SH Wave Propagation in Viscoelastic Media

When comparing solutions for the propagation of SH waves in plane parallel layered elastic and viscoelastic (anelastic) media, one of the first things that becomes apparent is that in the elastic case the location of the saddle points required to obtain a high frequency approximation are located on the real p axis. This is true of the branch points also. In a viscoelastic medium this is not typical. The saddle point corresponding to an arrival lies in the first quadrant of the complex p-plane as do the branch points. Additionally, in the elastic case the saddle point and branch points lie on a straight line drawn through the origin (the positive real axis in the complex p-plane), while in the viscoelastic case this is generally not the case and the saddle point and branch points lie in such a manner as to indicate the degree of their complex values.In this paper simple SH reflected and transmitted particle displacement arrivals due to a point torque source at the surface in a viscoelastic medium composed of a layer over a half space will be considered. The path of steepest descent defining the saddle point in the first quadrant will be parameterized in terms of a real variable and the high frequency solutions and intermediate analytic results obtained will be used to formulate more specific constraints and observations regarding saddle point location relative to branch point locations in the complex p-plane.As saddle point determination for an arrival is, in general, the solution of a non-linear equation in two unknowns (the real and imaginary parts of the complex saddle point p ₀), which must be solved numerically, the use of analytical methods for investigating this problem type is somewhat limited.Numerical experimentation using well documented solution methods, such as Newton's method, was undertaken and some observations were made. Although fairly basic, they did provide for the design of algorithms for the computation of synthetic traces that displayed more efficient convergence and accuracy than those previously employed. This was the primary motivation for this work and the results from the SH problem may be used with minimal modifications to address the more complicated subject of coupled P-SV wave propagation in viscoelastic media.Another reason for revisiting a problem that has received some attention in the literature was to approach it in a fairly comprehensive manner so that a number of specific observations may be made regarding the location of the saddle point in the complex p-plane and to incorporate these into computer software. These have been found to result in more efficient algorithms for the SH wave propagation and a significant enhancement of the comparable software in the P-SV problem.     

Recovery of the one and two dimensional windfields from chemical constituent observations using the constituent transport equation and an extended Kalman filter

Summary The recovery of windfields from chemical constituents is a difficult, but potentially rewarding inverse problem. Advanced data assimilation methods, such as the extended Kalman filter, are theoretically capable of performing this task; but, at this time, little work has been undertaken. Daley (1994) constructed a one-dimensional extended Kalman filter (EKF) system to examine this problem. This work is extended here to include a more systematic examination of the one-dimensional case, together with experiments with non-divergent two-dimensional flow. The emphasis is on determining when wind recovery is likely to be successful or unsuccessful.It was found that wind recovery is most successful with the EKF for constituent observations which are dense, frequent and accurate. Wind recovery is difficult or slow for the EKF (or any other procedure) when the true constituent time-tendency is small. This happens when the constituent spatial gradient is small, the true windspeeds are low or the stream-function and constituent fields are highly correlated. Wind recovery can also be difficult with constituent transport models which are highly damped, have significant phase errors or restrictive CFL criteria. Steady winds cannot be recovered inside data voids, although time-dependent winds may be recoverable. If constituent observations are too infrequent, estimates of the constituent time-tendency will be poor, and wind recovery (at least for the EKF) problematic.With 15 Figures     

Rhomboidal versus triangular spherical harmonic truncation: Some verification statistics

Abstract

In the construction of global primitive equation models, based on the spherical harmonic method, two forms of truncation are in general use. Theoretical considerations suggest the triangular truncation method is superior, but the easily coded rhomboidal truncation is more commonly used. A verification experiment employing the Canadian Operational Spectral Model has been performed to determine if the theoretical superiority of the triangular truncation can be realized in practice. It was found that at least in the restricted case of extra‐tropical forecasts of less than 48 h, that the two truncation methods produced forecasts of equivalent accuracy.     

Data assimilation with a barotropically unstable shallow water system using representer algorithms

The cycling representer algorithm of Xu and Daley (2000) is a weak constraint four-dimensional variational data assimilation algorithm. It was successfully applied to a one-dimensional transport problem and was able to successfully extract the signal from noisy and sparse observations. The algorithm, however, has not previously been applied to a multivariate, multidimensional system with dynamic instability. The algorithm is also very computationally demanding and awaits considerable enhancement in computer power before being practical for operational forecast models. We have two objectives in this paper. The first is to apply the cycling representer algorithm to a two-dimensional, multivariate barotropically unstable linear shallow water system. The second objective is to formulate and test an accelerated representer algorithm that is much more computationally tractable than the cycling representer algorithm itself. A linear shallow water system with a barotropically unstable basic state was used as a test bed to conduct data assimilation experiments. The evolution of a 'neutral' eastward-propagating singular vector was selected as the 'truth', against which all data assimilation experiments were to be evaluated. The results indicated that the cycling representer algorithm was capable of providing satisfying state estimates for a multivariate, multidimensional system. The results from the accelerated representer algorithm were very encouraging because it is sufficiently computationally tractable to be used on present day multi-processor machines for operational applications.     

Short‐term forecasting with a multi‐level spectral primitive equation model part I ‐ model formulation

A global baroclinic primitive equation model using the spectral technique has been constructed for short‐ and medium‐range numerical weather prediction. The spectral technique, which is a special case of the Galerkin method, employs spherical harmonic basis functions in the evaluation of all horizontal derivatives. The use of a transform technique allows all the horizontal operations to be performed efficiently and allows physical processes to be evaluated in real space. The model employs a semi‐implicit algorithm for time integration and finite differencing in the vertical. Physical processes include orography, moist convection, large scale precipitation and boundary layer processes.     

HF radio marine telex

The system of maritime mobile communications utilizing HF radio narrow-band direct-printing telegraph (HF marine telex) is expected to see expanded use during the next several years. Experience has shown the necessity for the system to embody both automatic error correction techniques and effective means of selective calling. Use of SITOR error correction has demonstrated that error rates in the order of10^{-5}is a realistic expectation. Two selective calling methods, the sequential single frequency code (SSFC) and the digital selective calling (SELCAL), have been adopted internationally, although the latter is still subject to final definition of technical characteristics. HF marine telex avoids most of the problems encountered with manual Morse radiotelegraph. It is tried and proven, efficient and economical. Equipment is readily available. Indications are for a rapid expansion of this system's use.     

Field testing of modular borehole monitoring with simultaneous distributed acoustic sensing and geophone vertical seismic profiles at Citronelle,Alabama

A modular borehole monitoring concept has been implemented to provide a suite of well‐based monitoring tools that can be deployed cost effectively in a flexible and robust package. The initial modular borehole monitoring system was deployed as part of a CO₂ injection test operated by the Southeast Regional Carbon Sequestration Partnership near Citronelle, Alabama. The Citronelle modular monitoring system transmits electrical power and signals, fibre‐optic light pulses, and fluids between the surface and a reservoir. Additionally, a separate multi‐conductor tubing‐encapsulated line was used for borehole geophones, including a specialized clamp for casing clamping with tubing deployment. The deployment of geophones and fibre‐optic cables allowed comparison testing of distributed acoustic sensing. We designed a large source effort (>64 sweeps per source point) to test fibre‐optic vertical seismic profile and acquired data in 2013. The native measurement in the specific distributed acoustic sensing unit used (an iDAS from Silixa Ltd) is described as a localized strain rate. Following a processing flow of adaptive noise reduction and rebalancing the signal to dimensionless strain, improvement from repeated stacking of the source was observed. Conversion of the rebalanced strain signal to equivalent velocity units, via a scaling by local apparent velocity, allows quantitative comparison of distributed acoustic sensing and geophone data in units of velocity. We see a very good match of uncorrelated time series in both amplitude and phase, demonstrating that velocity‐converted distributed acoustic sensing data can be analyzed equivalent to vertical geophones. We show that distributed acoustic sensing data, when averaged over an interval comparable to typical geophone spacing, can obtain signal‐to‐noise ratios of 18 dB to 24 dB below clamped geophones, a result that is variable with noise spectral amplitude because the noise characteristics are not identical. With vertical seismic profile processing, we demonstrate the effectiveness of downgoing deconvolution from the large spatial sampling of distributed acoustic sensing data, along with improved upgoing reflection quality. We conclude that the extra source effort currently needed for tubing‐deployed distributed acoustic sensing vertical seismic profile, as part of a modular monitoring system, is well compensated by the extra spatial sampling and lower deployment cost as compared with conventional borehole geophones.     

Statistical testing of a new testate amoeba‐based transfer function for water‐table depth reconstruction on ombrotrophic peatlands in north‐eastern Canada and Maine,United States

Proxy reconstructions of climatic parameters developed using transfer functions are central to the testing of many palaeoclimatic hypotheses on Holocene timescales. However, recent work shows that the mathematical models underpinning many existing transfer functions are susceptible to spatial autocorrelation, clustered training set design and the uneven sampling of environmental gradients. This may result in over‐optimistic performance statistics or, in extreme cases, a lack of predictive power. A new testate amoeba‐based transfer function is presented that fully incorporates the new recommended statistical tests to address these issues. Leave‐one‐out cross‐validation, the most commonly applied method in recent studies to assess model performance, produced over‐optimistic performance statistics for all models tested. However, the preferred model, developed using weighted averaging with tolerance downweighting, retained a predictive capacity equivalent to other published models even when less optimistic performance statistics were chosen. Application of the new statistical tests in the development of transfer functions provides a more thorough assessment of performance and greater confidence in reconstructions based on them. Only when the wider research community have sufficient confidence in transfer function‐based proxy reconstructions will they be commonly used in data comparison and palaeoclimate modelling studies of broader scientific relevance. Copyright © 2012 John Wiley & Sons, Ltd.