parasupercoherent states and color supergroups parabosonic coherent states are illustrated from the displacement operator point of view such a construction requires the use of the green cusson ansatze a specific representation of parastatistics leading to color supergroups a comparison with a previous result is shown through the annihilation operator and the minimum uncertainty contexts the extension to the parasupersymmetric case is also considered

lie structures in parasupersymmetric quantum mechanics i the standard supersymmetrization procedure parasupersymmetric quantum mechanics leads to the construction of new lie structures that are called lie parasuperalgebras they are characterized by double commutation relations between even and odd generators and include as particular substructures the usual lie superalgebras oscillatorlike systems in one spatial dimension are especially exploited in order to put such structures in evidence but n dimensional extensions are easily determined these developments in the standard supersymmetrization procedure will be considered first and the spin orbit coupling one will be considered in a subsequent article j beckers and n debergh j math phys 1991

a note on recent lie parasuperstructures the authors discuss two recently published triple products seen as generalizations in parasupersymmetric quantum mechanics of the usual anticommutator between odd operators in the supersymmetric context they lead to lie parasuperalgebras which are not isomorphic in general

velocity inversion using a stratified reference we present an inversion algorithm for backscattered stacked seismic data which will reconstruct the velocity profile in realistic earth conditions the basic approach follows that of the original constant reference speed cohen and bleistein paper 1979a in that hig hfrequency asymptotics and perturbation methods are used however we use a reference speed which may vary with depth and this greatly enhances the validity of the perturbation assumption and hence the inversion results the new algorithm enjoys the same economies and stability properties of the original algorithm making it very competitive with current migration schemes four major assumptions are made 1 the acoustic wave equation is an adequate model 2 stacked data have amplitude information worth preserving fairly accurately 3 the actual reflectivity coefficients can be adequately modeled as perturbations from a continuous reference velocity which depends only on the depth variable and 4 the subsurface can be adequately

on the imaging of reflectors in the earth in this paper i present a modification of the beylkin inversion operator this modification accounts for the band limited nature of the data and makes the role of discontinuities in the sound speed more precise the inversion presented here partially dispenses with the small parameter constraint of the born approximation this is shown by applying the proposed inversion operator to upward scattered data represented by the kirchhoff approximation using the angularly dependent geometrical optics reflection coefficient a fully nonlinear estimate of the jump in sound speed may be extracted from the output of this algorithm interpreted in the context of these kirchhoff approximate data for the forward problem the inversion of these data involves integration over the source receiver surface the reflecting surface and frequency the spatial integrals are computed by the method of stationary phase the output is asymptotically a scaled singular function of the reflecting surface the singular function of a

baker campbell hausdorff relations for supergroups one parameter subgroups the exponential mapping and canonical coordinates have previously been defined for connected supergroups in this paper a technique for obtaining analytical expressions linking different coordinate schemes for supergroups is presented these are the baker campbell hausdorff relations the method is illustrated in detail with the examples of supergroups based on the supersymmetric quantum mechanical superalgebra sqm 2 and on the inonu wigner contraction isop 1 2 of the simple superalgebra osp 1 2

iterated rippled noise discrimination at long durations iterated rippled noise irn was used to study discrimination of irn stimuli with a lower number of iterations from irn stimuli with a higher number of iterations as a function of stimulus duration 100 2000 ms such irn stimuli differ in the strength of the repetition pitch in some cases the gain used to generate irn stimuli was adjusted so that both irn stimuli in the discrimination task had the same height of the first peak in the autocorrelation function or autocorrelogram in previous work involving short duration irn stimuli 500 ms listeners were not able to discriminate between irn stimuli that had different numbers of iterations but the same height of the first peak in the autocorrelation function in the current study irn discrimination performance improved with increases in duration even in cases when the height of the first peak in the autocorrelation was the same for the two irn stimuli thus future studies involving discrimination of irn stimuli may need to use longer durations 1 s or greater than those that have been used in the past

a brief comparison of some kirchhoff integral formulas for migration and inversion kirchhoff migration has traditionally been viewed as an imaging procedure usually few claims are made regarding the amplitudes in the imaged section in recent years a number of inversion formulas similar in form to those of kirchhoff migration have been proposed a kirchhoff type inversion produces not only an image but also an estimate of velocity variations or perhaps reflection coefficients the estimate is obtained from the peak amplitudes in the image in this paper prestack kirchhoff migration and inversion formulas for the one parameter acoustic wave equation are compared following a heuristic approach based on the imaging principle a migration formula is derived which turns out to be identical to one proposed by bleistein for inversion prestack kirchhoff migration and inversion are thus seen to be the same both in terms of the image produced and the peak amplitudes of the output

fast 2 d ray born migration inversion in complex media in this paper we evaluate the capacity of a fast 2 d ray born migration inversion algorithm to recover the true amplitude of the model parameters in 2 d complex media the method is based on a quasi newtonian linearized inversion of the scattered wavefield asymptotic green s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method the model is described by velocity perturbations associated with diffractor points both the first traveltime and the strongest arrivals can be inverted the algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2 d marmousi example comparison between logs extracted from the exact marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations

the relative strength of the tone and noise components in iterated rippled noise rippled noise is constructed by delaying a random noise and adding it back to the original iterated rippled noise irn is constructed by repeating the delay and add process irn produces a two component perception i e a buzzy tone with a pitch equal to the reciprocal of the delay and a background noise that sounds like the original random noise the perceived tone noise ratio increases with the number of iterations the effective tone noise ratio in irn sounds with 1 16 iterations was measured in a discrimination matching experiment each irn was paired with a range of standard sounds having varying proportions of a broadband noise and a complex tone to find the point where their perceived tone noise ratios are the same the experiment shows that the tone noise ratio of the matching standard increases 3 8 db per doubling of the number of iterations in the irn stimulus spectral models of auditory perception explain the pitch of irn in terms of peaks in the region of the first five to eight harmonic

an autocorrelation model with place dependence to account for the effect of harmonic number on fundamental frequency discrimination fundamental frequency f0 difference limens dls were measured as a function of f0 for sine and random phase harmonic complexes bandpass filtered with 3 db cutoff frequencies of 2 5 and 3 5 khz low region or 5 and 7 khz high region and presented at an average 15 db sensation level approximately 48 db spl per component in a wideband background noise fundamental frequencies ranged from 50 to 300 hz and 100 to 600 hz in the low and high spectral regions respectively in each spectral region f0 dls improved dramatically with increasing f0 as approximately the tenth harmonic appeared in the passband generally f0 dls for complexes with similar harmonic numbers were similar in the two spectral regions the dependence of f0 discrimination on harmonic number presents a significant challenge to autocorrelation ac models of pitch in which predictions generally depend more on spectral region than harmonic number a modification involving a lag window is proposed and tested restricting the ac repr

on colour superalgebras in parasupersymmetric quantum mechanics the simplest lie parasuperalgebra psqm 2 is identified as an example with a c 2 s colour superalgebra through simple connections between trilinear and bilinear structure relations but by using green cusson ansatze developed in parastatistics some general properties and conclusions are then obtained and illustrated

a computer implementation of 2 5 d common shot inversion the computer implementation of a two and one half dimensional 2 5 d constant density prestack inversion formalism with laterally and depth dependent background propagation speed is a kirchhoff type inversion summing data from a line of receivers over traveltime curves in the depth dependent background medium with weights determined from born kirchhoff inversion theory this theory predicts that the output will be a reflector map with peak amplitudes on each reflector being in known proportion to the angularly dependent geometrical optics reflection coefficient the 2 5 d feature provides for out of plane spreading correction consistent with the prescribed background medium the method is applied to a synthetic data set and to a physically modeled data set generated at the seismic acoustic laboratory the graphical output demonstrates the validity of the formalism as a kirchhoff migration parameter estimation for the synthetic data confirmed the theory parameter estimation for the experimental data wa

pitch strength of iterated rippled noise when the pitch is ambiguous two versions of a cascade of delay gain following delay and add circuits were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit the repetition pitch of irn is different when the delayed noise is subtracted gain 0 to the undelayed noise in the case of subtraction irn pitch is often ambiguous having two or more pitches listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli generated with different gains different network circuits and different number of iterations for most conditions the gain was less than one the data were described by a description based on an exponential function of the largest peak of the autocorrelation function of irn stimuli w a yost j acoust soc am 100 511 518 1996 processed such that the spectral dominance region is emphasized these results suggest that the strength of the pitch of irn stimuli can be described by temporal processing mechanisms as might be revealed by autocorrelation

variable background born inversion by wavefield backpropagation the inverse scattering problem for an acoustic medium is formulated by using the variable background born approximation a constant density acoustic medium is probed by a wide band point source and the scattered field is observed along a curved receiver array located outside the region where the medium velocity is different from the assumed background velocity function the solution proposed relies on the introduction of a backpropagated field this field is obtained by using a finite difference scheme backward in time to backpropagate into the medium the scattered field observed along the receiver array the backpropagated field is imaged at the source travel times giving an image of the same type as obtained by reverse time finite difference migration techniques the gradient of this image is then taken along rays linking the source to points in the medium and after scaling this gives the reconstructed potential to relate the reconstructed potential to the true scattering potential high frequency

ray kirchhoff migration in inhomogeneous media a kirchhoff method that avoids possible singularities on the surface of integration and is more accurate than previous kirchhoff methods has been developed for seismic migration in laterally inhomogeneous media it is based on a newly derived integral solution to the acoustic wave equation this solution indicates that wave fields in an inhomogeneous medium can be expressed as a summation of ray solutions determined by the transport and extended eikonal equations the extended eikonal equation is in turn solved by an asymptotic series for implementation a perturbation scheme is developed for solving the ray and transport equations in addition to computing higher order terms of the asymptotic series this scheme can be used to avoid most of the ray tracing required for wave extrapolation in a medium where vertical variations may be large but lateral variations are small compared to velocity itself where an analytic ray solution for the reference velocity used in the perturbation scheme exists ray kirchhoff migration in such a medium can be carried out without numerical ray tracing

imaging method utilizing attenuation and speed parameters in inverse scattering techniques methods for imaging the internal structures of an object using an acoustic wave field are provided in one aspect for example a method of imaging internals of a physical object using acoustic waves may include transmitting an acoustic wave field toward the object receiving a resultant acoustic wave field with a receiver where the resultant acoustic wave field is in response to the transmitted acoustic wave field reflected from or transmitted through the object and determining a predicted resultant acoustic wave field derived from a model of the object the method may also include determining a residual between the predicted resultant acoustic wave field and the resultant acoustic wave field and back propagating the residual to determine corrections to the model of the object in another aspect the above recited steps may be further iterated to successively refine the model of the object over a number of iterations until a predefined condition is reached

hall littlewood symmetric functions and the bkp equation the connection between solutions of the bkp equation and hall littlewood symmetric functions is utilised in a unified approach to soliton and polynomial solutions this is analogous to the wronskian formulation of the solution of the kp equation as a by product two novel expressions for certain hall littlewood functions in terms of pfaffians are derived

pitch strength of iterated rippled noise two versions of a cascade add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose pitch strength relative to the noise percept can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to use pitch strength to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds the number of iterations and the attenuation in the network a description based on an exponential function of the first peak of the autocorrelation function of irn stimuli is consistent with the results the discrimination data were well fit by a function based on the difference in the exponential functions of the first peak of the autocorrelation functions a magnitude estimation experiment indicated that pitch strength was an exponential function of the height of the first peak in the autocorrelation function these results suggest that the strength of the pitch of irn stimuli is based on temporal processing as might be revealed by autocorrelation

the perceptual tone noise ratio of merged iterated rippled noises with octave harmonic and nonharmonic delay ratios the perceptual tone noise ratio was measured for merged iterated ripple noise stimuli irns in which one of the individual irns always had a delay of 16 ms the second irn was chosen to create merged irns with single octave delay ratios e g 16 ms 8 ms double octave delay ratios e g 16 ms 4 ms harmonic delay ratios e g 16 ms 12 ms and nonharmonic delay ratios e g 16 ms 3 9 ms all stimuli were high pass filtered at 800 hz the tone noise ratio was significantly enhanced for the octave ratios and there was a strong interaction between the single and double octave delay ratios and number of iterations but the perceptual tone noise ratio for nonoctave ratios was determined solely by the number of iterations the pattern of the results can be explained in terms of the height of the largest peak in the summary autocorrelogram meddis and hewitt j acoust soc am 89 2866 2882 1991 provided the model is modified to improve the simulation of the loss of phase locking

the perceptual tone noise ratio of merged iterated rippled noises iterated rippled noise irn is constructed by delaying a random noise by d ms adding it back to the same noise and repeating the process iteratively when two irns with the same power but slightly different delays are added together the perceptual tone noise ratio of the merged irn is markedly reduced with respect to that of either of the component irns in this paper the reduction in the perceptual tone noise ratio is measured for irns in which one of the delays is always 16 ms and the other is either 16 0 1 ms or 16 1 1 ms the component irns have the same number of iterations and the number varies across conditions from 4 to 256 the perceptual tone noise ratio is measured using a discrimination matching procedure developed for single irns each merged irn is compared with a range of standard stimuli having varying proportions of a complex tone and a broadband noise patterson et al j acoust soc am 100 3286 3294 1996 for single irns the function relating the signal to noise ratio of the matching standard to the number of iterations in the irn was found to be essentially straight this relationship was explained in terms of the height of the first peak in the autocorrelation of the stimulus wave or by the first peak in the summary autocorrelogram produced by a time domain auditory model for the merged irns in the current experiment the matching point functions are found to have pronounced downward curvature in addition to being well below the function for single irns to account for the reduction in the perceptual tone noise ratio of merged irns the autocorrelation model was extended to include a simple rule for combining adjacent peaks in the autocorrelation function of the wave and the autocorrelogram model was revised to improve the simulation of the loss of phase locking at higher frequencies in the autocorrelogram

two and one half dimensional born inversion with an arbitrary reference multidimensional inversion algorithms are presented for both prestack and poststack data gathered on a single line these algorithms both image the subsurface i e give a migrated section and given relative true amplitude data estimate reflection strength or impedance on each reflector the algorithms are two and one half dimensional 2 5 d in that they incorporate three dimensional 3 d wave propagation in a medium which varies in only two dimensions the use of 3 d sources does not entail any computational penalty and it avoids the serious degradation of amplitude incurred by using the 2 d wave equation our methods are based on the linearized inversion theory associated with the born inversion thus we assume that the sound speed profile is well approximated by a given background velocity plus a perturbation it is this perturbation that we seek to reconstruct we are able to treat the case of an arbitrary continuous background profile however the cost of implementation increases as one

a time domain description for the pitch strength of iterated rippled noise two versions of a cascaded add attenuate and delay circuit were used to generate iterated rippled noise irn stimuli irn stimuli produce a repetition pitch whose strength relative to the noise can be varied by changing the type of circuit the attenuation or the number of iterations in the circuit listeners were asked to discriminate between various pairs of irn stimuli which differed in the type of network used to generate the sounds or the number of iterations n 1 2 3 4 7 and 9 performance was determined for irn stimuli generated with delays of 2 4 and 8 ms and for four bandpass filter conditions 0 2000 250 2000 500 2000 and 750 2000 hz some irn stimuli were extremely difficult to discriminate despite relatively large spectral differences while other irn stimuli produced readily discriminable changes in perception despite small spectral differences these contrasting results are inconsistent with simple spectral explanations for the perception of irn stimuli an explanation based on the first peak of the autocorrelation function of irn stimuli is consistent with the results simulations of the processing performed by the peripheral auditory system i e interval histograms and correlograms produce results which are consistent with the involvement of these temporal processes in the perception of irn stimuli

the role of the envelope in processing iterated rippled noise iterated rippled noise irn is generated by a cascade of delay and add the gain after the delay is 1 0 or delay and subtract the gain is 1 0 operations the delay and add subtract operations impart a spectral ripple and a temporal regularity to the noise the waveform fine structure is different in these two conditions but the envelope can be extremely similar four experiments were used to determine conditions in which the processing of irn stimuli might be mediated by the waveform fine structure or by the envelope in experiments 1 and 3 listeners discriminated among three stimuli in a single interval task irn stimuli generated with the delay and add operations g 1 0 irn stimuli generated using the delay and subtract operations g 1 0 and a flat spectrum noise stimulus in experiment 2 the listeners were presented two irn stimuli that differed in delay 4 vs 6 ms and a flat spectrum noise stimulus that was not an irn stimulus in experiments 1 and 2 both the envelope and waveform fine structure contained the spectral ripple and temporal regularity in experiment 3 only the envelope had this spectral and temporal structure in all experiments discrimination was determined as a function of high pass filtering the stimuli and listeners could discriminate between the two irn stimuli up to frequency regions as high as 4000 6000 hz listeners could discriminate the irn stimuli from the flat spectrum noise stimulus at even higher frequencies as high as 8000 hz but these discriminations did not appear to depend on the pitch of the irn stimuli a control experiment fourth experiment suggests that irn discriminations in high frequency regions are probably not due entirely to low frequency nonlinear distortion products the results of the paper imply that pitch processing of irn stimuli is based on the waveform fine structure