A LAYER-STRIPPING TECHNIQUE FOR THE SUPPRESSION OF WATER-BOTTOM MULTIPLE REFLECTIONS*

A new method to suppress water-bottom multiples (water-bottom reverberations) uses the fact that in the domain of intercept time and ray parameter (τ–p domain) the water-bottom reverberations are strictly periodical for a horizontal flat sea bottom. Using this property a comb filter can be designed. The window of the filter should be approximately equal to the duration of a source pulse. The algorithm finds the maximum of the periodical energy throughout the τ–p domain and then designs the comb filter which eliminates the water bottom reverberations from each trace in the τ– p domain. This process can be repeated for higher order reverberations. Finally the τ–p domain with attenuated multiples is transformed back to the conventional x -- t space. The method is illustrated on a variety of synthetic data and on a set of real marine CMP data acquired in the North Sea near the Norwegian shore.     

The timing of runoff response in design flood analysis

This study presents an investigation of the time to peak of unit response functions for design flood studies. It is based on an empirical analysis of observed rainfall–runoff data for 49 basins in the UK and explores the relationship between unit response time to peak (t_p) and flood peak magnitude (Q_p). The results show that t_p varies significantly between events but suggest a systematic relationship between t_p and Q_p. The relationships which have been developed suggest that t_p decreases with flood magnitude and approaches to an asymptotic value for very large values of Q_p. These findings confirm numerous physical and field investigations and also support the reduction in response time for probable maximum flood (PMF) recommended in the Soil Conservation Services method, the Flood Studies Report method and the Flood Estimation Handbook. The findings also suggest that t_p should be modified in unit hydrograph methods of design flood analysis for return periods that differ from those used in deriving unit hydrographs. A simple correction curve has been developed for adjusting t_p according to the design flood return period. Copyright © 2000 John Wiley & Sons, Ltd.     

THREE-TERM TAYLOR SERIES FOR t2 - x2-CURVES OF P- AND S-WAVES OVER LAYERED TRANSVERSELY ISOTROPIC GROUND*

The arrival-time curve of a reflection from a horizontal interface, beneath a homogeneous isotropic layer, is a hyperbola in the x - t-domain. If the subsurface is one-dimensionally inhomogeneous (horizontally layered), or if some or all of the layers are transversely isotropic with vertical axis of symmetry, the statement is no longer strictly true, though the arrival-time curves are still hyperbola-like. In the case of transverse isotropy, however, classical interpretation of these curves fails. Interval velocities calculated from t² - x²-curves do not always approximate vertical velocities and therefore cannot be used to calculate depths of reflectors. To study the relationship between velocities calculated from t² - x²-curves and the true velocities of a transversely isotropic layer, we approximate t² - x²-curves over a vertically inhomogeneous transversely isotropic medium by a three-term Taylor series and calculate expressions for these terms as a function of the elastic parameters. It is shown that both inhomogeneity and transverse isotropy affect slope and curvature of t² - x²-curves. For P-waves the effect of transverse isotropy is that the t² - x²-curves are convex upwards; for SV-waves the curves are convex downwards. For SH-waves transverse isotropy has no effect on curvature.     

FREQUENCY WAVENUMBER APPROACH OF THE τ-p TRANSFORM: SOME APPLICATIONS IN SEISMIC DATA PROCESSING*

The τ-p transform is an invertible transformation of seismic shot records expressed as a function of time and offset into the τ (intercept time) and p (ray parameter) domain. The τ-p transform is derived from the solution of the wave equation for a point source in a three-dimensional, vertically non-homogeneous medium and therefore is a true amplitude process for the assumed model. The main advantage of this transformation is to present a point source shot record as a series of plane wave experiments. The asymptotic expansion of this transformation is found to be useful in reflection seismic data processing. The τ-p and frequency-wavenumber (or f-k) processes are closely related. Indeed, the τ-p process embodies the frequency-wavenumber transformation, so the use of this technique suffers the same limitations as the f-k technique. In particular, the wavefield must be sampled with sufficient spatial density to avoid wavenumber aliasing. The computation of this transform and its inverse transform consists of a two-dimensional Fast Fourier Transform followed by an interpolation, then by an inverse-time Fast Fourier Transform. This technique is extended from a vertically inhomogeneous three-dimensional medium to a vertically and laterally inhomogeneous three-dimensional medium. The τ-p transform may create artifacts (truncation and aliasing effects) which can be reduced by a finer spatial density of geophone groups by a balancing of the seismic data and by a tapering of the extremities of the seismic data. The τ-p domain is used as a temporary domain where the attack of coherent noise is well addressed; this technique can be viewed as ‘time-variant f-k filtering’. In addition, the process of deconvolution and multiple suppression in the τ-p domain is at least as well addressed as in the time-offset domain.     

Receiver function method in reflection seismology

The receiver function method was originally developed to analyse earthquake data recorded by multicomponent (3C) sensors and consists in deconvolving the horizontal component by the vertical component. The deconvolution process removes travel path effects from the source to the base of the target as well as the earthquake source signature. In addition, it provides the possibility of separating the emergent P and PS waves based on adaptive subtraction between recorded components if plane waves of constant ray parameters are considered. The resulting receiver function signal is the local PS wave's impulse response generated at impedance contrasts below the 3C receiver.We propose to adapt this technique to the wide‐angle multi‐component reflection acquisition geometry. We focus on the simplest case of land data reflection acquisition. Our adapted version of the receiver function approach consists in a multi‐step procedure that first removes the P wavefield recorded on the horizontal component and next removes the source signature. The separation step is performed in the τ?p domain while the source designature can be achieved in either the τ?p or the t?x domain. Our technique does not require any a priori knowledge of the subsurface. The resulting receiver function is a pure PS‐wave reflectivity response, which can be used for amplitude versus slowness or offset analysis. Stack of the receiver function leads to a high‐quality S wave image.     

THE INDUCED POLARIZATION RESPONSE OF A THIN HIGHLY-CONDUCTIVE ORE BODY*

Consider a lamina of ore of thickness 2t whose electrical resistivity p₂ is much smaller than the resistivity p₁ of the surrounding host rock. The induced polarization response of such an ore body is investigated under the assumption that it arises from the variation of p₂ with the frequency of measurement. Let p2l and p2h be the resistivities of the ore-body for the low and high frequencies of measurement and L a length of the order of the distance between the transmitting electrodes. A theory is developed under the assumptions that each of the quantities t/L, p2l/p1, p2h/p1, Lp2l/2tp1, and Lp2h/tp1 is small. The main conclusion is that the frequency effect parameter P is given approximately by P=cL(p2l ? p2h)/2tp1, where the constant c is independent of t, p2l, p2h, and p1. Thus for a family of similar ore bodies having differing values of t, P will be the larger the smaller t. Detailed results are given for a semi-infinite submerged dipping dyke and the two dimensional Wenner array.     

Point-source inertial particle dispersion

The dispersion of inertial particles continuously emitted from a point source is analytically investigated in the limit of small but finite inertia. Our focus is on the evolution equation of the particle joint probability density function p(x,?v,?t), x and v being the particle position and velocity, respectively. For arbitrary inertia, position and velocity variables are coupled, with the result that p(x,?v,?t) can be determined by solving a partial differential equation in a 2d-dimensional space, d being the physical-space dimensionality. For small (but nevertheless finite) inertia, (x,?v)-variables decouple and the determination of p(x,?v,?t) is reduced to solve a system of two standard forced advection–diffusion equations in the space variables x. The latter equations are derived here from first principles, i.e., from the well-known Lagrangian evolution equations for position and particle velocity.     

Study of dynamic behaviour of recession curves

Since Brutsaert and Neiber (1977), recession curves are widely used to analyse subsurface systems of river basins by expressing ? dQ/dt as a function of Q, which typically take a power law form: ? dQ/dt = kQ^α, where Q is the discharge at a basin outlet at time t. Traditionally recession flows are modelled by single reservoir models that assume a unique relationship between ? dQ/dt and Q for a basin. However, recent observations indicate that ? dQ/dt ‐ Q relationship of a basin varies greatly across recession events, indicating the limitation of such models. In this study, the dynamic relationship between ? dQ/dt and Q of a basin is investigated through the geomorphological recession flow model which models recession flows by considering the temporal evolution of its active drainage network (the part of the stream network of the basin draining water at time t). Two primary factors responsible for the dynamic relationship are identified: (i) degree of aquifer recharge (ii) spatial variation of rainfall. Degree of aquifer recharge, which is likely to be controlled by (effective) rainfall patterns, influences the power law coefficient, k. It is found that k has correlation with past average streamflow, which confirms the notion that dynamic ? dQ/dt ‐ Q relationship is caused by the degree of aquifer recharge. Spatial variation of rainfall is found to have control on both the exponent, α, and the power law coefficient, k. It is noticed that that even with same α and k, recession curves can be different, possibly due to their different (recession) peak values. This may also happen due to spatial variation of rainfall. Copyright © 2012 John Wiley & Sons, Ltd.     

Modified state–space procedures for pseudodynamic testing

The existing on‐line numerical integration algorithms are derived from the Newmark method, which is based on an approximation of derivatives in the differential equation. The state–space procedure (SSP), based on an interpolation of the discrete excitation signals for piecewise convolution integral, has been confirmed as more reliable than the Newmark method in terms of numerical accuracy and stability. In an attempt to enhance the pseudodynamic test, this study presents an on‐line integration algorithm (referred to as the OS–SSP method) via an integration of the state–space procedure with Nakashima's operator‐splitting concept. Numerical stability and accuracy assessment of the proposed algorithm in addition to the explicit Newmark method and the OS method were investigated via an eigenvalue, frequency‐domain and time‐domain analysis. Of the on‐line integration algorithms investigated, the OS–SSP method is demonstrated as the most accurate method with an acceptable stability (although not unconditionally stable) characteristic. Therefore, the OS–SSP method is the most desirable method for pseudodynamic testing if the numerical stability criterion (Δt/T⩽0.5) is ensured for every vibration mode involved. Copyright © 2001 John Wiley & Sons, Ltd.     

Numerical evaluation of the damping‐solvent extraction method in the frequency domain

The damping‐solvent extraction method for the analysis of unbounded visco‐elastic media is evaluated numerically in the frequency domain in order to investigate the influence of the computational parameters—domain size, amount of artificial damping, and mesh density—on the accuracy of results. An analytical estimate of this influence is presented, and specific questions regarding the influence of the parameters on the results are answered using the analytical estimate and numerical results for two classical problems: the rigid strip and rigid disc footings on a visco‐elastic half‐space with constant hysteretic material damping. As the domain size is increased, the results become more accurate only at lower frequencies, but are essentially unaffected at higher frequencies. Choosing the domain size to ensure that the static stiffness is computed accurately leads to an unnecessarily large domain for analysis at higher frequencies. The results improve by increasing artificial damping but at a slower rate as the total (material plus artificial) damping ratio ζ_t gets closer to 0.866. However, the results do not deteriorate significantly for the larger amounts of artificial damping, suggesting that ζ_t≈0.6 is appropriate; a larger value is not likely to influence the accuracy of results. Presented results do not support the earlier suggestion that similar accuracy can be achieved by a large bounded domain with small damping or by a small domain with larger damping. Copyright © 2002 John Wiley & Sons, Ltd.     

Artificial ground motion compatible with specified peak velocity and target spectrum

In this paper, a method, which synthesizes the artificial ground motion compatible with the specified peak velocity as well as the target acceleration response spectrum, was proposed. In this method, firstly, an initial acceleration time history α8^（0） （t）, which satisfies the prescribed peak ground acceleration, the target spectral acceleration ST（ω, ζ）,and the specified intensity envelope, is generated by the traditional method that generates the requency domain; secondly,α8^（0） （t）is further modulated by superimposing narrow-band time histories upon it in the time domain to make its peak velocity, approach the target peak ground velocity, and at the same time to improve its fitting precision to the target spectrum. Numerical examples show that this algorithm boasts high calculation precisions.     

Seismic anomalies in the aftershock sequence of November 16, 2000, in Papua New Guinea

The study of seismic anomalies, related both to the temporal trend of aftershock sequences and to the temporal series of mainshocks, is important for an understanding of the physical processes relating to the existence and the characteristics of seismic precursors. The purpose of this work is to highlight some methodological aspects related to the observation of possible anomalies in the temporal decay of an aftershock sequence. It is realized by means of several parameters. We focused our work on an analysis of the Papua New Guinea seismic sequence that occurred on November 16, 2000. The magnitude of the mainshock is M = 8.2. The observed temporal series of shocks per day can be considered as a sum of a deterministic contribution and a stochastic contribution. If the decay can be modeled as a nonstationary Poisson process where the intensity function is equal to n(t) = K(t + c)^−p + K ₁, the number of aftershocks in a small time interval Δt is the mean value n(t)Δt, with a standard deviation σ = √n(t)Δt. We observe that there are some variations in seismicity that can be considered as seismic anomalies before the occurrence of a large aftershock. The data, checked according to completeness criteria, come from the website of the USGS NEIC data bank (). The text was submitted by the authors in English.     

Rainfall interception in a lower montane forest in Ecuador: effects of canopy properties

Rainfall interception in forests is influenced by properties of the canopy that tend to vary over small distances. Our objectives were: (i) to determine the variables needed to model the interception loss of the canopy of a lower montane forest in south Ecuador, i.e. the storage capacity of the leaves S and of the trunks and branches S_t, and the fractions of direct throughfall p and stemflow p_t; (ii) to assess the influence of canopy density and epiphyte coverage of trees on the interception of rainfall and subsequent evaporation losses. The study site was located on the eastern slope of the eastern cordillera in the south Ecuadorian Andes at 1900–2000 m above sea level. We monitored incident rainfall, throughfall, and stemflow between April 1998 and April 2001. In 2001, the leaf area index (LAI), inferred from light transmission, and epiphyte coverage was determined. The mean annual incident rainfall at three gauging stations ranged between 2319 and 2561 mm. The mean annual interception loss at five study transects in the forest varied between 591 and 1321 mm, i.e. between 25 and 52% of the incident rainfall. Mean S was estimated at 1·91 mm for relatively dry weeks with a regression model and at 2·46 mm for all weeks with the analytical Gash model; the respective estimates of mean S_t were 0·04 mm and 0·09 mm, of mean p were 0·42 and 0·63, and of mean p_t were 0·003 and 0·012. The LAI ranged from 5·19 to 9·32. Epiphytes, mostly bryophytes, covered up to 80% of the trunk and branch surfaces. The fraction of direct throughfall p and the LAI correlated significantly with interception loss (Pearson's correlation coefficient r = −0·77 and 0·35 respectively, n = 40). Bryophyte and lichen coverage tended to decrease S_t and vascular epiphytes tended to increase it, although there was no significant correlation between epiphyte coverage and interception loss. Our results demonstrate that canopy density influences interception loss but only explains part of the total variation in interception loss. Copyright © 2004 John Wiley & Sons, Ltd.     

Infiltration and runoff generation processes in fire‐affected soils

Post‐wildfire runoff was investigated by combining field measurements and modelling of infiltration into fire‐affected soils to predict time‐to‐start of runoff and peak runoff rate at the plot scale (1 m²). Time series of soil‐water content, rainfall and runoff were measured on a hillslope burned by the 2010 Fourmile Canyon Fire west of Boulder, Colorado during cyclonic and convective rainstorms in the spring and summer of 2011. Some of the field measurements and measured soil physical properties were used to calibrate a one‐dimensional post‐wildfire numerical model, which was then used as a ‘virtual instrument’ to provide estimates of the saturated hydraulic conductivity and high‐resolution (1 mm) estimates of the soil‐water profile and water fluxes within the unsaturated zone. Field and model estimates of the wetting‐front depth indicated that post‐wildfire infiltration was on average confined to shallow depths less than 30 mm. Model estimates of the effective saturated hydraulic conductivity, K_s, near the soil surface ranged from 0.1 to 5.2 mm h^?1. Because of the relatively small values of K_s, the time‐to‐start of runoff (measured from the start of rainfall), t_p, was found to depend only on the initial soil‐water saturation deficit (predicted by the model) and a measured characteristic of the rainfall profile (referred to as the average rainfall acceleration, equal to the initial rate of change in rainfall intensity). An analytical model was developed from the combined results and explained 92–97% of the variance of t_p, and the numerical infiltration model explained 74–91% of the variance of the peak runoff rates. These results are from one burned site, but they strongly suggest that t_p in fire‐affected soils (which often have low values of K_s) is probably controlled more by the storm profile and the initial soil‐water saturation deficit than by soil hydraulic properties. Published 2013. This article is a U.S. Government work and is in the public domain in the USA.     

Combined structure and velocity stacks via the tau–p transform

Reflection and refraction data are normally processed with tools designed to deal specifically with either near- or far-offset data. Furthermore, the refraction data normally require the picking of traveltimes prior to analysis. Here, an automatic processing algorithm has been developed to analyse wide-angle multichannel streamer data without resorting to manual picking or traveltime tomography. Time–offset gathers are transformed to the tau–p domain and the resulting wavefield is downward continued to the depth–p domain from which a velocity model and stacked section are obtained. The algorithm inputs common-depth-point (CDP) gathers and produces a depth-converted stacked section that includes velocity information. The inclusion of long-offset multichannel streamer data within the tau–p transformation enhances the signal from high-velocity refracted basalt arrivals. Downward continuation of the tau–p transformed wavefield to the depth–p domain allows the reflection and refraction components of the wavefield to be treated simultaneously. The high-slowness depth–p wavefield provides the velocity model and the low-slowness depth–p wavefield may be stacked to give structural information. The method is applied to data from the Faeroe Basin from which sub-basalt velocity images are obtained that correlate with an independently derived P-wave model from the line.     

Solute dynamics across the stream‐to‐riparian continuum under different flood waves

To enhance the understanding of solute dynamics within the stream‐to‐riparian continuum during flood event‐driven water fluctuation (i.e., flood wave), a variable saturated groundwater flow and solute transport model were developed and calibrated against in situ measurements of the Inbuk stream, Korea, where seasonal flooding prevails. The solute dynamics were further investigated for flood waves (varying by amplitude [A], duration [T], roundness [r], and skewness [t_p]) that were parameterised by real‐time stream stage fluctuations. We found that the solute transferred faster and farther in the riparian zone, especially within the phreatic zone, above which in the variable saturated zone the concentration required a significantly longer time, particularly at higher altitudes, to return to the initial state. By comparison, solute transferred shallowly in the streambed where the solute plume exhibited an exponential growth trend from the centre to the bank. The dynamic changes of solute flux and mass along the stream–aquifer interface and stream concentration were linked to the shape of flood wave. As the flood wave became higher (A↗), wider (T↗), rounder (r↘), and less skewed (t_p↗), the maximum solute storage in aquifer increased. Maximum stream concentration (C_str?max) not only presented a positive linear relationship with A or t_p but also showed a negative logarithmic trend with increasing T or r. The sensitivity of C_{str_max} to A was approximately two times that of t_p, and between these values, the r was slightly more sensitive than T. C_str?max linearly increased as hydraulic conductivity increased and logarithmically increased as longitudinal dispersivity increased. The former relationship was more sensitive than the latter.     

The motion of magnetic fronts in spiral galaxies

Abstract

We study the nonlinear asymptotic thin disc approximation to the mean field dynamo equations, as applicable to spiral galaxies. The circumstances in which sharp magnetic field structures (fronts) can propagate radially are investigated, and an expression for the speed of propagation derived. We find that the speed of an interior front is proportional to η//R _? (where η is the diffusivity and R_t the galactic radius), whereas an exterior front moves with speed of order , where γ is the local growth rate of the dynamo. Numerical simulations are presented, that agree well with our asymptotic results. Further, we perform numerical experiments using the 'no-z' approximation for thin disc dynamos, and show that the propagation of magnetic fronts in this approximation can also be understood in terms of our asymptotic results.     

CONVERSION POINTS AND TRAVELTIMES OF CONVERTED WAVES IN PARALLEL DIPPING LAYERS1

For converted waves, stacking as well as AVO analysis requires a true common reflection point gather which, in this case, is also a common conversion point (CCP) gather. The coordinates of the conversion points for PS or SP waves, in a single homogeneous layer can be calculated exactly as a function of the offset, the reflector depth and the ratio v_p/v_s. An approximation of the conversion point on a dipping interface as well as for a stack of parallel dipping layers is given. Numerical tests show that the approximation can be used for offsets smaller than the depth of the reflector under consideration. The traveltime of converted waves in horizontal layers can be expanded into a power series. For small offsets a two-term truncation of the series yields a good approximation. This approximation can also be used in the case of dipping reflectors if a correction is applied to the traveltimes. This correction can be calculated from the approximated conversion point coordinates.     

INVERSION METHOD IN THE SLANT STACK DOMAIN USING AMPLITUDES OF REFLECTION ARRIVALS*

Almost all ray-tracing methods ignore the analysis of the amplitudes of seismic arrivals and therefore utilize only half of the available information. We propose a method which is a combination of ray-tracing imaging and transformation of the amplitudes of wide-aperture data. Seismic data in the conventional X-T domain are first transformed to the domain of intercept time τ and ray parameter p to recover the plane wave response. The next step is the derivation of a series of plane wave reflection coefficients, which are mapped as a function of τ and p. The reflection coefficients R(τ, p) for two arbitrarily chosen traces can then be used in our inversion method to derive a slowness-depth and a density-depth profile. It is shown that the inclusion of amplitudes of seismic arrivals (in this method, we consider the acoustic case) makes the inverse method highly stable and accurate. In a horizontally stratified medium one can recover separate profiles of velocity and density. Since this method utilizes large-offset data, it can be used for separate recovery of velocity and density to a greater depth.