共查询到20条相似文献，搜索用时 31 毫秒
1.
A Gaussian correlation function characterizes smoothly heterogeneous media, while real heterogeneities in the Earth are often non-Gaussian in nature. Using the Born approximation, mean square amplitudes of the scattered waves have been derived for an elastic media characterized by the Von Karman correlation function. Heterogeneities with different power laws can be defined by the Von Karman correlation function. The sensitivity of fore- and backscattering to heterogeneities with different scales and properties (that is velocity and impedance) is discussed in this paper. The analytical expression for total scattered energy for the incident P waves is also derived for a random medium having the Von Karman correlation function. We find that at high frequencies, the scattered power of converted waves is a function of frequency. In the case of codawave excitation by local earthquakes, which must be handled by the full elastic-wave theory, we can define any type of inhomogeneity by the Von Karman correlation function. It also supports the idea that the lithosphere might have multiple-scale inhomogeneities. 相似文献
2.
A tomographic inversion technique that inverts traveltimes to obtain a model of the subsurface in terms of velocities and interfaces is presented. It uses a combination of refraction, wide-angle reflection and normal-incidence data, it simultaneously inverts for velocities and interface depths, and it is able to quantify the errors and trade-offs in the final model. The technique uses an iterative linearized approach to the non-linear traveltime inversion problem. The subsurface is represented as a set of layers separated by interfaces, across which the velocity may be discontinuous. Within each layer the velocity varies in two dimensions and has a continuous first derivative. Rays are traced in this medium using a technique based on ray perturbation theory, and two-point ray tracing is avoided by interpolating the traveltimes to the receivers from a roughly equidistant fan of rays. The calculated traveltimes are inverted by simultaneously minimizing the misfit between the data and calculated traveltimes, and the roughness of the model. This 'smoothing regularization' stabilizes the solution of the inverse problem. In practice, the first iterations are performed with a high level of smoothing. As the inversion proceeds, the level of smoothing is gradually reduced until the traveltime residual is at the estimated level of noise in the data. At this point, a minimum-feature solution is obtained, which should contain only those features discernible over the noise.
The technique is tested on a synthetic data set, demonstrating its accuracy and stability and also illustrating the desirability of including a large number of different ray types in an inversion. 相似文献
The technique is tested on a synthetic data set, demonstrating its accuracy and stability and also illustrating the desirability of including a large number of different ray types in an inversion. 相似文献
3.
Seismic traveltimes and amplitudes in reflection-seismic data show different dependences on the geometry of reflection interfaces, and on the variation of interval velocities. These dependences are revealed by eigenanalysis of the Hessian matrix, defined in terms of the Fréchet matrix and its adjoint associated with different norms chosen in the model space. The eigenvectors and eigenvalues of the Hessian clearly show that for reflection tomographic inversion, traveltime and amplitude data contain complementary information. Both for reflector-geometry and for interval-velocity variations, the traveltimes are sensitive to the model components with small wavenumbers, whereas the amplitudes are more sensitive to the components with high wavenumbers. The model resolution matrices, after the rejection of eigenvectors corresponding to small eigenvalues, give us some insight into how the addition of amplitude information could potentially contribute to the recovery of physical parameters.
In order to cooperatively invert seismic traveltimes and amplitudes simultaneously, we propose an empirical definition of the data covariance matrix which balances the relative sensitivities of different types of data. We investigate the cooperative use of both data types for, separately, interface-geometry and 2-D interval-velocity variations. In both cases we find that cooperative inversions can provide better solutions than those using traveltimes alone. The potential benefit of including amplitude-data constraints in seismic-reflection traveltime tomography is therefore that it may be possible to resolve the known ambiguity between the reflector-depth uncertainty and the interval-velocity uncertainty better. 相似文献
In order to cooperatively invert seismic traveltimes and amplitudes simultaneously, we propose an empirical definition of the data covariance matrix which balances the relative sensitivities of different types of data. We investigate the cooperative use of both data types for, separately, interface-geometry and 2-D interval-velocity variations. In both cases we find that cooperative inversions can provide better solutions than those using traveltimes alone. The potential benefit of including amplitude-data constraints in seismic-reflection traveltime tomography is therefore that it may be possible to resolve the known ambiguity between the reflector-depth uncertainty and the interval-velocity uncertainty better. 相似文献
4.
Toshinori Sato 《Geophysical Journal International》2007,171(3):1135-1143
We develop a systematic approach to the phase identification of late-arriving groups in 2-D seismic data. Waveforms in the same traveltime branch are grouped, and synthetic traveltimes for all phases are calculated using an initial approximation to the 2-D structure. For each group, we identify the two synthetic phases providing the smallest RMS residuals. If their ratio is less than some predetermined threshold, then the group's phase is ambiguous and both assignments must be tested by traveltime inversion. If there are n unidentified groups, we construct 2 n phase tables and perform a traveltime inversion on every plausible phase assignment. The phase table that provides the highest value of the posterior probability density is taken as correct, and a 2-D velocity model is constructed from the data. This approach is shown to be effective and efficient on both simulated and real data. In addition, the residuals associated with late-arriving groups provide a means of identifying deficiencies in the initial model. 相似文献
5.
A self-adaptive automated parametrization approach is suggested for the sequential inversion of controlled-source seismic tomography and gravity data. The velocities and interfaces are parametrized by their Haar wavelet expansion coefficients. Only those coefficients that are well constrained by the data, as measured by the number of rays that cross the corresponding wavelet function support area and their angular coverage, are inverted for, others are set to zero. This approach results in a reasonable distribution of resolution throughout the model even in cases of irregular ray coverage and does overcome the trade-off between different types of model parameters. A modified sequential inversion approach is suggested to join the traveltimes and gravity anomalies inversion. An algorithm is developed that inverts for smooth velocity and density variations inside the seismic layer, the position of its bottom interface as well as for optimal values of the velocity-to-density regression coefficients. The algorithm makes use of direct (diving), reflected and head (critically refracted) wave traveltimes. The algorithm workflow is demonstrated on a synthetic data example. 相似文献
6.
We have developed an inversion formuialion for velocity and attenuation structure using seismic attributes, including envelope amplitude, instantaneous frequency and arrival times of selected seismic phases. We refer to this approach as AFT inversion for amplitude, (instantaneous) frequency and time. Complex trace analysis is used to extract the different seismic attributes. The instantaneous frequency data are converted to t * using a matching procedure that approximately removes the effects of the source spectra. To invert for structure, ray-perturbation methods are used to compute the sensitivity of the seismic attributes to variations in the model. An iterative inversion procedure is then performed from smooth to less smooth models that progressively incorporates the shorter-wavelength components of the model. To illustrate the method, seismic attributes are extracted from seismic-refraction data of the Ouachita PASSCAL experiment and used to invert for shallow crustal velocity and attenuation structure. Although amplitude data are sensitive to model roughness, the inverted velocity and attenuation models were required by the data to maintain a relatively smooth character. The amplitude and t * data were needed, along with the traveltimes, at each step of the inversion in order to fit all the seismic attributes at the final iteration. 相似文献
7.
Generalized Born scattering of elastic waves in 3-D media 总被引：1，自引：0，他引：1
It is well known that when a seismic wave propagates through an elastic medium with gradients in the parameters which describe it (e.g. slowness and density), energy is scattered from the incident wave generating low-frequency partial reflections. Many approximate solutions to the wave equation, e.g. geometrical ray theory (GRT), Maslov theory and Gaussian beams, do not model these signals. The problem of describing partial reflections in 1-D media has been extensively studied in the seismic literature and considerable progress has been made using iterative techniques based on WKBJ, Airy or Langer type ansätze. In this paper we derive a first-order scattering formalism to describe partial reflections in 3-D media. The correction term describing the scattered energy is developed as a volume integral over terms dependent upon the first spatial derivatives (gradients) of the parameters describing the medium and the solution. The relationship we derive could, in principle, be used as the basis for an iterative scheme but the computational expense, particularly for elastic media, will usually prohibit this approach. The result we obtain is closely related to the usual Born approximation, but differs in that the scattering term is not derived from a perturbation to a background model, but rather from the error in an approximate Green's function. We examine analytically the relationship between the results produced by the new formalism and the usual Born approximation for a medium which has no long-wavelength heterogeneities. We show that in such a case the two methods agree approximately as expected, but that in a media with heterogeneities of all wavelengths the new gradient scattering formalism is superior. We establish analytically the connection between the formalism developed here and the iterative approach based on the WKBJ solution which has been used previously in 1-D media. Numerical examples are shown to illustrate the examples discussed. 相似文献
8.
The BABEL marine seismic experiment has been carried out to investigate the lithospheric structure and antecedent tectonic signatures of the Baltic Shield, including the Archaean-Proterozoic collisional structure in the northern part of the Gulf of Bothnia.
Lithospheric seismic-reflection streamer data and simultaneously recorded wide-angle reflection and refraction data collected in the Gulf of Bothnia as part of the BABEL project have been used for 3-D modelling. The distribution of land stations around the Gulf provides a good 3-D ray coverage of the PMP reflection data recorded at the eight stations in the area and allows an estimation of strikes and dips of the Moho boundary in the area. The traveltimes of reflected phases are calculated using a method that utilizes the finite-difference solution of the eikonal equation. The Moho wide-angle-reflection (PMP) traveltimes are modelled using an inversion method. A 2-D model from the Gulf of Bothnia extended into the third dimension is used as an initial model. During the inversion the velocity is kept constant and only the Moho boundary is allowed to vary. To estimate the strike of the Moho boundary and the stability of the inversion, two initial models with different strikes are examined.
The results indicate that the Moho depth in the Gulf of Bothnia undulates and has a maximum depth of 55 km in the south, rising to 42 km in the north. The Moho depth variations seem to be step-like. This change in the Moho depth coincides with the location of the presumed fossil subduction zone in the area. The crustal-thickness variations seem to be well approximated by a nearly 2-D structure striking parallel to a postulated subduction zone immediately to the south of the Skellefte area. The presence of the step at the crust/mantle boundary can be interpreted as a result of a plate-collision event at about 2 Ga. 相似文献
Lithospheric seismic-reflection streamer data and simultaneously recorded wide-angle reflection and refraction data collected in the Gulf of Bothnia as part of the BABEL project have been used for 3-D modelling. The distribution of land stations around the Gulf provides a good 3-D ray coverage of the PMP reflection data recorded at the eight stations in the area and allows an estimation of strikes and dips of the Moho boundary in the area. The traveltimes of reflected phases are calculated using a method that utilizes the finite-difference solution of the eikonal equation. The Moho wide-angle-reflection (PMP) traveltimes are modelled using an inversion method. A 2-D model from the Gulf of Bothnia extended into the third dimension is used as an initial model. During the inversion the velocity is kept constant and only the Moho boundary is allowed to vary. To estimate the strike of the Moho boundary and the stability of the inversion, two initial models with different strikes are examined.
The results indicate that the Moho depth in the Gulf of Bothnia undulates and has a maximum depth of 55 km in the south, rising to 42 km in the north. The Moho depth variations seem to be step-like. This change in the Moho depth coincides with the location of the presumed fossil subduction zone in the area. The crustal-thickness variations seem to be well approximated by a nearly 2-D structure striking parallel to a postulated subduction zone immediately to the south of the Skellefte area. The presence of the step at the crust/mantle boundary can be interpreted as a result of a plate-collision event at about 2 Ga. 相似文献
9.
10.
Wide-angle seismic velocities in heterogeneous crust 总被引：5，自引：0，他引：5
Seismic velocities measured by wide-angle surveys are commonly used to constrain material composition in the deep crust. Therefore, it is important to understand how these velocities are affected by the presence of multiscale heterogeneities. The effects may be characterised by the scale of the heterogeneity relative to the dominant seismic wavelength (λ); what is clear is that heterogeneities of all scales and strengths bias wide-angle velocities to some degree. Waveform modelling was used to investigate the apparent wide-angle P -wave velocities of different heterogeneous lower crusts. A constant composition (50 per cent felsic and 50 per cent ultramafic) was formed into a variety of 1- and 2-D heterogeneous arrangements and the resulting wide-angle seismic velocity was estimated. Elastic, 1-D models produced the largest velocity shift relative to the true average velocity of the medium (which is the velocity of an isotropic mixture of the two components). Thick (width > λ) horizontal layers, as a result of Fermat's Principle, provided the largest increase in velocity; thin (width ≪λ) vertical layers produced the largest decrease in velocity. Acoustic 2-D algorithms were shown to be inadequate for modelling the kinematics of waves in bodies with multiscale heterogeneities. Elastic, 2-D modelling found velocity shifts (both positive and negative) that were of a smaller magnitude than those produced by 1-D models. The key to the magnitude of the velocity shift appears to be the connectivity of the fast (and/or slow) components. Thus, the models with the highest apparent levels of connectivity between the fast phases, the 1-D layers, produced the highest-magnitude velocity shifts. To understand the relationship between measured seismic velocities and petrology in the deep crust it is clear that high-resolution structural information (which describes such connectivity) must be included in any modelling. 相似文献
11.
Finite-frequency traveltime tomography of San Francisco Bay region crustal velocity structure 总被引：1，自引：0，他引：1
F. F. Pollitz 《Geophysical Journal International》2007,171(2):630-656
Seismic velocity structure of the San Francisco Bay region crust is derived using measurements of finite-frequency traveltimes. A total of 57 801 relative traveltimes are measured by cross-correlation over the frequency range 0.5–1.5 Hz. From these are derived 4862 'summary' traveltimes, which are used to derive 3-D P -wave velocity structure over a 341 × 140 km2 area from the surface to 25 km depth. The seismic tomography is based on sensitivity kernels calculated on a spherically symmetric reference model. Robust elements of the derived P -wave velocity structure are: a pronounced velocity contrast across the San Andreas fault in the south Bay region (west side faster); a moderate velocity contrast across the Hayward fault (west side faster); moderately low velocity crust around the Quien Sabe volcanic field and the Sacramento River delta; very low velocity crust around Lake Berryessa. These features are generally explicable with surface rock types being extrapolated to depth ∼10 km in the upper crust. Generally high mid-lower crust velocity and high inferred Poisson's ratio suggest a mafic lower crust. 相似文献
12.
Anisotropy in multi-offset deep-crustal seismic experiments 总被引：1，自引：0，他引：1
Modelling of deep-seismic wide-angle data commonly assumes that the Earth is heterogeneous and isotropic. It is important to know the magnitudes of errors that may be introduced by isotropic-based wide-angle models when the Earth is anisotropic. It is equally important to find ways of detecting anisotropy and determining its properties.
This paper explores the errors introduced by interpreting anisotropic seismic data with isotropic models. Errors in P -wave reflector depths are dependent on the magnitude of the velocity anisotropy and the direction of the fast axis. The interpreted, isotropic, model velocity function is found to correspond closely to the horizontal velocity of the anisotropic medium. An additional observed parameter is the time mismatch , which we define to be the difference between the vertical two-way traveltime to a reflector and the time-converted wide-angle position of the reflector. The magnitude of the time mismatch is typically <1.0 s (when the whole crust is anisotropic) and is found to be closely related to the magnitude and sign of the anisotropic anellipticity. The relationships are extendible to more complicated models, including those with vertical velocity gradients, crustal zonation, and lower symmetry orders.
A time mismatch may be symptomatic of the presence of anisotropy. We illustrate the observation of a time mismatch for a real multi-offset seismic data set collected north of Scotland and discuss the implications for crustal anisotropy in that region. 相似文献
This paper explores the errors introduced by interpreting anisotropic seismic data with isotropic models. Errors in P -wave reflector depths are dependent on the magnitude of the velocity anisotropy and the direction of the fast axis. The interpreted, isotropic, model velocity function is found to correspond closely to the horizontal velocity of the anisotropic medium. An additional observed parameter is the time mismatch , which we define to be the difference between the vertical two-way traveltime to a reflector and the time-converted wide-angle position of the reflector. The magnitude of the time mismatch is typically <1.0 s (when the whole crust is anisotropic) and is found to be closely related to the magnitude and sign of the anisotropic anellipticity. The relationships are extendible to more complicated models, including those with vertical velocity gradients, crustal zonation, and lower symmetry orders.
A time mismatch may be symptomatic of the presence of anisotropy. We illustrate the observation of a time mismatch for a real multi-offset seismic data set collected north of Scotland and discuss the implications for crustal anisotropy in that region. 相似文献
13.
G. D. Spence R. S. White G. K. Westbrook S. R. Fowler 《Geophysical Journal International》1989,96(2):273-294
Summary. The Hatton Bank passive continental margin exhibits thick seaward dipping reflector sequences which consist of basalts extruded during rifting between Greenland and Rockall Plateau. Multichannel seismic reflection profiling across the margin reveals three reflector wedges with a maximum thickness near 7 km, extending from beneath the upper continental slope to the deep ocean basin. We present results of the velocity structure within the dipping reflector sequences at eight locations across the margin, interpreted by synthetic seismogram modelling a set of multichannel expanding spread profiles parallel to the margin. At the top of some reflector sequences, we observe a series of 100 m thick high- and low-velocity zones, which are interpreted as basalt flows alternating with sediments or weathered and rubble layers. At the profile locations, the base of the dipping reflectors correlates with P -wave velocities near 6.5 km s−1 . However, elsewhere the reflectors appear to extend significantly deeper than the inferred 6.5 km s−1 velocity contour, indicating that the velocity structure may not be controlled solely by lithological boundaries but also by metamorphic effects. Shear-waves were observed on two lines, permitting the calculation of Poisson's ratio. The decrease in Poisson's ratio from 0.28 to near 0.25 in the upper 5 km of crust may also indicate the effect of metamorphism on seismic properties, or alternatively may be explained by crack closure under load. 相似文献
14.
David L. Vasconcelos Fernando O. Marques Francisco C. C. Nogueira Yoe A. R. Perez Francisco H. R. Bezerra Rmulo C. Stohler Jorge A. B. Souza 《Basin Research》2021,33(1):705-728
Common basin models assume that the post‐rift tectonic evolution of most basins is usually associated with tectonic quiescence. However, tectonic inversion during the post‐rift phase has been proposed for several sedimentary basins worldwide, but how and why it happens is still a matter of debate, especially in intracontinental settings where the lithosphere is old and thick. Here, we use geological and geophysical data from the Rio do Peixe Basin in NE Brazil to show evidence that intracontinental sedimentary basins can be tectonically inverted by far‐field compressive stresses acting on pre‐existing weakness zones of lithospheric‐scale where stresses can concentrate and inversion can occur. Geomorphological and field data combined with seismic reflection, gravimetric and borehole data show that: (a) inversion occurred along two main Precambrian lithospheric‐scale shear zones, the Patos (E‐W trending) and Portalegre (NE‐SW trending), which had already been reactivated as basin‐bounding faults during the earlier rift stage; (b) post‐rift reactivation affected (mostly) the original master normal faults with the largest rift displacements, and locally produced new reverse faults; (c) during contraction, deformation was partitioned between fault reactivation and buckling of the incompetent sediment pushed against the hard basement; (d) all these signs of inversion have been observed in the field and can be demonstrated on seismic reflection profiles; and (e) combined gravimetric and seismic data show that the main structures of the basin were followed by an inversion. These data are consistent with the operation of WSW‐ENE horizontal maximum compressive stress as a result of combined pushes of the Mid‐Atlantic Ridge (towards the W) and the Andes (towards the E), responsible for the post‐rift oblique inversion of normal faults inherited from the rift phase and formed with vertical maximum compressive stress. 相似文献
15.
We present a technique based on the single-scattering approximation that relates time-lapse localized changes in the propagation velocity to changes in the traveltime of singly scattered waves. We describe wave propagation in a random medium with homogeneous statistical properties as a single-scattering process where the fluctuations of the velocity with respect to the background velocity are assumed to be weak. This corresponds to one of two end-member regimes of wave propagation in a random medium, the first being single scattering, and the second multiple scattering. We present a formulation that relates the change in the traveltime of the scattered waves to a localized change in the propagation velocity by means of the Born approximation for the scattered wavefield. We validate the methodology with synthetic seismograms calculated with finite differences for 2-D acoustic waves. Potential applications of this technique include non-destructive evaluation of heterogeneous materials and time-lapse monitoring of heterogeneous reservoirs. 相似文献
16.
Summary. The three-dimensional seismic structure of the Mont Dore volcano is studied by inversion of the arrival times of seismic waves. With this aim two new methods are developed. First, the arrival times are those of Moho-reflected waves at a critical distance from artificial sources in different azimuths. Secondly, the inversion uses a technique which does not require the traditional a priori partition of the space into blocks. The resulting picture reveals such features as: (1) a circular caldera within the basement, the rim of which is marked by magnetic anomalies associated with post-caldera activity; (2) a clear lower limit of the volcano-sedimentary sequence under part of the caldera, opposed to low velocity anomalies extending deeper beneath another part and which may have been the site of volcanic material transport, and (3) eeper heterogeneities possibly related to foundered basement blocks. 相似文献
17.
Michael McCaughey Penny Barton & Satish Singh 《Geophysical Journal International》2000,141(1):100-114
We report results from the Seismic Wide-Angle and Broadband Survey carried out over the Mid North Sea High. This paper focuses on integrating the information from a conventional deep multichannel reflection profile and a coincident wide-angle profile obtained by recording the same shots on a set of ocean bottom hydrophones (OBH). To achieve this integration, a new traveltime inversion scheme was developed (reported elsewhere) that was used to invert traveltime information from both the wide-angle OBH records and the reflection profile simultaneously. Results from the inversion were evaluated by producing synthetic seismograms from the final inversion model and comparing them with the observed wide-angle data, and an excellent match was obtained. It was possible to fine-tune velocities in less well-resolved parts of the model by considering the critical distance for the Moho reflection. The seismic velocity model was checked for compatibility with the gravity field, and used to migrate and depth-convert the reflection profile. The unreflective upper crust is characterized by a high velocity gradient, whilst the highly reflective lower crust is associated with a low velocity gradient. At the base of the crust there are several subhorizontal reflectors, a few kilometres apart in depth, and correlatable laterally for several tens of kilometres. These reflectors are interpreted as representing a strike section through northward-dipping reflectors at the base of the crust, identified on orthogonal profiles by Freeman et al. (1988) as being slivers of subducted and imbricated oceanic crust, relics of the mid-Palaeozoic Iapetus Ocean. 相似文献
18.
Traveltime measurements from noise correlation: stability and detection of instrumental time-shifts 总被引：1，自引：0，他引：1
We test the feasibility of using Green's functions extracted from records of ambient seismic noise to monitor temporal changes in the Earth crust properties by repeated measurements at regional distances. We use about 11 yr of continuous recordings to extract surface waves between three pairs of stations in California. The correlations are computed in a moving 1-month window and we analyse the temporal evolution of measured interstation traveltimes. The comparison of the arrival times in the positive and negative correlation time of Rayleigh and Love waves allows us to separate time-shifts associated with any form of physical change in the medium, those resulting from clock drift or other instrumental errors, and those due to change in the localization of the noise sources. This separation is based on the principle of time symmetry. When possible, we perform our analysis in two different period bands: 5–10 and 10–20 s. The results indicate that significant instrumental time errors (0.5 s) are present in the data. These time-shifts can be measured and tested by closure relation and finally corrected independently of any velocity model. The traveltime series show a periodic oscillation that we interpret as the signature of the seasonal variation of the region of origin of the seismic noise. Between 1999 and 2005, the final arrival time fluctuations have a variance of the order of 0.01 s. This allows us to measure interstation traveltimes with errors smaller than 0.3 per cent of the interstation traveltime and smaller than 1 per cent of the used wave period. This level of accuracy was not sufficient to detect clear physical variation of crustal velocity during the considered 11 yr between the three stations in California. Such changes may be more easily detectable when considering pairs of stations more closely located to each other and in the vicinity of tectonically active faults or volcanoes. 相似文献
19.
This paper presents an updated interpretation of seismic anisotropy within the uppermost mantle of southern Germany. The dense network of reversed and crossing refraction profiles in this area made it possible to observe almost 900 traveltimes of the Pn phase that could be effectively used in a time-term analysis to determine horizontal velocity distribution immediately below the Moho. For 12 crossing profiles, amplitude ratios of the Pn phase compared to the dominant crustal phase were utilized to resolve azimuthally dependent velocity gradients with depth. A P -wave anisotropy of 3–4 per cent in a horizontal plane immediately below the Moho at a depth of 30 km, increasing to 11 per cent at a depth of 40 km, was determined. For the axis of the highest velocity of about 8.03 km s−1 at a depth of 30 km a direction of N31°F was obtained. The azimuthal dependence of the observed Pn amplitude is explained by an azimuth-dependent sub-Moho velocity gradient decreasing from 0.06 s−1 in the fast direction to 0 s−1 in the slow direction of horizontal P -wave velocity. From the seismic results in this study a petrological model suggesting a change of modal composition and percentage of oriented olivine with depth was derived. 相似文献
20.
Large scale seismic anisotropy in the Earth's mantle is likely dynamically supported by the mantle's deformation; therefore, tomographic imaging of 3-D anisotropic mantle seismic velocity structure is an important tool to understand the dynamics of the mantle. While many previous studies have focused on special cases of symmetry of the elastic properties, it would be desirable for evaluation of dynamic models to allow more general axis orientation. In this study, we derive 3-D finite-frequency surface wave sensitivity kernels based on the Born approximation using a general expression for a hexagonal medium with an arbitrarily oriented symmetry axis. This results in kernels for two isotropic elastic coefficients, three coefficients that define the strength of anisotropy, and two angles that define the symmetry axis. The particular parametrization is chosen to allow for a physically meaningful method for reducing the number of parameters considered in an inversion, while allowing for straightforward integration with existing approaches for modelling body wave splitting intensity measurements. Example kernels calculated with this method reveal physical interpretations of how surface waveforms are affected by 3-D velocity perturbations, while also demonstrating the non-linearity of the problem as a function of symmetry axis orientation. The expressions are numerically validated using the spectral element method. While challenges remain in determining the best inversion scheme to appropriately handle the non-linearity, the approach derived here has great promise in allowing large scale models with resolution of both the strength and orientation of anisotropy. 相似文献