processing induced anisotropy processing of seismic data is often performed under the assumption that the velocity distribution in the subsurface can be approximated by a macromodel composed of isotropic homogeneous layers or blocks despite being physically unrealistic such models are believed to be sufficient for describing the kinematics of reflection arrivals in this paper we examine the distortions in normal moveout nmo velocities caused by the intralayer vertical heterogeneity unaccounted for in velocity analysis to match p wave moveout measurements from a horizontal or a dipping reflector overlaid by a vertically heterogeneous isotropic medium the effective homogeneous overburden has to be anisotropic this apparent anisotropy is caused not only by velocity monotonically increasing with depth but also by random velocity variations similar to those routinely observed in well logs assuming that the effective homogeneous medium is transversely isotropic with a vertical symmetry axis vti we express the vti parameters thro

p wave fracture prediction algorithm using data with limited azimuthal distribution many carbonate reservoirs are present in china s tarim basin the storage spaces are mostly secondary and about 99 of the porosity is from fractures and dissolution caves or holes fractures represent both the storage space and migration channels of hydrocarbon fluids therefore predicting fracture development is a challenge that confronts us in this area

3d velocity independent elliptically anisotropic moveout correction azimuthal anisotropy or lateral velocity variations cause azimuthal variations in moveout velocity which can degrade seismic images if handled improperly in cases in which apparent azimuthally anisotropic moveout is present a single picked velocity is inadequate to flatten an event on a 3d cmp gather conventional velocity analysis techniques require a significant amount of time and effort especially in areas where apparent anisotropy is observed we propose a velocity independent imaging approach to perform an elliptically anisotropic moveout correction in three dimensions the velocity independent approach relies on volumetric local traveltime slopes rather than aggregate velocities and therefore provides an azimuthally flexible description of traveltime geometries throughout the gather we derive theoretical expressions for extracting the moveout slowness matrix and the angle between the symmetry and acquisition axes as volumetric local attributes a practical inversion scheme to extract the same p

a comment on the form of the geometrical spreading equations with some numerical examples of seismic ray tracing in inhomogeneous anisotropic media summary we point out that while the equations of seismic ray geometrical spreading given recently by norris do differ as stated from equations given by cerveny it does not imply that the latter equations are wrong the two sets of equations differ only in form and in a way which in part at least can be ascribed to different choices of hamiltonian by the two authors quantitatively though the two sets of equations are entirely equivalent we also present some numerical results of ray tracing in anisotropic models simulating a continential rift a spreading ridge and a subduction zone these three structures span a range of geological mechanisms for seismic anisotropy though definitive conclusions cannot be easily drawn when there is both anisotropy and inhomogeneity the results do indicate the magnitude of ray path travel time and amplitude variations to be expected for p waves when anisotropy is introduced

nmo velocity surfaces and dix type formulas in anisotropic heterogeneous media reflection moveout of pure modes recorded on conventional length spreads is described by a normal moveout nmo velocity that depends on the orientation of the common midpoint cmp line here we introduce the concept of nmo velocity surfaces which are obtained by plotting the nmo velocity as the radius vector along all possible directions in 3 d space and use it to develop dix type averaging and differentiation algorithms in anisotropic heterogeneous media the intersection of the nmo velocity surface with the horizontal plane represents the nmo ellipse that can be estimated from wide azimuth reflection data we demonstrate that the nmo ellipse and conventional spread moveout as a whole can be modeled by dix type averaging of specifically oriented cross sections of the nmo velocity surfaces along the zero offset reflection raypath this formalism is particularly simple to implement for a stack of homogeneous anisotropic layers separated by plane dipping boundaries since our method involves computing j

full azimuth anisotropic prestack time migration in the local angle domain and its applications on fracture detection abstractconsidering that geologic structures disturb prestack amplitude relationships anisotropic migration is thus advocated not only for extracting azimuth preserved common image gathers cigs but also for preserving fracture induced amplitude responses however most conventional anisotropic migration methods are hindered by their inefficiency in either modeling azimuthal traveltime variations at large offsets or characterizing subsurface reflections given that prestack time migration is widely applied for most practical purposes we began with reformulations on a quartic traveltime formula through which a new set of anisotropic parameters was developed then an anisotropic migration method was established in the local angle domain lad for more reasonable uses of subsurface wavefield information we also used a traveltime inversion scheme to estimate those anisotropic parameters required by anisotropic migration using this methodology on a physical model with a fracture medium we derived bett

a case study of azimuthal avo analysis with anisotropic spreading correction geomechanical properties of tight low porosity reservoirs are largely governed by natural fracture networks hence reliable estimation of fracture density and orientation is extremely important for cost effective hydraulic completion and hydrocarbon production direct information about fracturing can be obtained using borehole methods such as image log analysis which provide estimates of fracture counts and orientations on various scales the main shortcoming of borehole measurements is that they are sensitive only to formation properties in the immediate vicinity of the well in some cases the spatial distribution of fractures can be inferred from fault maps obtained by coherence analysis of surface seismic data however the correlation between areas of high fracture density and fault locations is not always straightforward

seismic characterization of vertical fractures described as general linear slip interfaces fluid flow in many hydrocarbon reservoirs is controlled by aligned fractures which make the medium anisotropic on the scale of seismic wavelength applying the linear slip theory we investigate seismic signatures of the effective medium produced by a single set of general vertical fractures embedded in a purely isotropic host rock the generality of our fracture model means the allowance for coupling between the normal to the fracture plane stress and the tangential jump in displacement and vice versa despite its low triclinic symmetry the medium is described by just nine independent effective parameters and possesses several distinct features which help to identify the physical model and estimate the fracture compliances and background velocities for example the polarization vector of the vertically propagating fast shear wave s1 and the semi major axis of the s1 wave normal moveout nmo ellipse from a horizontal reflector always point in the direction of the fracture strike moreover for the s1 wave both the vertical velocity and the nmo velocity along the fractures are equal to the shear wave velocity in the host rock analysis of seismic signatures in the limit of small fracture weaknesses allows us to select the input data needed for unambiguous fracture characterization the fracture and background parameters can be estimated using the nmo ellipses from horizontal reflectors and vertical velocities of p waves and two split s waves combined with a portion of the p wave slowness surface reconstructed from multi azimuth walkaway vertical seismic profiling vsp data the stability of the parameter estimation procedure is verified by performing non linear inversion based on the exact equations

normal moveout coefficients for horizontally layered triclinic media abstractsedimentary layers affected by vertical compaction and strong lateral tectonic stresses are often characterized by low anisotropic symmetry e g tilted orthorhombic tor monoclinic or even triclinic considering all types of pure mode and converted waves we derive the normal moveout nmo series coefficients of near normal incidence reflected waves in arbitrarily anisotropic horizontally layered media for a leading error term of order six the nmo series can be either a function of the invariant horizontal slowness slowness domain or the surface offset offset domain the nmo series coefficients referred to also as effective parameters are associated with the corresponding azimuthally varying nmo velocity functions we distinguish between local single layer and global overburden multilayer effective parameters which are related by forward and inverse dix type transforms we derive the local effective parameters for an arbitrary anisotropic triclinic layer which is the main contr

changes in the bathymetry and volume of glacial lake agassiz between 11 000 and 9300 14c yr b p abstract computer reconstructions of the bathymetry of the lake were used to quantify variations in the size and form of lake agassiz during its final two phases the nipigon and ojibway phases between about 9200 and 7700 14c yr b p ca 10 300 8400 cal yr b p new bathymetric models for four nipigon phase stages corresponding to the mccauleyville hillsboro burnside and the pas strandlines indicate that lake agassiz ranged between about 19 200 and 4600 km3 in volume and 254 000 and 151 000 km2 in areal extent at those times a bathymetric model of the last ponton stage of the lake corresponding to the period in which lake agassiz was combined with glacial lake ojbway to the east shows that lake agassiz ojibway was about 163 000 km3 in volume and 841 000 km2 in areal extent prior to the final release of lake waters into the tyrrell sea during the nipigon phase a number of catastrophic releases of water from lake agassiz occurred as more northerly lower outlets were made available by the retreating southern margin of the laurentide ice sheet we estimate that each of the four newly investigated nipigon phase releases involved water volumes of between 1600 and 2300 km3 the final release of lake agassiz waters into the tyrrell sea at about 7700 14c yr b p is estimated to have been about 163 000 km3 in volume

velocity independent layer stripping of pp and ps reflection traveltimes buildingaccurateintervalvelocitymodelsiscriticallyimportant for seismic imaging and avo amplitude variation withoffsetanalysis here weadaptthepp ps ssmethodtodevelopanexacttechniqueforconstructingtheinterval traveltime offset function in a target zone beneath a horizontally layered overburden all layers in the model can be anisotropic with an essential assumption that the overburden hasahorizontalsymmetryplanei e up downsymmetry our layer stripping algorithm is entirely data driven and in contrast to the generalized dix equations does not require knowledgeofthevelocityfieldanywhereinthemedium important advantages of our approach compared to the dixstyle formalism also include the ability to handle mode converted waves long offset data and laterally heterogeneous targetlayerswithmultiple curvedreflectors numericaltests confirm the high accuracy of the algorithm in computing the interval traveltimes of both pp and ps waves in a dipping transversely isotropic layer with a tilted symmetry axis tti mediumbeneathananisotropicoverburden in combination with the inversion techniques developed forhomogeneousttimodels theproposedlayerstrippingof pp and ps data can be used to estimate the interval parameters oftti formations in such important exploration areas as thecanadianfoothills potentialapplicationsofthismethodology also include the dip moveout inversion for the p wave time processing parameter and stable computation of the interval long spread nonhyperbolic moveout for purposes ofanisotropicvelocityanalysis

velocity analysis for tilted transversely isotropic media a physical modeling example transverse isotropy with a tilted symmetry axis tti media has been recognized as a common feature of shale formations in overthrust areas such as the canadian foothills since tti layers cause serious problems in conventional imaging it is important to be able to reconstruct the velocity model suitable for anisotropic depth migration here we discuss the results of anisotropic parameter estimation on a physical modeling data set the model represents a simplified version of a typical overthrust section from the alberta foothills with a horizontal reflector overlaid by a bending transversely isotropic layer assuming that the tti layer is homogeneous and the symmetry axis stays perpendicular to its boundaries we invert p wave normal moveout nmo velocities and zero offset traveltimes for the symmetry direction velocity v0 and the anisotropic parameters e and the coefficient e is obtained using the traveltimes of a wave that crosses a dipping tti block and reflects from the bottom of the model t

imaging salt with turning seismic waves turning seismic waves which first travel downward and then upward before and after reflection have been recorded in a 3 d seismic survey conducted over an overhanging salt dome careful processing of these turning waves enables the imaging of the underside of the salt dome and of intrusions of salt into vertical faults radiating from the dome when seismic wave velocity increases with depth waves that initially travel downward are reflected and may turn so as to travel upward before reflection a simple geometrical argument suggests that these turning waves are likely to exhibit abnormal moveout in com mon midpoint cmp gathers in that reflection time decreases with increasing source receiver offset this abnormal moveout and the attenuation of turning waves by most migration methods suggest that conventional seismic processing does not properly image turning waves the most important step in imaging turning waves assuming that they have been recorded is the migration process simple and inexpensive modifications to the conventional phase shift migration method enable turning waves to be imaged for little additional computational cost the examples provided in this paper suggest that these and other such modifications to conventional processing should be used routinely when imaging salt domes

non hyperbolic moveout inversion of wide azimuth p wave data for orthorhombic media the azimuthally varying non hyperbolic moveout of p waves in orthorhombic media can provide valuable information for characterization of fractured reservoirs and seismic processing here we present a technique to invert long spread wide azimuth p wave data for the orientation of the vertical symmetry planes and five key moveout parameters the symmetry plane nmo velocities v 1 nmo and v 2 nmo and the anellipticity parameters 1 2 and 3 the inversion algorithm is based on a coherence operator that computes the semblance for the full range of offsets and azimuths using a generalized version of the alkhalifah tsvankin non hyperbolic moveout equation the moveout equation provides a close approximation to the reflection traveltimes in layered anisotropic media with a uniform orientation of the vertical symmetry planes numerical tests on noise contaminated data for a single orthorhombic layer show that the best constrained parameters are the azimuth of one of the symmetry planes and the velocities v 1 nmo and v 2 nmo while the resolution in 1 and 2 is somewhat compromised by the trade off between the quadratic and quartic moveout terms the largest uncertainty is observed in the parameter 3 which influences only long spread moveout in off symmetry directions for stratified orthorhombic models with depth dependent symmetry plane azimuths the moveout equation has to be modified by allowing the orientation of the effective nmo ellipse to differ from the principal azimuthal direction of the effective quartic moveout term the algorithm was successfully tested on wide azimuth p wave reflections recorded at the weyburn field in canada taking azimuthal anisotropy into account increased the semblance values for most long offset reflection events in the overburden which indicates that fracturing is not limited to the reservoir level the inverted symmetry plane directions are close to the azimuths of the off trend fracture sets determined from borehole data and shear wave splitting analysis the effective moveout parameters estimated by our algorithm provide input for p wave time imaging and geometrical spreading correction in layered orthorhombic media

effective anisotropy of layered media in situ seismic anisotropy can be estimated using a variety of techniques since they require data that are typically collected over some finite intervals of inevitably heterogeneous earth one usually needs to separate the influence of anisotropy on the measurements from that of heterogeneity it is not an easy task because depending on the frequency of propagating waves heterogeneity and anisotropy might mimic each other the well known example of this is a finely layered isotropic solid that effectively behaves as a vertically transversely isotropic vti rock when probed by sufficiently long seismic waves backus 1962 similar transitions from heterogeneity to anisotropy and back occur over the whole range of seismic frequencies for instance grechka and tsvankin 2002 recently showed that a layered isotropic structure also looks like a vti one at high frequencies when the ray tracing and dix type averaging of the normal moveout nmo velocities can be applied

dip moveout of converted waves and parameter estimation in transversely isotropic media for transverse isotropy with a vertical symmetry axis vti media p wave reflection data alone are insufficient for building velocity models in depth here we show that all parameters of vti media responsible for propagation of p and sv waves the p wave and s wave vertical velocities vp0 and vs0 and the anisotropic parameters e and can be obtained by combining p wave traveltimes with the moveout of ps waves converted at a horizontal and dipping interface using converted modes rather than pure s waves avoids the need for expensive shear wave excitation on land and makes the method suitable for offshore exploration the inversion algorithm is based on a new analytic description of the dip moveout of ps waves developed for symmetry planes of anisotropic media and for any vertical plane in models with weak azimuthal anisotropy the common midpoint cmp traveltime offset relationship derived in a parametric form and represented through the components of the slowness vector of the p and s waves makes it possible to compute the moveout curve of the ps wave without two point ray tracing this formalism also leads to closed form solutions for moveout attributes such as the coordinates xmin tmin of the traveltime minimum the normal moveout nmo velocity defined at x xmin and the slope of the moveout curve apparent slowness at zero offset the parameter estimation algorithm operates with reflection moveout of p and ps waves from a horizontal and dipping reflector the nmo velocities of p and ps waves from horizontal events and the ratio of the corresponding zero offset traveltimes yield three equations for the four unknown medium parameters the remaining parameter is found from an overdetermined system of equations that includes the p wave nmo velocity and moveout attributes of the ps wave for a dipping event numerical analysis shows that the ps wave dip moveout signature plays a crucial role in obtaining accurate estimates of the anisotropic parameters the joint inversion of p and ps data provides the necessary information not only for p wave depth imaging in vti media but also for the processing of ps waves including re sorting of ps traces into common reflection point gathers and transformation to zero offset tzo

3d description and inversion of reflection moveout of ps waves in anisotropic media common midpoint moveout of converted waves is generally asymmetric with respect to zero offset and cannot be described by the traveltime series t2 x2 conventionally used for pure modes here we present concise parametric expressions for both common midpoint cmp and common conversion point ccp gathers of ps waves for arbitrary anisotropic horizontally layered media above a plane dipping reflector this analytic representation can be used to model 3d multi azimuth cmp gathers without time consuming two point ray tracing and to compute attributes of ps moveout such as the slope of the traveltime surface at zero offset and the coordinates of the moveout minimum in addition to providing an efficient tool for forward modelling our formalism helps to carry out joint inversion of p and ps data for transverse isotropy with a vertical symmetry axis vti media if the medium above the reflector is laterally homogeneous p wave reflection moveout cannot constrain the depth scale of the model needed for depth migration extending our previous results for a single vti layer we show that the interval vertical velocities of the p and s waves vp0 and vs0 and the thomsen parameters e and can be found from surface data alone by combining p wave moveout with the traveltimes of the converted ps psv wave if the data are acquired only on the dip line i e in 2d stable parameter estimation requires including the moveout of p and ps waves from both a horizontal and a dipping interface at the first stage of the velocity analysis procedure we build an initial anisotropic model by applying a layer stripping algorithm to cmp moveout of p and ps waves to overcome the distorting influence of conversion point dispersal on cmp gathers the interval vti parameters are refined by collecting the ps data into ccp gathers and repeating the inversion for 3d surveys with a sufficiently wide range of source receiver azimuths it is possible to estimate all four relevant parameters vp0 vs0 e and using reflections from a single mildly dipping interface in this case the p wave nmo ellipse determined by 3d azimuthal velocity analysis is combined with azimuthally dependent traveltimes of the ps wave on the whole the joint inversion of p and ps data yields a vti model suitable for depth migration of p waves as well as processing e g transformation to zero offset of converted waves

estimation of interval anisotropy parameters using velocity independent layer stripping moveout analysis of long spread p wave data is widely used toestimatethekeytime processingparameter inlayeredtransversely isotropic media with a vertical symmetry axis vti inversion for interval values however suffers from instability caused by the trade off between the effective moveout parameters and by subsequent error amplification during dix type layer stripping we propose an alternative approach to nonhyperbolic moveout inversion based on the velocity independent layerstripping vils method of dewangan and tsvankin also we developthe3dversionofvilsandapplyittointervalparameter estimation in orthorhombic media using wide azimuth longspreaddata iftheoverburdenislaterallyhomogeneousandhasa horizontal symmetry plane vils produces the exact interval traveltime offset function in the target layer without knowledge of the velocity field hence dix type differentiation of moveout parameters used in existing techniques is replaced by the much morestablelayerstrippingofreflectiontraveltimes theinterval traveltimes are then inverted for the moveout parameters using the single layer nonhyperbolic moveout equation the superior accuracy and stability of the algorithm are illustrated on raytraced synthetic data for typical vti and orthorhombic models even small correlated noise in reflection traveltimes causes substantial distortions in the interval values computed by conventional dix type differentiation in contrast the output ofvils is insensitive to mild correlated traveltime errors the algorithm is also tested on wide azimuth p wave reflection data recorded above a fractured reservoir at rulison field in colorado the interval moveout parameters estimated by vils in the shale layer above the reservoir are more plausible and less influenced by noisethanthoseobtainedbythedix typemethod

generalized dix equation and analytic treatment of normal moveout velocity for anisotropic media despite the complexity of wave propagation in anisotropic media reflection moveout on conventional common midpoint cmp spreads is usually well described by the normal moveout nmo velocity defined in the zero offset limit in their recent work grechka and tsvankin showed that the azimuthal variation of nmo velocity around a fixed cmp location generally has an elliptical form i e plotting the nmo velocity in each azimuthal direction produces an ellipse and is determined by the spatial derivatives of the slowness vector evaluated at the cmp location this formalism is used here to develop exact solutions for the nmo velocity in anisotropic media of arbitrary symmetry for the model of a single homogeneous layer above a dipping reflector we obtain an explicit nmo expression valid for all pure modes and any orientation of the cmp line with respect to the reflector strike the contribution of anisotropy to nmo velocity is contained in the slowness components of the zero offset ray along with the derivatives of the vertical slowness with respect to the horizontal slownesses quantities that can be found in a straightforward way from the christoffel equation if the medium above a dipping reflector is horizontally stratified the effective nmo velocity is determined through a dix type average of the matrices responsible for the interval nmo ellipses in the individual layers this generalized dix equation provides an analytic basis for moveout inversion in vertically inhomogeneous arbitrarily anisotropic media for models with a throughgoing vertical symmetry plane i e if the dip plane of the reflector coincides with a symmetry plane of the overburden the semi axes of the nmo ellipse are found by the more conventional rms averaging of the interval nmo velocities in the dip and strike directions modelling of normal moveout in general heterogeneous anisotropic media requires dynamic ray tracing of only one zero offset ray remarkably the expressions for geometrical spreading along the zero offset ray contain all the components necessary to build the nmo ellipse this method is orders of magnitude faster than multi azimuth multi offset ray tracing and therefore can be used efficiently in traveltime inversion and in devising fast dip moveout dmo processing algorithms for anisotropic media this technique becomes especially efficient if the model consists of homogeneous layers or blocks separated by smooth interfaces the high accuracy of our nmo expressions is illustrated by comparison with ray traced reflection traveltimes in piecewise homogeneous azimuthally anisotropic models we also apply the generalized dix equation to field data collected over a fractured reservoir and show that p wave moveout can be used to find the depth dependent fracture orientation and to evaluate the magnitude of azimuthal anisotropy

characterization of dipping fractures in a transverselyisotropic background although it is believed that natural fracture sets predominantly have near vertical orientation oblique stresses and some other mechanisms may tilt fractures away from the vertical here we examine an effective medium produced by a single system of obliquely dipping rotationally invariant fractures embedded in a transversely isotropic with a vertical symmetry axis vti background rock this model is monoclinic with a vertical symmetry plane that coincides with the dip plane of the fractures multicomponent seismic data acquired over such a medium possess several distinct features that make it possible to estimate the fracture orientation for example the vertically propagating fast shear wave and the fast converted ps wave is typically polarized in the direction of the fracture strike the normal moveout nmo ellipses of horizontal reflection events are co orientated with the dip and strike directions of the fractures which provides an independent estimate of the fracture azimuth however the polarization vector of the slow shear wave at vertical incidence does not lie in the horizontal plane an unusual phenomenon that can be used to evaluate fracture dip also for oblique fractures the shear wave splitting coefficient at vertical incidence becomes dependent on fracture infill saturation a complete medium characterization procedure includes estimating the fracture compliances and orientation dip and azimuth as well as the thomsen parameters of the vti background we demonstrate that both the fracture and background parameters can be obtained from multicomponent wide azimuth data using the vertical velocities and nmo ellipses of pp waves and two split ss waves or the traveltimes of ps waves reflected from horizontal interfaces numerical tests corroborate the accuracy and stability of the inversion algorithm based on the exact expressions for the vertical and nmo velocities

seismic traveltime analysis for azimuthally anisotropic media theory and experiment natural fractures in reservoirs and in the caprock overlying the reservoir play an important role in determining fluid flow during production the density and orientation of sets of fractures is therefore of great interest rocks possessing an anisotropic fabric and a preferred orientation of fractures display both polar and azimuthal anisotropy sedimentary rocks containing several sets of vertical fractures may be approximated as having monoclinic symmetry with symmetry plane parallel to the layers if in the absence of fractures the rock is transversely isotropic with symmetry axis perpendicular to the bedding plane a nonhyperbolic traveltime equation which can be used in the presence of azimuthally anisotropic layered media can be obtained from an expansion of the inverse squared ray velocity in spherical harmonics for a single set of aligned fractures application of this equation to traveltime data acquired at a sufficient number of azimuths allows the strike of the fractures to be estimated analysis of the traveltimes measured in a physical model simulation of a reverse vertical seismic profile in an azimuthally anisotropic medium shows the medium to be orthorhombic with principal axes in agreement with those given by an independent shear wave experiment in contrast to previous work no knowledge of the orientation of the symmetry planes is required the method is therefore applicable to p wave data collected at multiple azimuths using multiple offset vertical seismic profiling vsp techniques

seismic data processing in vertically inhomogeneous ti media the first and most important step in processing data in transversely isotropic ti media for which velocities vary with depth is parameter estimation the multilayer normal moveout nmo equation for a dipping reflector provides the basis for extending the ti velocity analysis of alkhalifah and tsvankin to vertically inhomogeneous media this nmo equation is based on a root mean square rms average of interval nmo velocities that correspond to a single ray parameter that of the dipping event therefore interval nmo velocities including the normal moveout velocity for horizontal events vnmo 0 can be extracted from the stacking velocities using a dix type differentiation procedure on the other hand which is a key combination of thomsen s parameters that time related processing relies on is extracted from the interval nmo velocities using a homogeneous inversion within each layer time migration like dip moveout depends on the same two parameters in vertically inhomogeneous media namely vnmo

moveout analysis of wide azimuth data in the presence of lateral velocity variation moveout analysis of wide azimuth reflection data seldom takes into account lateral velocity variations on the scale of spreadlength however velocity lenses such as channels and reefs in the overburden can cause significant laterally varying errors in the moveout parameters and distortions in data interpretation here we present an analytic expression for the normal moveout nmo ellipse in stratified media with lateral velocity variation the contribution of lateral heterogeneity lh is controlled by the second derivatives of the interval vertical traveltime with respect to the horizontal coordinates along with the depth and thickness of the lh layer this equation provides a quick estimate of the influence of velocity lenses and can be used to substantially mitigate the lens induced distortions in the effective and interval nmo ellipses to account for velocity lenses in nonhyperbolic moveout inversion of wide azimuth data we propose a prestack correction algorithm that involves computation of the lens induced traveltime distortion for each recorded trace the overburden is assumed to be composed of horizontal layers one of which contains the lens but the target interval can be laterally heterogeneous with dipping or curved interfaces synthetic tests for horizontally layered models confirm that our algorithm accurately removes lens related azimuthally varying traveltime shifts and errors in the moveout parameters the developed methods should increase the robustness of seismic processing of wide azimuth surveys especially those acquired for fracture characterization purposes

inversion of azimuthally dependent nmo velocity in transversely isotropic media with a tilted axis of symmetry just as the transversely isotropic model with a vertical symmetry axis vti media is typical for describing horizontally layered sediments transverse isotropy with a tilted symmetry axis tti describes dipping ti layers such as tilted shale beds near salt domes or crack systems p wave kinematic signatures in tti media are controlled by the velocity vp0 in the symmetry direction thomsen s anisotropic coefficients e and and the orientation tilt and azimuth of the symmetry axis here we show that all five parameters can be obtained from azimuthally varying p wave nmo velocities measured for two reflectors with different dips and or azimuths one of the reflectors can be horizontal the shear wave velocity vs0 in the symmetry direction which has negligible influence on p wave kinematic signatures can be found only from the moveout of shear waves using the exact nmo equation we examine the propagation of errors in observed moveout velocities into estimated values of the anisotropic parame

seismic anisotropy in exploration and reservoir characterization an overview recent advances in parameter estimation and seismic processing have allowed incorporation of anisotropic models into a wide range of seismic methods in particular vertical and tilted transverse isotropy are currently treated as an integral part of velocity fields employed in prestack depth migration algorithms especially those based on the wave equation we briefly review the state of the art in modeling processing and inversion of seismic data for anisotropic media topics include optimal parameterization body wave modeling methods p wave velocity analysis and imaging processing in the p domain anisotropy estimation from vertical seismic profiling vsp surveys moveout inversion of wide azimuth data amplitude variation with offset avo analysis processing and applications of shear and mode converted waves and fracture characterization when outlining future trends in anisotropy studies we emphasize that continued progress in data acquisition technology is likely to spur transition from t

an analysis of avo inversion for postcritical offsets in hti media abstractazimuthal variations of wavefield characteristics such as traveltime or reflection amplitude play an important role in the identification of fractured media a transversely isotropic medium with a horizontal symmetry axis hti medium is the simplest azimuthally anisotropic model typically used to describe one set of vertical fractures there exist many techniques in industry to recover anisotropic parameters based on moveout equations and linearized reflection coefficients using such a model however most of the methods have limitations in defining properties of the fractures due to linearizations and physical approximations used in their development thus azimuthal analysis of traveltimes based on normal moveout ellipses recovers a maximum of three medium parameters instead of the required five linearizations made in plane wave reflection coefficients pwrcs limit the amplitude versus offset avo analysis to small incident angles and weak contrast interfaces inversion based on azimuthal

concentration and divergence of sediment in an erosional landscape abstract in an eroding landscape the erosional source area ae may be larger or smaller than the depositional or storage area ad this corresponds to areal concentration ae ad 1 or divergence ae ad