De Hoop Research Articles

Patterns of endemism in the limestone flora of South African lowland fynbos

Taxonomie and biological aspects of endemism and Red Data Book status were studied amongst the limestone endemics of the lowland fynbos in the Cape Floristic Region, South Africa. Of the 110 limestone endemics, 1.8% are widely distributed in the Cape Floristic Region and 56.4% are regional endemics. Relative to flora of non-limestone lowland fynbos (n=538 species), the families which were overrepresented in terms of limestone endemics included the Ericaceae, Fabaceae, Polygalaceae, Rutaceae and Sterculiaceae. The Restionaceae was the only underrepresented family. The local limestone endemics were not significantly different from regional endemics in terms of their biological attributes. An analysis of the frequency of the biological traits associated with the limestone-endemic flora established a biological profile for a limestone endemic: a dwarf-to-low shrub with soil-stored seeds which are ant or wind dispersed. In terms of the species richness of limestone endemics, the De Hoop Nature Reserve was the ‘hotspot’ within the region. Relative to the total species richness, the Hagelkraal and Stilbaai areas contained higher-than-predicted numbers of rare species. These areas require urgent attention if the unique floral diversity associated with limestone substrata within the Bredasdorp-Riversdale centre of endemism is to be conserved.

Lamb’s problem for an anisotropic half-space studied by the Cagniard de Hoop method

The 3-D Green’s tensor is obtained for an anisotropic half-space, by using the Cagniard-de Hoop method. Some numerical results of the normal displacement field component are outlined for the cases of cubic and hexagonal symmetries. The novelty of the present approach deals with the fact that the diffraction effects related to the free surface are taken into account. The numerical method, which has been used, shows up, for instance, the diffraction of the head waves.

Modeling space-time domain acoustic wave fields in media with attenuation: The symbolic manipulation approach

A method is presented for the determination of the space-time domain acoustic wave field, and in particular the space-time domain Green’s function, in homogeneous, isotropic, lossy equivalent fluid media that represent solids with a complicated viscoelastic behavior. The loss properties of the equivalent fluids are modeled with the aid of arbitrarily intricate compliance memory functions and, eventually, inertia memory functions. The presented integral transformation-type method consists of three steps. First, a temporal Laplace transformation and a horizontal spatial Fourier transformation are performed. Due to the application of the temporal Laplace transformation, causality of the acoustic wave field is automatically dealt with. Second, the resulting transform domain problem is solved using a convergent Neumann series solution. Analytical expressions for the terms of this Neumann series solution are obtained by means of a recurrence scheme that can ideally be evaluated with the aid of symbolic manipulation. Third, the transformation back to the space-time domain is performed analytically using the Cagniard–De Hoop method. No numerically imposed limitation of the bandwidth of the wave field quantities or the Green’s function shows up. In principle, the method offers the possibility of generating space-time domain results, both for the acoustic wave field and the Green’s function, for any time instant with any desired degree of accuracy. After deriving the general theory, numerical results for several lossy equivalent fluids with an almost constant-Q behavior, as shown by many types of rock, are presented.

Dynamic Response of A Half-Space to A Buried Spherical Source

SUMMARY The dynamic response of an elastic half-space due to a buried spherical source is investigated for points on the surface of the half-space. an analytical model for the spherical source is obtained by modifying the point source theory of de Hoop for a source pressure function of the form P(t)=p0tn exp(-αt). However, since any point source cannot involve reflections from the source itself, our model is only an approximation to the real case which must involve reflections from the boundary of the spherical source itself. the present treatment is also cast in a scale-independent form in order to generalize the application. A comparison of our analytical model with the results of dynamic finite-element modelling (DFEM) shows excellent agreement for deep sources. However, for near-surface sources the tails of the waveforms are quite different, although the agreement for the peak amplitudes is good. This waveform discrepancy is due to reflection from the boundary of the spherical source itself; this boundary is naturally present in the DFEM solution. Furthermore, if reflections from the source boundary are neglected, the displacement directly above a near-surface source is, to a good approximation, directly proportional to the source pressure function. On the other hand, the displacement directly above a deep source is, to a good approximation, directly proportional to the first derivative of the source pressure function.

Transient acoustic wave fields in continuously layered fluids with attenuation

The space-time domain acoustic wave field in an isotropic, lossy, continuously layered fluid is analyzed using a method that employs a combination of higher-order WKBJ asymptotics and the Cagniard–De Hoop method of inversion. The loss behavior of the fluid is described with the aid of general temporal compliance and inertia memory functions. The continuous layering of the medium manifests itself in the acoustic wave speed, the density of mass, and both memory functions, which are independent, continuous functions of the vertical coordinate. After the application of forward transformations, higher-order WKBJ asymptotic representations of the transform domain solution are derived. The coefficients that occur in these representations satisfy a recurrence scheme, which is well suited for implementation in a symbolic manipulation program. The transform domain WKBJ asymptotic representations are analytically transformed back to the space-time domain with the aid of the Cagniard–De Hoop method. Numerical results for several configurations with an intricate loss behavior are presented.

Calculation of the transient acoustic wave field emitted by a focused transducer with an arbitrary rim

Closed-form analytic expressions are derived for the transient acoustic wave field emitted by a focused transducer with an arbitrary rim. The radiating part of the transducer is a spherical surface bounded by a simply connected closed curve of arbitrary shape. Starting from the Kirchhoff–Huygens representation of the emitted acoustic wave field, the expression for the acoustic pressure is transformed into a line integral along the rim of the transducer by employing the Maggi–Rubinowicz transformation in the Kirchhoff theory of diffraction by a black screen. The resulting line integral for the transient acoustic pressure is evaluated numerically to study the shape of the beam emitted by the transducer in its dependence on the shape of the rim and to analyze the resolving power of the transducer in ultrasonic applications. For a focused transducer with a circular rim, a closed-form analytic expression is derived for the transient acoustic pressure on its axis. These results serve as a check on the numerical results obtained for the more general cases. For all cases, the acoustic pressure at the focus admits a closed-form analytic representation. [Adrianus T. de Hoop performed this research as a Visiting Scientist with Schlumberger-Doll Research, Ridgefield, CT.]

A discrete wavenumber and normal-mode superposition method for synthetic seismograms

Abstract A discrete wavenumber and normal-mode superposition method for synthetic seismograms is presented. This method is based on representing the solution of an elastic layered medium in the form of a discrete wavenumber series for the normal modes obtained by the finite-element technique. A rigid basement is added to the bottom of the layered structure to obtain normal modes. Causality arguments are used to define time windows for which the responses are not affected by the rigid basement. A comparison is made between the solutions of the present method and those of the Cagniard de Hoop method, DWFE, by Olson et al. (1984) and the locked mode approximation by Harvey (1981).

Variation in Dispersal of Galjoen (Coracinus capensis) (Teleostei: Coracinidae) from a Marine Reserve

The dispersal of the surf-zone teleost galjoen (Coracinus capensis) from the De Hoop Marine Reserve, South Africa, was investigated. Over a period of 5.5 yr, 11 022 galjoen were tagged in the centre of the reserve. Most of the 1008 recoveries were at the site of release, while the remainder covered a distance of up to 1040 km. There was no difference with respect to age, sex, or season between those that dispersed and those that did not. Six models were developed to test the hypotheses that (1) galjoen are polymorphic with respect to dispersal behaviour, (2) nonreporting of tags masks a random dispersal process, and (3) the recovery distribution is the result of unequal movement rates in different areas. It is inferred from the likelihoods of the various models that the tagged population was polymorphic, with fish displaying either resident or nomadic behaviour. This conclusion is unaffected by a large uncertainty in the extent of nonreporting of recoveries, or by spatial variability of movement rates. The estimate of emigration from the reserve implies that the unharvested reserve population is restocking adjacent exploited areas with adult fish.

Space-time domain acoustic wave fields in media with attenuation: An analysis based on the symbolic manipulation approach

A method is presented for the determination of the space-time domain acoustic wave field, and in particular the space-time domain Green’s function, in homogeneous, isotropic equivalent fluid media that represent materials with a complicated viscoelastic behavior. The viscoelastic properties are modeled with the aid of arbitrarily intricate compliance memory functions, and the inertia behavior of the media is allowed to show memory effects as well. The presented integral transformation-type method consists of the transform domain Neumann series solution or WKBJ iterative solution, and the Cagniard–De Hoop method of inverse transformation. Analysis of the terms of the Newmann series solution yields a recurrence scheme that can ideally be evaluated using symbolic manipulation. Application of the Cagniard–De Hoop method results in an analytical transformation back to the space-time domain, which makes the method computationally fast. After explaining the theory, numerical results for several lossy media with an almost constant-Q behavior, like many types of rock, are presented. It is shown that it is sufficient to take into account only a few terms of the Newmann series solution to obtain accurate results, even for media with high losses.

Génération d'ondes acoustiques dans un milieu anisotrope par impact laser

The Lamb's problem for an elastic, anisotropic and homogeneous half space is solved. The source is linear and contains in the free surface of this half space. A numerical calculation based on the Cagniard de Hoop method is performed, in the case of cubic symmetry. The free surface is parallel to a plane of symmetry. In addition, the line source may be parallel, or not, to an axis of symmetry. The displacement field is then calculated at any point of this half space, for various directions of this line source. This theoretical study may be applied to the generation of acoustic waves when using a laser beam focused by a cylindrical lens on a sample. The impact is then linear

DIFFRACTION BY A WEDGE IN AN ACOUSTIC CONSTANT DENSITY MEDIUM1

AbstractA new method is presented for solving the 2D problem of diffraction of a plane wave by a wedge of arbitrary angle in a purely acoustic, constant‐density medium with different constant compressional wave speeds inside and outside the wedge. The diffraction problem is formulated as integral equations, and a wavenumber–frequency representation of the scattered field is obtained. With the aid of the Cagniard–de Hoop method, exact analytical expressions in the space–time domain are obtained for the different wave constituents, i.e. geometric optical scattered waves and edge diffracted waves including head waves. These expressions can be computed to any degree of accuracy within reasonable computation times on a computer, and the semi‐analytical method of solution presented thus constitutes a means of constructing reference solutions for wedge configurations. Such highly accurate reference solutions are of importance for verification of results that include diffraction phenomena modelled by general numerical approximate methods, e.g. finite differences, finite elements and spectral methods. Examples of such applications of the method of solution are given.

Performance analysis of transient acoustic wave modeling using higher‐order WKBJ asymptotics and symbolical manipulation

The method of modeling transient acoustic waves in continuously layered media using a combination of higher‐order WKBJ asymptotic representations and the Cagniard–De Hoop method is addressed. The coefficients of the WKBJ asymptotic representations satisfy a recurrence scheme, which is easily dealt with by applying symbolical manipulation. Moreover, an efficient use of the Cagniard–De Hoop method of inversion is achieved [M. D. Verweij, J. Acoust. Soc. Am. 92, 2223–2238 (1992)]. The performance of this method is discussed on the basis of numerical results for a series of configurations. In particular it is shown how the method performs if transcendental parameter profile functions are replaced by least‐square‐fit polynomials. From the results it is concluded that the method performs best for low‐order polynomial parameter profiles.

The distribution, seasonality and trends in abundance of southern right whalesEubalaena australisoff De Hoop Nature Reserve, South Africa

Between September 1984 and January 1993, monthly counts of southern right whales were made from up to four vantage points in the De Hoop Nature Reserve, South Africa. Evidence from aerial surveys indicates that these vantage points are well situated in relation to the main concentration of right whales off De Hoop. Right whales arrive in June, reach peak abundance in September and depart in December or January. The incidence of calves increases from zero in June to 15–22% between August and October (reflecting the season of births), before increasing again to 33% in November and 42% in December (reflecting the earlier departure of animals without calves). The numbers of right whales seen off De Hoop on aerial surveys from 1971 to 1992 have increased at a rate faster than that of the inshore population as a whole, indicating a degree of net immigration into the area. The rate of this immigration may have slowed down during the past 10 years. Shore counts for adults show a positive correlation with aerial c...

Shore-angling catches in the De Hoop Nature Reserve, South Africa, and further evidence for the protective value of marine reserves

Data on the species composition, size, seasonality and capture rates of surf-zone fish sampled by shore-angling at two sites in the De Hoop Marine Reserve are presented. In all, 21 969 fish of 33 species were caught during 11 344 angler-hours of effort. The overall catch rates were 163 and 233 fish·100h−1 at Koppie Alleen and Lekkerwater respectively. Coracinus capensis (57%N) and Diplodus sargus (33%N) were the most frequently captured species and four others (Lithognathus lithognathus, D. cervinus, Umbrina canariensis and Rhabdosargus holubi) each contributed >1% of the combined catch. Catch rates of most species varied seasonally, the overall catch rate being high (175–215 fish·100h−1) between March and November and lower (135-150 fish-100h−1) during summer. Differences in the species composition of catches, catch rates and seasonality at the two sampling sites are attributed to differences in the seasonal distribution of sampling effort and exploitation histories. Despite the fact that comparisons with other angling catch data from around southern Africa are complicated by a number of factors, a clear relationship between catch per unit effort and degree of exploitation is evident, suggesting that abundance of angling fish is particularly sensitive to exploitation and that marine reserves are a viable management option.

Aerial photogrammetry of southern right whales, Eubalaena australis

Between July or August and November 1988 and 1989, 72 cow‐calf pairs of right whales (Eubalaena australis) were measured photogrammetrically from the air off De Hoop, South Africa. Median coefficients of variation ranged from 1.29 to 4.56%, being lowest in cows and calves for measurements of total length. Fifty‐seven adult cows measured from 12.37 to 15.54 m in length, with females photographed for the first time with a calf (= primiparous) being smaller than females that had been seen for the first time with a calf at least five years previously. The lengths of 72 calves ranged from 4.53 to 9.24 m, with those from primiparous females being significantly smaller than calves of multiparous females in every month except July. For 37 calves photographed on more than one occasion the growth rate averaged 2.8±0.7 cm per day, with no significant difference between growth rates of calves from primiparous and from other females, and no significant decrease in growth rate between July/September and September/November. Calves grew from an average of 40% of their mother's length in late July to 51% by mid‐October. The size distribution of the adult females was no different from that of 25 adult females landed at South African whaling stations between 1911 and 1963 (after adjustment for possible differences in measurement techniques). Five near‐term foetuses recovered in June‐August in the same whaling operations also agree closely with the size of calves predicted for 1 August. In a comparison with 17 calves stranded or dying accidentally on the South African coast, most of the accidentally caught animals agreed closely in size with the sample of photogrammetrically measured animals, while most of the stranded animals were equal to or smaller in size than the smallest length interval in the photogrammetrically measured animals. The calves of primiparous females may therefore suffer a higher natural mortality rate than those of multiparous females.

Transient acoustic wave modeling: Higher-order Wentzel–Kramers–Brillouin–Jeffreys asymptotics and symbolic manipulation

A combination of Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) asymptotics and the Cagniard–De Hoop method is used to determine the space-time domain acoustic wave field in a continuously horizontally layered configuration. First, a Laplace transformation with real and positive transform parameter is applied with respect to the time coordinate, followed by a two-dimensional Fourier transformation with respect to the horizontal coordinates. Using the integral equations of the resulting transform domain problem, a recurrence scheme is derived for the coefficients of the WKBJ asymptotic expansions of the transform domain solutions. This scheme is well-suited for implementation in a symbolical manipulation program. The transformation of the resulting higher-order WKBJ asymptotic representations back to the space-time domain is performed with the aid of the Cagniard–De Hoop method, which is particularly efficient in this case. If both the source and the receiver are located in one homogeneous half-space of the configuration, the Cagniard–De Hoop method allows for an almost completely analytical transformation back to the space-time domain. For various configurations numerical results are presented, which show that the method is valid for instants ranging up to several times the arrival time.

Analytical elements of time domain bem for two-dimensional scalar wave problems

An accurate and efficient time domain BEM for 2-D scalar wave problems is presented. Emphasis is on developing analytical boundary elements (explicit solutions of the element matrices). The solutions are obtained under the condition of straight line elements and by bringing the problem to a simple and genral form of double convolution equation which is then solved by the Cagniard–De Hoop method. Six kinds of elements for any combination of the spatial interpolation functions of order 0, 1, 2 with the temporal interpolation functions of order 0, 1 are given in a compact form. It is pointed out that if the order of temporal interpolation function is higher than 1, or if the continuity of velocity or acceleration is required, the time-stepping technique will face difficulty. A method to solve this problem is also presented. Advantages of using the analytical elements instead of a numerical integral procedure are apparent. Problems with such things as singular integrals, accuracy and stability are solved. Methodology and solutions are demonstrated by a comparative study of two example problems. Numerical solutions reveal that the computation is efficient, accurate and stable.

Transient acoustic wave modeling with higher-order WKBJ asymptotic expansions and symbolic manipulation.

A combination of the WKBJ asymptotic expansion and the Cagniard–De Hoop method is used to determine the total space-time domain acoustic wave field in a continuously layered configuration. In the transform domain, a recurrence scheme for the coefficients of the WKBJ asymptotic expansion is derived from the integral equations of the problem. This scheme is well suited for implementation in a symbolical manipulation program, e.g., Mathematica. The WKBJ asymptotic expansion is transformed back to the space-time domain by applying the Cagniard–De Hoop method in a particularly efficient way. For various configurations numerical results are presented, which show that the presented approach yields accurate results for instants ranging up to many times the arrival time.

TRENDS IN THE INSHORE RIGHT WHALE POPULATION OFF SOUTH AFRICA, 1969–1987

AbstractResults of annual aerial surveys of the right whale population along the southern coast of South Africa from 1971 to 1987 are analysed. About 91.5% of cows with calves and 82% of unaccompanied adults on the South African coast in spring are found within the standard survey area, with some indications that the range is expanding up the west coast. In the nearshore region, most right whales (90%) are found within 1.85 km, and all cows with calves within 0.93 km, of the coast. Within the standard survey area, specific areas of concentration can be predictably identified, both for cows with calves and unaccompanied adults. Although total counts (and counts expressed per hour flown) have increased overall, by a best estimate of 6.8% (95% CL 4.6, 9.0) per year from 1971 to 1987, some concentration areas for both classes have failed to show an increase over the same time period. Photographic flights since 1979 have permitted the movements of individually identified adult females to be monitored between successive calves. In at least one concentration area for which no overall increase between 1971 and 1987 was apparent (Mossel Bay), a large net emigration rate was found, nearly all of which involved a shift to the main nursery area to the west, off De Hoop. Reasons for the dissimilar dynamics of different concentration areas are not yet known.

The seaweeds of De Hoop Nature Reserve and their phytogeographical significance

Detailed collections of the seaweeds of De Hoop Nature Reserve have produced a list of 126 taxa (12 Chlorophyta, 23 Phaeophyta, 91 Rhodophyta). The reserve is in a poorly collected area immediately to the east of a major marine biogeographic discontinuity around Cape Agulhas. An analysis of the southern African distributions of these species reveals that they have predominantly warm-water affinities, with the majority of the species occurring throughout the south coast marine province, and 40% occurring east of Durban in true tropical waters. Very few of the De Hoop species (18%) grow on the west coast proper, despite the geographic proximity. These distribution patterns are explained by a consideration of the changes in ambient sea temperatures in the region.