Reflector Depth Research Articles

Possible ways of improvement of FEM oscillator with Bragg resonator

Two methods of efficiency enhancement of free-electron maser (FEM) oscillator with the Bragg resonator having a shift of corrugation phase were studied. The first one is a “starting mode” regime using an additional high-frequency mode located in the vicinity of the main mode. The Bragg resonator having a shift of corrugation phase seems to represent the most attractive oscillator configuration. Another possibility is a special variation of corrugation depth of Bragg reflectors (mirror profiling) providing the possibility of optimizing the longitudinal distribution of the RF field amplitude inside the interaction space and depressing of parasitic side modes of the resonator. Optimization of RF power extraction from FEM, based on Talbot effect, has also been considered. Perspectives of future FEM development are discussed including schemes of pulse power compression and submillimeter wave generation.

Possible ways of improvement of FEM oscillator with Bragg resonator

Two methods of efficiency enhancement of free-electron maser (FEM) oscillator with the Bragg resonator having a shift of corrugation phase were studied. The first one is a “starting mode” regime using an additional high-frequency mode located in the vicinity of the main mode. The Bragg resonator having a shift of corrugation phase seems to represent the most attractive oscillator configuration. Another possibility is a special variation of corrugation depth of Bragg reflectors (mirror profiling) providing the possibility of optimizing the longitudinal distribution of the RF field amplitude inside the interaction space and depressing of parasitic side modes of the resonator. Optimization of RF power extraction from FEM, based on Talbot effect, has also been considered. Perspectives of future FEM development are discussed including schemes of pulse power compression and submillimeter wave generation.

Overview of the MITI Nankai Trough Wells: A Milestone in the Evaluation of Methane Hydrate Resources

Abstract. Bottom‐simulating reflectors suggestive of the presence of methane hydrates are widely distributed below the ocean floor around Japan. In late 1999, drilling of the MITI Nankai Trough wells was conducted to explore this potential methane hydrate resource and a Tertiary conventional structure. The wells are located in the Northwest Pacific Ocean off Central Japan at a water depth of 945 m. A total of six wells were drilled, including the main well, two pilot wells, and three post survey wells at intervals of 10–100 m. All wells except the first confirmed the occurrence of hydrates based on logging‐while‐drilling, wire‐line logging and/or coring using a pressure and temperature coring system in addition to conventional methods. Based on the various well profiles, four methane hydrate‐bearing sand‐rich intervals in turbidite fan deposits were recognized. Methane hydrates fill the pore spaces in these deposits, reaching saturation of up to 80 % in some layers. The methane hydrate‐bearing turbiditic sand layers are less than 1 m thick, with a total thickness of 12–14 m. The bottom depth of high hydrate concentration correlates well with the depth of the bottom‐simulating reflector. Based on these exploration results, the Japanese government inaugurated a 16‐year methane hydrate exploitation program in 2001.

Analysis of image gathers in factorized VTI media

Because events in image gathers generated after prestack depth migration are sensitive to the velocity field, they are often used in migration velocity analysis for isotropic media. Here, we present an analytic and numerical study of P‐wave image gathers in transversely isotropic media with a vertical symmetry axis (VTI) and establish the conditions for flattening such events and positioning them at the true reflector depth. Application of the weak‐anisotropy approximation leads to concise expressions for reflections in image gathers from homogeneous and factorized v(z) media in terms of the VTI parameters and the vertical velocity gradient kz. Flattening events in image gathers for any reflector dip requires accurate values of the zero‐dip NMO velocity at the surface [Vnmo (z = 0)], the gradient kz, and the anellipticity coefficient η. For a fixed error in Vnmo and kz, the magnitude of residual moveout of events in image gathers decreases with dip, while the moveout caused by an error in η initially increases for moderate dips but then decreases as dips approach 90°. Flat events in image gathers in VTI media, however, do not guarantee the correct depth scale of the model because reflector depth depends on the vertical migration velocity. For factorized v(x, z) media with a linear velocity variation in both the x‐ and z‐directions, the moveout on image gathers is controlled by Vnmo (x = z = 0), kz, η, and a combination of the horizontal velocity gradient kx and the Thomsen parameter δ (specifically, kx[Formula: see text]). If too large a value of any of these four quantities is used in migration, reflections in the image gathers curve downward (i.e., they are undercorrected; the inferred depth increases with offset), while a negative error results in overcorrection. Lateral heterogeneity tends to increase the sensitivity of moveout of events in image gathers to the parameter η, and errors in η may lead to measurable residual moveout of horizontal events in v(x, z) media even for offset‐to‐depth ratios close to unity. These results provide a basis for extending to VTI media conventional velocity analysis methods operating with image gathers. Although P‐wave traveltimes alone cannot be used to separate anisotropy from lateral heterogeneity (i.e., kx is coupled to δ), moveout of events in image gathers does constrain the vertical gradient kz. Hence, it may be possible to build VTI velocity models in depth by supplementing reflection data with minimal a priori information, such as the vertical velocity at the top of the factorized VTI layer.

Converted-wave moveout and conversion-point equations in layered VTI media: theory and applications

We have developed improved equations for calculating the conversion point of the P-SV converted wave (C-wave) in transversely isotropic media with a vertical symmetry axis (vertical transverse isotropy (VTI)). We have also derived modified C-wave moveout equations for layered VTI media. The derived equations for the conversion-point are valid for offsets about three-times the reflector depth (x/z=3.0) and those for the C-wave moveout about twice the reflector depth (x/z=2.0). The new equations reveal some additional analytical insights into the converted-wave properties. The anisotropy has a more significant effect on the conversion point than on the move-out, and using the effective binning velocity ratio γeff only is often insufficient to account for the anisotropic effect, even when higher-order terms are considered. Also for C-wave propagation, the anisotropy appears to affect the P-wave leg more than the S-wave leg. The ratio of the anisotropic contributions from P- and S-waves is close to the vertical velocity ratio γ0. Consequently S-wave anisotropic parameters may be recovered from converted-waves when P-wave anisotropic parameters are known. The new equations suggest that the C-wave moveout in layered VTI media over intermediate-to-far offsets is determined by the anisotropic parameter χeff in addition to C-wave stacking velocity VC2, and the velocity ratios γ0 and γeff. We refer to these four parameters as the C-wave “stacking velocity model”. Two practical work flows are presented for determining this model: the double-scanning flow and the single-scanning flow. Applications to synthetic and real data show that although the single-scanning flow is less accurate than the double-scanning flow, it is more efficient and, in most cases, can yield sufficiently accurate results.

Seismic reflection imaging of an ultrashallow interface from a P‐wave data set with a poor signal‐to‐noise ratio

ABSTRACTIt is well known that pitfalls are commonly encountered in the acquisition and processing of shallow reflection data. Although they can often lead to misinterpretations, the obsession with these difficulties can generate an excessively pessimistic attitude and ultimately lead to rejecting data that contain genuine reflections. The authors revisited a data set acquired during an ultrashallow P‐wave reflection experiment conducted in December 1996 on a subsurface model characterized by one main, complex interface. The model had been purpose‐built to control acquisition and processing decisions, and to contribute to clarifying at least some of the critical aspects inherent in the ultrashallow seismic reflection method. For the experiment, the acquisition geometry was purposely designed regardless of the known characteristics of the model, considering only a target depth of less than ten metres. The data, which had been acquired with CMP techniques, were generally characterized by a poor signal‐to‐noise ratio and had been considered completely useless. Initially, inexperience in acquiring and, above all, processing ultrashallow reflection data, in conjunction with mise‐valuations, had led to disappointing failures. Velocity analysis on reflection data had proved very difficult and standard processing sequences were inadequate. However, in this case a good result was obtained by modelling the near‐surface velocity using direct‐wave traveltimes analysis and by adopting a simple but segregated processing sequence, which proved necessary due to significant velocity gradients and large relative variations of the reflector depth. Time‐to‐depth conversion afforded a more than acceptable result.

Traveltime formulas of near‐zero‐offset primary reflections for a curved 2D measurement surface

Analytic moveout formulas for primary near‐zero‐offset reflections in various types of gathers (e.g., common midpoint, common shot, zero offset) play a significant role in the seismic reflection method. They are required in stacking methods like the common midpoint (CMP) or the common‐reflection‐surface (CRS) stack. They also play a very important role in Dix‐type traveltime inversions and are of prime interest for seismic imaging. They are particularly attractive if they can be given a physical interpretation, involving for instance the wavefront curvatures of specific waves. The new formulas presented here have such a form. They give particular attention to the influence that a smooth curved measurement surface has on the computation of the traveltime and the moveout in various gathers as well as on the normal‐moveout (NMO) velocity in the CMP gather. This influence should be accounted for in the CMP or CRS stack as well as in the Dix‐type inversion. In the computation of interval velocities and the recovery of the depth of reflectors, the new NMO velocity formula is therefore more suited than the root‐mean‐square or NMO velocity for a planar measurement surface. It can be extended to a rugged free surface (mountainous terrain), but this extension requires a different derivation and different considerations. The influence of the surface curvature on the NMO velocity can be estimated with the new formula given here.

The effect of crustal anisotropy on reflector depth and velocity determination from wide-angle seismic data: a synthetic example based on South Island, New Zealand

When deriving velocity models by forward modelling or inverting travel time arrivals from seismic refraction data, a heterogeneous but isotropic earth is usually assumed. In regions where the earth is not isotropic at the scale at which it is being sampled, the assumption of isotropy can lead to significant errors in the velocities determined for the crust and the depths calculated to reflecting boundaries. Laboratory velocity measurements on rocks collected from the Haast Schist terrane of South Island, New Zealand, show significant (up to 20%) compressional (P) wave velocity anisotropy. Field data collected parallel and perpendicular to the foliation of the Haast Schist exhibit as much as 11% P-wave velocity anisotropy. We demonstrate, using finite-difference full-wavefield modelling, the types of errors and problems that might be encountered if isotropic methods are used to create velocity models from data collected in anisotropic regions. These reflector depth errors could be as much as 10–15% for a 10-km thick layer with significant (20%) P-wave velocity anisotropy. The implications for South Island, New Zealand, where the problem is compounded by extreme orientations of highly anisotropic rocks (foliation which varies from horizontal to near vertical), are considered. Finally, we discuss how the presence of a significant subsurface anisotropic body might manifest itself in wide-angle reflection/refraction and passive seismic datasets, and suggest ways in which such datasets may be used to determine the presence and extent of such anisotropic bodies.

A simple, exact solution for the P‐SV wave conversion point via prestack migration

The conversion point (CP) is the lateral position of the reflection point, relative to the source-receiver midpoint, for a laterally homogeneous earth (horizontal reflectors) and the P-SV converted-wave (C-wave) geometry depicted in Figure 1. The source emits a P-wave, which propagates to the horizontal reflector where it reflects as an SV-wave and then propagates to the receiver. Common conversion point (CCP) binning and stacking are tools that use CP modeling for processing C-wave data. Applications include iterative statics and velocity analysis procedures. Acquisition design methods also use CP modeling (see Thomsen, 1999). Calculation of the CP is complicated, unfortunately, and exact solutions exist only for homogeneous and isotropic media. Thomsen (1999) developed asymptotic expansions that approximate the CP in vertically inhomogeneous isotropic and anisotropic media. Yuan and Li (2001) extended these expressions, improving their accuracy for large source-receiver offsets. Exact solutions for the CP exist only in simple media, and that is the subject of this paper. Tessmer and Behle (1988) used Fermat9s principle to find a quartic equation for the exact CP in homogeneous, isotropic media. I show that the equation for the C-wave prestack migration impulse response yields a cubic equation for the exact CP in homogeneous, isotropic media. Analytically solving the cubic equation is less cumbersome than analytically solving the quartic equation, and I have obtained the exact solution of the new cubic equation in simple trigonometric form. The Tessmer and Behle (1998) quartic CP equation depends upon the reflector depth, whereas the new cubic CP equation depends instead upon the two-way reflection traveltime of the C-wave. Thus, the new result directly specifies the CP for each sample of a prestack seismic trace (assuming reflectors are horizontal).

Electromagnetic wave speed in polar ice: validation of the common-midpoint technique with high-resolution dielectric-profiling and γ-density measurements

AbstractThe accuracy of the travel-time–velocity and travel-time–depth profile derived from ground-penetrating radar (GPR) common-midpoint (CMP) surveys at different frequencies is investigated for the first time ever by direct comparison with the profile calculated from high-resolution dielectric-profiling (DEP) ice-core data. In addition, we compare two travel-time profiles calculated from ice-core density data by means of different dielectrical mixture models with the DEP-based profile. CMP surveys were carried out at frequencies of 25,50,100 and 200 MHz near the new European deep-drilling site DML05 in Dronning Maud Land, Antarctica, during the 1998/99 field season. An improved scanning capacitor for high-resolution DEP and a γ-densiometer for density measurements were used to determine the complex dielectric constant and the density at 5 mm increments along the ice core B32, retrieved in 1997/98 at DML05. The comparisons with DEP- and density-based velocity series show that the CMP velocity series are slightly higher but asymptotically approach the core-based velocities with depth. Root-mean-square differences of the DEP velocity series range between 8% for the 25 MHz CMP and 2% in the case of the 200 MHz survey. Density-based velocities differ from the DEP velocities by 51 %. The travel-time–depth series calculated from the interval velocities show a better agreement between all series than the velocity series. Differences are 5.7–1.4% for the 25 and 200 MHz CMP measurements, and <0.6% for the density data. Based on these comparisons, we evaluate the accuracy with which the depth of electromagnetic reflectors observed in common-offset profiles can be determined, and discuss reasons for the observed differences between CMP- and core-based profiles. Moreover, we compare the errors determined from the field measurements with those estimated from GPR system characteristics to provide a measure that can be used to estimate the accuracy of GPR analyses for the planning of GPR campaigns. Our results show that CMP surveys are a useful technique to determine the depth of radar reflectors in combination with common-offset measurements, especially on a region-wide basis.

Depth‐domain velocity analysis in VTI media using surfaceP-wave data: Is it feasible?

The main difficulties in anisotropic velocity analysis and inversion using surface seismic data are associated with the multiparameter nature of the problem and inherent trade‐offs between the model parameters. For the most common anisotropic model, transverse isotropy with a vertical symmetry axis (VTI media), P-wave kinematic signatures are controlled by the vertical velocity V0and the anisotropic parameters ε and δ. However, only two combinations of these parameters—NMO velocity from a horizontal reflector Vnmo(0) and the anellipticity coefficient η—can be determined from P-wave reflection traveltimes if the medium above the reflector is laterally homogeneous. While Vnmo(0) and η are sufficient for time‐domain imaging in VTI media, they cannot be used to resolve the vertical velocity and build velocity models needed for depth migration. Here, we demonstrate that P-wave reflection data can be inverted for all three relevant VTI parameters (V0, ε and δ) if the model contains nonhorizontal intermediate interfaces. Using anisotropic reflection tomography, we carry out parameter estimation for a two‐layer medium with a curved intermediate interface and reconstruct the correct anisotropic depth model. To explain the success of this inversion procedure, we present an analytic study of reflection traveltimes for this model and show that the information about the vertical velocity and reflector depth was contained in the reflected rays which crossed the dipping intermediate interface. The results of this work are especially encouraging because the need for depth imaging (such as prestack depth migration) arises mostly in laterally heterogeneous media. Still, we restricted this study to a relatively simple model and constrained the inversion by assuming that one of the layers is isotropic. In general, although lateral heterogeneity does create a dependence of P-wave reflection traveltimes on the vertical velocity, there is no guarantee that for more complicated models all anisotropic parameters can be resolved in a unique fashion.

Reflection waveform inversion using local descent methods: Estimating attenuation and velocity over a gas‐sand deposit

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

Slip-slidin' away—some practical implications of seismic velocity anisotropy on depth imaging

Recent advances in imaging mean that we no longer need to ignore seismic velocity anisotropy. Laboratory and field studies provide compelling evidence that shales exhibit intrinsic transverse isotropy (TI). In this symmetry class, the seismic velocity parallel to the laminations is greater than that perpendicular to the layering, and the difference can be as high as 30%. In flat-layered clastic sequences, such as in the Western Canada sedimentary basin, the TI axis of symmetry is essentially vertical, and isotropic depth migration of reflection seismic data tends to overestimate the true depths of reflectors. This occurs because the imaging velocity, based on moveout analysis, is generally greater than the true vertical velocity.

Estimation of fracture parameters from reflection seismic data—Part II: Fractured models with orthorhombic symmetry

Existing geophysical and geological data indicate that orthorhombic media with a horizontal symmetry plane should be rather common for naturally fractured reservoirs. Here, we consider two orthorhombic models: one that contains parallel vertical fractures embedded in a transversely isotropic background with a vertical symmetry axis (VTI medium) and the other formed by two orthogonal sets of rotationally invariant vertical fractures in a purely isotropic host rock. Using the linear‐slip theory, we obtain simple analytic expressions for the anisotropic coefficients of effective orthorhombic media. Under the assumptions of weak anisotropy of the background medium (for the first model) and small compliances of the fractures, all effective anisotropic parameters reduce to the sum of the background values and the parameters associated with each fracture set. For the model with a single fracture system, this result allows us to eliminate the influence of the VTI background by evaluating the differences between the anisotropic parameters defined in the vertical symmetry planes. Subsequently, the fracture weaknesses, which carry information about the density and content of the fracture network, can be estimated in the same way as for fracture‐induced transverse isotropy with a horizontal symmetry axis (HTI media) examined in our previous paper (part I). The parameter estimation procedure can be based on the azimuthally dependent reflection traveltimes and prestack amplitudes of P-waves alone if an estimate of the ratio of the P- and S-wave vertical velocities is available. It is beneficial, however, to combine P-wave data with the vertical traveltimes, NMO velocities, or AVO gradients of mode‐converted (PS) waves. In each vertical symmetry plane of the model with two orthogonal fracture sets, the anisotropic parameters are largely governed by the weaknesses of the fractures orthogonal to this plane. For weak anisotropy, the fracture sets are essentially decoupled, and their parameters can be estimated by means of two independently performed HTI inversions. The input data for this model must include the vertical velocities (or reflector depth) to resolve the anisotropic coefficients in each vertical symmetry plane rather than just their differences. We also discuss several criteria that can be used to distinguish between the models with one and two fracture sets. For example, the semimajor axis of the P-wave NMO ellipse and the polarization direction of the vertically traveling fast shear wave are always parallel to each other for a single system of fractures, but they may become orthogonal in the medium with two fracture sets.

Basaltic lava domes, lava lakes, and volcanic segmentation on the southern East Pacific Rise

Meter‐scale DSL‐120 sonar mapping and coregistered Argo II photographic observations reveal changes in eruptive style that closely follow the third‐order structural segmentation of the ridge axis on the southern East Pacific Rise, 17°11′–18°37′S. Near segment ends we observe abundant basaltic lava domes which average 20 m in height and 200 m in basal diameter and have pillow lava as the dominant lava morphology. The ubiquity of pillow lava suggests low effusion rate eruptions. The abundance of lava domes suggests that the fissure eruptions were of sufficient duration to focus and produce a line of volcanic edifices. Near segment centers we observe fewer but larger lava domes, voluminous drained and collapsed lava lakes, and smooth lobate and sheet lava flows with very little pillow lava. The abundance of sheet flows suggests that high effusion rate eruptions are common. Fewer lava domes and large lava lakes suggest that fissure eruptions do not focus to point sources. This pattern was observed on eight third‐order ridge segments suggesting that a fundamental volcanic segmentation of the ridge occurs on this scale. The third‐order segment boundaries also correlate with local maxima in the seismic axial magma chamber reflector depth throughout the study area and decreased across‐axis width of the region of seismic layer 2A thickening along the one segment where sufficient cross‐axis seismic lines exist. The geochemically defined magmatic segment boundaries in the study area match the locations of our volcanic segment boundaries, although rock sampling density is not adequate to constrain the variation across all the third‐order volcanic segments that we identify. These observations suggest that variation in the processes of crustal accretion along axis occurs at a length scale of tens of kilometers on superfast spreading (>140 km/Myr full rate) mid‐ocean ridges.

Fast Estimation of Parameters of a Layered-dipping Earth Model by Inverting Reflected Waves

Shallow high-resolution reflection data provide information about near-surface geology from [Formula: see text] depth. Within a receiver-spread range of [Formula: see text], a layered-dipping earth model is a simple and valid model in most cases of shallow reflection surveying. We formulated an approach to quickly estimate parameters such as interval velocity, reflector depth, and dip by inverting reflected traveltime of a layered-dipping earth model. To reduce the ambiguity of inverted solutions, we apply constraints on dip directions and depth to reflectors. Accuracy of modifications to update the model is controlled by: 1) using an explicit expression of the Jacobian matrix; 2) inverting model parameters layer by layer from shallow to deep, which is equivalent to solving a diagonal matrix; 3) employing the Levenberg-Marquardt method that is simplified and numerically stabilized by the singular value decomposition technique. Root-mean-square error and maximum deviation were introduced to track iteration convergence, thereby reducing the possibility of rejecting an acceptably modified model. Error-free synthetic examples, tested on a PC computer, showed the stability and speed of this approach. Application of this approach to real shallow seismic reflection field data confirms its accuracy and applicability on inexpensive personal computers.

Inversion of normal moveout for monoclinic media1

Multiple vertical fracture sets, possibly combined with horizontal fine layering, produce an equivalent medium of monoclinic symmetry with a horizontal symmetry plane. Although monoclinic models may be rather common for fractured formations, they have hardly been used in seismic methods of fracture detection due to the large number of independent elements in the stiffness tensor. Here, we show that multicomponent wide‐azimuth reflection data (combined with known vertical velocity or reflector depth) or multi‐azimuth walkaway VSP surveys provide enough information to invert for all but one anisotropic parameters of monoclinic media.In order to facilitate the inversion procedure, we introduce a Thomsen‐style parametrization for monoclinic media that includes the vertical velocities of the P‐wave and one of the split S‐waves and a set of dimensionless anisotropic coefficients. Our notation, defined for the coordinate frame associated with the polarization directions of the vertically propagating shear waves, captures the combinations of the stiffnesses responsible for the normal‐moveout (NMO) ellipses of all three pure modes. The first group of the anisotropic parameters contains seven coefficients (ε(1,2), δ(1,2,3) and γ(1,2)) analogous to those defined by Tsvankin for the higher‐symmetry orthorhombic model. The parameters ε(1,2), δ(1,2) and γ(1,2) are primarily responsible for the pure‐mode NMO velocities along the coordinate axes x1 and x2 (i.e. in the shear‐wave polarization directions). The remaining coefficient δ(3) is not constrained by conventional‐spread reflection traveltimes in a horizontal monoclinic layer. The second parameter group consists of the newly introduced coefficients ζ(1,2,3) which control the rotation of the P‐, S1‐ and S2‐wave NMO ellipses with respect to the horizontal coordinate axes. Misalignment of the P‐wave NMO ellipse and shear‐wave polarization directions was recently observed on field data by Pérez et al.Our parameter‐estimation algorithm, based on NMO equations valid for any strength of the anisotropy, is designed to obtain anisotropic parameters of monoclinic media by inverting the vertical velocities and NMO ellipses of the P‐, S1‐ and S2‐waves. A Dix‐type representation of the NMO velocity of mode‐converted waves makes it possible to replace the pure shear modes in reflection surveys with the PS1‐ and PS2‐waves. Numerical tests show that our method yields stable estimates of all relevant parameters for both a single layer and a horizontally stratified monoclinic medium.

Englacial water distribution in a temperate glacier from surface and borehole radar velocity analysis

AbstractWe have obtained common offset, common midpoint (CMP) and borehole vertical (VRP) ground-penetrating radar profiles close to the margin of Falljökull, a small, steep temperate valley glacier situated in southeast Iceland. Velocity analysis of CMP and VRP surveys provided a four-layered velocity model. This model was verified by comparison between the depths of englacial reflectors and water channels seen in borehole video, and from the depths of boreholes drilled to the bed. In the absence of sediment within the glacier ice, radar velocity is inversely proportional to water content. Using mixture models developed by Paren and Looyenga, the variation of water content with depth was determined from the radar velocity profile. At the glacier surface the calculated water content is 0.23–0.34% (velocity 0.166 m ns−1), which rises sharply to 3.0–4.1% (velocity 0.149 m ns−1) at 28 m depth, interpreted to be the level of the piezometric surface. Below the piezometric surface the water content drops slowly to 2.4–3.3% (velocity 0.152 m ns−1) until ∼102 m depth where it falls to 0.09–0.14% (velocity 0.167 m ns−1). The water content of the ice then remains low to the glacier bed at about 112 m. These results suggest storage of a substantial volume of water within the glacier ice, which has significant implications for glacier hydrology, ice rheology and interpretations of both radar and seismic surveys.

Numerical investigation of axisymmetric shock wave focusing over paraboloidal reflectors

The problem of a plane shock wave incident to a paraboloidal reflector is numerically investigated. The numerical solver used is developed by an improved, implicit, upwind total variation diminishing scheme in a finite-volume approach. The real-gas effect is taken into account if high temperature occurs. The solver is validated on four test problems. The complicated flow fields of axisymmetric shock wave focusing for different-depth reflectors at various incident shock Mach numbers are studied. An interesting result of a maximum pressure happening at the reflector center is found. This is due to the occurrence of an implosion phenomenon. A maximum temperature might occur at the reflector center or at other locations, depending on the incident shock Mach number and the reflector depth. Moreover, vortical flows induced by shock wave focusing and their formation mechanism are explored. It was found that the vortices near the reflector are caused by a ring-shaped shock/slipline interaction. Owing to the slipline on the symmetry axis, a jet flow is induced, resulting in the formation of vortices near the symmetry axis.

The null space of a generally anisotropic medium in linearized surface reflection tomography

The null space of a generally anisotropic medium in linearized surface reflection tomography