Wavefield extrapolation and prestack depth migration in anelastic inhomogeneous media

Wavefield depth extrapolation and prestack depth migration in complex anelastic media are studied. Kjartansson's frequency‐independent Q law is used to describe the absorption of seismic energy. The macromodel used is analogous to the macromodel used for current migration schemes except that an additional frequency‐independent Q macromodel needs to be provided. Absorption in the forward one‐way propagator is introduced by assuming a complex phase velocity, and the inverse one‐way propagator is obtained using the reciprocity theorem for one‐way wavefields in dissipative media. The stability of the inverse propagator is achieved by limiting the angle of propagation of wavefields. A table‐driven explicit operator scheme for imaging complex 2D anelastic media is presented. High‐accuracy, short convolution operators are designed by the weighted least‐squares method, and two kinds of imaging conditions are proposed. Numerical examples of depth extrapolation in laterally varying media, the migration of a spatial impulse with dispersion as well as shot record depth migration demonstrate the potential of the proposed explicit forward operator, the explicit inverse operator and the prestack depth migration scheme, respectively.     

Ecological evaluation of the Cumberland Basin ecosystem model

A holistic ecosystem simulation model has been developed for the Cumberland Basin and upper Chignecto Bay, a turbid macrotidal estuary at the head of the Bay of Fundy. This one-dimensional deterministic model has three compartments, three boundaries and three interacting submodels (physical, pelagic and benthic). Twenty-eight biological state variables represent broad functional groups of organisms and non-living organic carbon pools. All major components of the estuarine ecosystem are included. At the present stage of development, individual pelagic state variables give reasonable annual simulations which are in general agreement with available calibration data. Major problems remain with some benthic state variables, especially the subtidal ones about which little is known. In aggregate, the model performs well and output at the ecosystem level agrees with field observations. In the Cumberland Basin water column, annual community respiration exceeds phytoplankton net production (1–3 g C m⁻³) by a factor of 2–5 suggesting the importance of carbon imported from surrounding saltmarshes and the seaward boundary. Annual community respiration and microalgal net production (28 g C m⁻²) on the other hand are closely balanced in intertidal sediments. Respiration in subtidal sediments is entirely dependent upon sedimented carbon. The model supports the hypothesis that the Cumberland Basin is a heterotrophic ecosystem with low primary production which requires imported organic carbon to support the production and respiration of higher trophic levels.     

Palaeomagnetic constraints on formation of the Mianwali reentrant, Trans-Indus and western Salt Range, Pakistan

Successions of Lower to lower Middle Cambrian, Upper Permian to Upper Triassic and Lower Tertiary carbonates and arenites have been sampled in five sections, representative of the three main segments of the Mianwali reentrant in the (Trans-Indus) Salt Range (northern Pakistan), i.e.: the southern Khisor Range, the northern Surghar Range and the western Salt Range. Comparison of primary and secondary magnetization directions with the Indian APWP demonstrates the secondary origin of the Mianwali reentrant and shows a pattern of rotations which varies in sense and magnitude along the reentrant with the main structural trends. Data from the Trans-Indus and western Salt Range and published Early Cambrian, Early Permian and Late Tertiary palaeomagnetic results from the southern Salt Range and the Potwar Plateau show that the Hazara Arc underwent a 20–45° counterclockwise rotation relative to the Indian Shield. A contrasting clockwise rotation over about 45° has recently been established for thrust sheets in the opposing eastern limb of the Western Himalayan Syntaxis, i.e. for the Panjal Nappe [1] and the Riasi thrust sheet [2]. These palaeomagnetically established rotations conform with the about 75° azimuthal change in structural trend along the Syntaxis, and support Crawford's [3] suggestion that the Salt Range was originally in line with the northwestern Himalaya. The Salt Range front prograded and moved southwards as part of the Hazara Arc thrust sheet, detached from basement along the evaporitic Salt Range Formation. The Mianwali reentrant originated through obstruction of the southwards advancing thrust sheet by moulding around basement topography of the northwest oriented Sarghoda Ridge.     

Transforming identity discourses to promote local interests during municipal amalgamations

This paper discusses the different ways in which local identities are used in two Dutch municipalities. Like all local administrations these Dutch municipalities have to deal with external forces by plotting their own course between closing-off and opening-up. Local identities are used not only for resisting external threats like municipal amalgamations, but also to attract external resources. It proved useful to distinguish between primary identity discourses based on the widely recognised dominant characteristics of the local community, and secondary identity discourses based on how communities within a municipality have over time learned to deal with these different primary local identities. During an amalgamation this secondary identity discourse disappears with the old municipality. The disappearance of the protective shield of a secondary identity discourse can threaten the underlying primary local identities, and can bring local identities into the centre of the local political debate. A perceived external threat frequently changes the character of these local identities. They can become more inward oriented, focus more on their historical roots and their differences with others; they ‘thicken’ into resistance identity discourses. In other cases the secondary identity discourse of a municipality is too weak and indistinct to support the primary local identities of its communities. Municipal amalgamation can then help to promote a new more attractive secondary, ‘thin’ regional identity discourse based on a selection of characteristics used in established primary local identity discourses.     

A Comparison of Strategies for Seismic Interferometry

The extraction of the response from field fluctuations excited by random sources has received considerable attention in a variety of different fields. We present three methods for the extraction of the systems response that are based on cross-correlation, deconvolution, and the solution of an integral equation, respectively. For systems that are invariant for time-reversal the correlation method requires random sources on a bounding surface only, but when time-reversal invariance is broken, for example by attenuation, a volume distribution of sources is needed. For this reason the correlation method is not useful for diffusive or strongly attenuating systems. We provide examples of the three methods and compare their merits and drawbacks. We show that the extracted field may satisfy different boundary conditions than does the physical field. This can be used, for example, to suppress surface-related multiples in exploration seismology, to study the coupling of buildings to the subsurface, and to remove the airwave in controlled source electromagnetics (CSEM).     

Modeling time series of ground water head fluctuations subjected to multiple stresses

The methods behind the predefined impulse response function in continuous time (PIRFICT) time series model are extended to cover more complex situations where multiple stresses influence ground water head fluctuations simultaneously. In comparison to autoregressive moving average (ARMA) time series models, the PIRFICT model is optimized for use on hydrologic problems. The objective of the paper is twofold. First, an approach is presented for handling multiple stresses in the model. Each stress has a specific parametric impulse response function. Appropriate impulse response functions for other stresses than precipitation are derived from analytical solutions of elementary hydrogeological problems. Furthermore, different stresses do not need to be connected in parallel in the model, as is the standard procedure in ARMA models. Second, general procedures are presented for modeling and interpretation of the results. The multiple-input PIRFICT model is applied to two real cases. In the first one, it is shown that this model can effectively decompose series of ground water head fluctuations into partial series, each representing the influence of an individual stress. The second application handles multiple observation wells. It is shown that elementary physical knowledge and the spatial coherence in the results of multiple wells in an area may be used to interpret and check the plausibility of the results. The methods presented can be used regardless of the hydrogeological setting. They are implemented in a computer package named Menyanthes (www.menyanthes.nl).     

Seismic reflection coefficients of faults at low frequencies: a model study

We use linear slip theory to evaluate seismic reflections at non‐welded interfaces, such as faults or fractures, sandwiched between general anisotropic media and show that at low frequencies the real parts of the reflection coefficients can be approximated by the responses of equivalent welded interfaces, whereas the imaginary parts can be related directly to the interface compliances. The imaginary parts of low frequency seismic reflection coefficients at fault zones can be used to estimate the interface compliances, which can be related to fault properties upon using a fault model. At normal incidence the expressions uncouple and the complex‐valued P‐wave reflection coefficient can be related linearly to the normal compliance. As the normal compliance is highly sensitive to the infill of the interface, it can be used for gas/fluid identification in the fault plane. Alternatively, the tangential compliance of a fault can be estimated from the complex‐valued S‐wave reflection coefficient. The tangential compliance can provide information on the crack density in a fault zone. Coupling compliances can be identified and quantified by the observation of PS conversion at normal incidence, with a comparable linear relationship.     

Review paper: Virtual sources and their responses,Part II: data‐driven single‐sided focusing

In Part I of this paper, we defined a focusing wave field as the time reversal of an observed point‐source response. We showed that emitting a time‐reversed field from a closed boundary yields a focal spot that acts as an isotropic virtual source. However, when emitting the field from an open boundary, the virtual source is highly directional and significant artefacts occur related to multiple scattering. The aim of this paper is to discuss a focusing wave field, which, when emitted into the medium from an open boundary, yields an isotropic virtual source and does not give rise to artefacts. We start the discussion from a horizontally layered medium and introduce the single‐sided focusing wave field in an intuitive way as an inverse filter. Next, we discuss single‐sided focusing in two‐dimensional and three‐dimensional inhomogeneous media and support the discussion with mathematical derivations. The focusing functions needed for single‐sided focusing can be retrieved from the single‐sided reflection response and an estimate of the direct arrivals between the focal point and the accessible boundary. The focal spot, obtained with this single‐sided data‐driven focusing method, acts as an isotropic virtual source, similar to that obtained by emitting a time‐reversed point‐source response from a closed boundary.     

Review paper: Virtual sources and their responses,Part I: time‐reversal acoustics and seismic interferometry

A focusing acoustic wave field, emitted into a medium from its boundary, converges to a focal spot around the designated focal point. Subsequently, the focused field acts as a virtual source that emits a field propagating away from the focal point, mimicking the response to a real source at the position of the focal point. In this first part of a two‐part review paper on virtual sources and their responses, we define the focusing wave field as the time reversal of an observed point‐source response. This approach underlies time‐reversal acoustics and seismic interferometry. We analyse the propagation of a time‐reversed point‐source response through an inhomogeneous medium, paying particular attention to the effect of internal multiples. We investigate the differences between emitting the focusing field from a closed boundary and from an open boundary, and we analyse in detail the properties of the virtual source. Whereas emitting the time‐reversed field from a closed boundary yields an accurate isotropic virtual source, emitting the field from an open boundary leads to a highly directional virtual source and significant artefacts related to multiple scattering. The latter problems are addressed in Part II, where we define the focusing wave field as an inverse filter that accounts for primaries and multiples.