not match those in the connected system and can in fact be strongly anticorrelated with pressure variations in the connected system if the water pressure variations in the connected system are viewed as a forcing and those in the unconnected system as a response to this forcing the input output relation between forcing and response can be efficiently represented as a low order nonlinear ordinary differential equation the response of the unconnected system to forcing from the connected system is governed by time constants having approximate magnitudes of 1 7 hours and 7 4 hours that we believe are associated with process rates for substrate compression and pore water diffusion respectively

angle domain common image gathers from anisotropic migration i present a general methodology for computing angle domain common image gathers adcigs in conjunction with anisotropic wavefield continuation migration the method is based on transforming the prestack image from the subsurface offset domain to the angle domain using slant stacks the processing sequence is the same as that for computing adcigs for the isotropic case though the interpretation of the relationship between the slopes measured in the prestack image and the aperture angles is more complex i demonstrate that the slopes measured by performing slant stacks along the subsurface offset axis of the prestack image provide a good approximation of the phase aperture angles and they are exactly equal to the phase aperture angles for flat reflectors in vertical transversly isotropic vti media in the general case of dipping reflectors the angles computed using slant stacks can be easily corrected by applying the relationships that i present in this paper and the accurate aperture angles can be determined as a function of the reflector dip and anisotropic slowness at the reflector i derive these relationships from both plane wave and ray viewpoints this theoretical development links the kinematics in adcigs with migration velocity errors i apply the proposed method to compute adcigs from the prestack image obtained by anisotropic migration of a 2d line recorded in the gulf of mexico i analyze the error introduced by neglecting the difference between the true phase aperture angle and the angle computed through slant stacks showing that at least for this data set these errors are negligible and can be safely ignored in contrast group aperture angles can be quite different from phase aperture angles thus ignoring the distinction between these two angles can be detrimental to practical applications

separated wavefield imaging using primary and multiple energy imaging with separated wavefields swim is an innovative depth imaging technology that uses upgoing and downgoing wavefields at the surface to deliver high resolution images of the subsurface it takes advantage of the extended illumination provided by surface multiple energy and thus it exploits data that the seismic industry historically has treated as unwanted noise the fundamental concept behind swim is based on using each receiver as a virtual source effectively expanding the surface coverage of the seismic experiment and enhancing the subsurface illumination particularly for shallow reflectors by effectively turning the streamer spread into a source and receiver array the resulting equivalent survey has spatial sampling that is much improved and a richer distribution of offsets and azimuths the improved spatial sampling enhances the angular illumination greatly at every image point therefore swim produces densely sampled angle gathers that provide greater opportunities for velocity model building and for improved interpretation of complex structures several issues need to be considered for proper imaging with swim migration imaging conditions attenuation of cross talk and acquisition design the latter must be addressed to support proper sampling of both upgoing and downgoing wavefields used for imaging a broad overview and examples of these subjects are presented applications to a deepwater wide azimuth waz survey from the gulf of mexico and a shallow water narrow azimuth naz data set from offshore malaysia demonstrate the enhanced areal illumination and improved imaging resolution from imaging using multiple reflection energy

wave equation angle domain common image gathers for converted waves wavefield extrapolation methods can produce angle domain common image gathers adcigs to obtainadcigs for converted wave seismic data information about the image dip and the p to s velocity ratio must be included in the computation of angle gathers theseadcigs are a function of the half aperture angle i e the average between the incidence angle and the reflection angle we have developed a method that exploits the robustness of computing 2d isotropic single modeadcigs and incorporates both the converted wave velocity ratio and the local image dipfield it also maps the final converted wave adcigs into two adcigs one a function of the p incidence angle and the other a functionofthes reflectionangle resultswithbothsyntheticand real data show the practical application for converted wave adcigs the proposed approach is valid in any situation as long as the migration algorithm is based on wavefield downward continuation and the final prestack image is a function ofthehorizontalsubsurfaceoffset

azimuth preserved local angle domain prestack time migration in isotropic vertical transversely isotropic and azimuthally anisotropic media conventional prestack migration does not preserve local directional information of the seismic waves at the image points new attempts such as sectored migration of azimuth limited or common offset vector data only concern source receiver azimuth and offset on the surface which can be poor representation of subsurface wavepath direction moreover they could result in inaccurate imaging because they do not account for the energy propagation between azimuths or offset vectors in the past decade local angle domain seismic imaging has been highly advocated to avoid migration artifacts and to improve velocity estimation in complex media considering prestack time migration pstm is still widely used in seismic imaging and seismic data preconditioning for amplitude variations with offset or incident angle avo ava analysis fracture detection and reservoir characterization we present an azimuth preserved local angle domain kirchhoff pstm approach for such purposes we apply a seismic imaging condition i

use of rtm full 3d subsurface angle gathers for subsalt velocity update and image optimization case study at shenzi field various reverse time migration rtm angle gather generation techniques have been developed to address poor subsalt data quality and multiarrival induced problems in gathers from kirchhoff migration but these techniques introduce new problems such as inaccuracies in 2d subsurface angle gathers and edge diffraction artifacts in 3d subsurface angle gathers the unique rich azimuth data set acquired over the shenzi field in the gulf of mexico enabled the generally artifact free generation of 3d subsurface angle gathers using this data set we carried out suprasalt tomography and salt model building steps and then produced 3d angle gathers to update the subsalt velocity we used tilted transverse isotropy rtm with extended image condition to generate full 3d subsurface offset domain common image gathers which were subsequently converted to 3d angle gathers the angle gathers were substacked along the subsurface azimuth axis into azimuth sectors residual moveout analysis was carried out and ray based tom

anisotropic migration velocity analysis using reverse time migration abstractseismic anisotropy if not accounted for can cause significant mispositioning of the reflectors in depth migrated images accounting for anisotropy in depth migration requires velocity analysis tools that can estimate the anisotropic background velocity field we extended wave equation migration velocity analysis to deal with 2d tilted transverse isotropic media the velocities were obtained automatically by nonlinear optimization of the focusing and stack power of common image point gathers constructed using an extended imaging condition we used the elastic two way wave equation to reconstruct the wavefields needed for the image and gradient computations this led to an anisotropic migration velocity analysis algorithm based on reverse time migration we illustrated the method with synthetic and field data examples based on marine surface seismic acquisition the results showed that the method significantly improves the quality of the depth migrated image however as is common in the case of v

stereographic imaging condition for wave equation migration imaging under the single scattering approximation consists of two steps wavefield reconstruction of source and receiver wavefields from simulated and recorded data respectively andimagingfromtheextrapolatedwavefieldsoflocations where reflectors occur conventionally the imaging condition indicates the presence of reflectors when propagationtimesofreflectionsinthesourceandreceiverwavefields match the main drawback of a conventional crosscorrelation imaging condition is that it ignores the local spatial coherence of reflection events and relies only on their propagationtime thisleadstointerferencebetweenunrelatedevents thatoccuratthesametime sourcesofcrosstalkincludeseismic events corresponding to different seismic experiments propagation paths types of reflectionsprimary or multiple orwavemodespors analternativeimagingconditionoperates on the same extrapolated wavefields but crosscorrelationtakesplaceinahigher dimensiondomainwhereseismic events are separated based on their local space time slope events are matched based on two parameters time and local slope thus justifying the name stereographic for this imagingcondition stereographicimagingattenuateswavefield crosstalk and reduces imaging artifacts compared with conventional imaging applications of the stereographic imagingconditionincludesimultaneousimagingofmultipleseismic experiments multiple attenuation in the imaging condition andattenuationofcrosstalkbetweenmultiplewavefield branchesormultiplewavemodes