surface consistent matching filters for time lapse seismic processing abstractwe evaluated the concept of surface consistent matching filters for processing time lapse seismic data in which matching filters are convolutional filters that minimize the sum squared error between two signals because in the fourier domain a matching filter is the spectral ratio of the two signals we extended the well known surface consistent hypothesis such that the data term is a trace by trace spectral ratio of two data sets instead of only one i e surface consistent deconvolution to avoid unstable division of spectra we computed the spectral ratios in the time domain by first designing trace sequential least squares matching filters then fourier transforming them a subsequent least squares solution then factored the trace sequential matching filters into four operators two surface consistent source and receiver and two subsurface consistent offset and midpoint we evaluated a time lapse synthetic data set with nonrepeatable acquisition parameters complex near surface geology

schubert polynomials and the nilcoxeter algebra abstract schubert polynomials were introduced and extensively developed by lascoux and schutzenberger after an earlier less combinatorial version had been considered by bernstein gelfand and gelfand and demazure we give a new development of the theory of schubert polynomials based on formal computations in the algebra of operators u1 u2 satisfying the relations u2i 0 uiuj ujui if i j 2 and uiui 1ui ui 1uiui 1 we call this algebra the nilcoxeter algebra of the symmetric group s n our development leads to simple proofs of many standard results in particular a symmetry of the stable schubert polynomials fw b an explicit combinatorial formula for schubert polynomials due to billey jockusch and stanley c the cauchy formula for schubert polynomials and d a formula of macdonald for s w 1 1 our main new result is a proof of a conjectured q analogue of d due to macdonald which gives a formula for s w 1 q q2

bases for some reciprocity algebras i for a complex vector space v let p v be the algebra of polynomial functions on v in this paper we construct bases for the algebra of all gl n c x gl m1 c x gl m2 c x x gl mr c highest weight vectors in p c n c m where m m 1 m r and mj n for all 1 j r and the algebra of gl n c x gl k c x gl 1 c highest weight vectors in p c n c k c n c l

integrable systems toric degenerations and okounkov bodies let x be a smooth projective variety of dimension n over mathbb c equipped with a very ample hermitian line bundle mathcal l in the first part of the paper we show that if there exists a toric degeneration of x satisfying some natural hypotheses which are satisfied in many settings then there exists a surjective continuous map from x to the special fiber x 0 which is a symplectomorphism on an open dense subset u from this we are then able to construct a completely integrable system on x in the sense of symplectic geometry more precisely we construct a collection of real valued functions h 1 ldots h n on x which are continuous on all of x smooth on an open dense subset u of x and pairwise poisson commute on u moreover our integrable system in fact generates a hamiltonian torus action on u in the second part we show that the toric degenerations arising in the theory of newton okounkov bodies satisfy all the hypotheses of the first part of the paper in this case the image of the moment map mu h 1 ldots h n x rightarrow mathbb r n is precisely the newton okounkov body delta delta r v associated to the homogeneous coordinate ring r of x and an appropriate choice of a valuation v on r our main technical tools come from algebraic geometry differential kahler geometry and analysis specifically we use the gradient hamiltonian vector field and a subtle generalization of the famous ojasiewicz gradient inequality for real valued analytic functions since our construction is valid for a large class of projective varieties x this manuscript provides a rich source of new examples of integrable systems we discuss concrete examples including elliptic curves flag varieties of arbitrary connected complex reductive groups spherical varieties and weight varieties

toric degeneration of branching algebras abstract for each classical symmetric pair g h there is a naturally defined multi graded algebra a g h called the branching algebra for g h which encodes the branching rule from g to h this algebra has a natural family of subalgebras depending on integer parameters for a certain range of the parameters the subalgebras have a particularly simple structure and are called stable branching algebras in this paper we show that the stable branching algebras for eight out of the ten families of classical symmetric pairs are flat deformations of the semigroup algebras of explicitly described lattice cones

the gelfand cetlin system and quantization of the complex flag manifolds the construction of angle action variables for collective completely integrable systems is described and the associated bohr sommerfeld sets are determined the quantization method of sniatycki applied to such systems gives formulas for multiplicities for the gelfand cetlin system on complex flag manifolds we show that these formulas give the correct answers for the multiplicities of the associated representations

toric degenerations of gelfand cetlin systems and potential functions abstract we define a toric degeneration of an integrable system on a projective manifold and prove the existence of a toric degeneration of the gelfand cetlin system on the flag manifold of type a as an application we calculate the potential function for a lagrangian torus fiber of the gelfand cetlin system

lagrangian fibers of gelfand cetlin systems abstract a gelfand cetlin system is a completely integrable system defined on a partial flag manifold whose image is a rational convex polytope called a gelfand cetlin polytope motivated by the study of nishinou nohara ueda 24 on the floer theory of gelfand cetlin systems we provide a detailed description of topology of gelfand cetlin fibers in particular we prove that any fiber over an interior point of an r dimensional face of the gelfand cetlin polytope is an isotropic submanifold and is diffeomorphic to t r n for some smooth manifold n and t r s 1 r we also prove that such n s are exactly the vanishing cycles shrinking to points in the associated toric variety via the toric degeneration we also devise an algorithm of reading off lagrangian fibers from the combinatorics of the ladder diagram

toric degeneration of schubert varieties and gelfand tsetlin polytopes this note constructs the flat toric degeneration of the manifold fln of flags in cn due to gonciulea and lakshmibai transform groups 1 3 1996 215 as an explicit git quotient of the grobner degeneration due to knutson and miller grobner geometry of schubert polynomials ann math 2 to appear this implies that schubert varieties degenerate to reduced unions of toric varieties associated to faces indexed by rc graphs reduced pipe dreams in the gelfand tsetlin polytope our explicit description of the toric degeneration of fln provides a simple explanation of how gelfand tsetlin decompositions for irreducible polynomial representations of gln arise via geometric quantization

grobner geometry of schubert polynomials given a permutation w sn we consider a determinantal ideal iw whose generators are certain minors in the generic n n matrix filled with independent variables using emultidegrees f as simple algebraic substitutes for torus equivariant cohomology classes on vector spaces our main theorems describe for each ideal iw

standard monomial theory for flag algebras of gl n and sp 2n let g be the general linear group or the symplectic group over the complex numbers and u be its maximal unipotent subgroup we study standard monomial theory for the ring of regular functions on g u called the flag algebra using the philosophy of grobner bases and sagbi bases combined with classical invariant theory from the realization of the flag algebra in a concrete polynomial setting we obtain explicit standard monomial bases for irreducible representations we also recreate known combinatorics of young tableaux and gelfand tsetlin patterns and toric degenerations of flag varieties from the structure of leading monomials

chern class formulas for quiver varieties our goal in this paper is to prove a formula for the general degeneracy locus xr associated to an oriented quiver of type an if we are given a sequence of vector bundles and vector bundle maps e0 1 e1 2 e2 y y eny1 n en on an algebraic variety x and a collection r rij 0 i j n of non negative integers there is a degeneracy locus xr xr e xr e de ned by xr fx 2 x j rank ei x ej x rij 8 i jg 1 1

a non crossing standard monomial theory abstract the second author has introduced non crossing tableaux objects whose non nesting analogues are semi standard young tableaux we relate non crossing tableaux to gelfand tsetlin patterns and develop the non crossing analogue of standard monomial theory leclerc and zelevinsky s weakly separated sets are special cases of non crossing tableaux and we suggest that non crossing tableaux may help illuminate the theory of weakly separated sets

four component surface consistent deconvolution when performing four component surface consistent deconvolution it is assumed that the decomposition of amplitude spectra into source receiver offset and common depth point components enables accurate deconvolution filters to be derived however relatively little effort has been put into the verification of this assumption some verification of the assumption is available by analyzing the results of the surface consistent decomposition of real seismic data the surface consistent log amplitude spectra of land seismic data are able to provide convincing evidence that the source component collects effects of the source signature and near source structural effects and that the receiver component collects receiver characteristics and near receiver structural effects in addition the offset component collects effects due to ground roll and average reflectivity and the cdp component collects mostly random noise unless it is constrained to be smooth based on the results of this analysis deconvolution f

surface consistent deconvolution using reciprocity and waveform inversion source and receiver responses must be equalized when their behavior or coupling changes with location within a given survey existing surface consistent deconvolution techniques that account for these effects assume that common midpoint cmp gathering is valid the seismic trace is decomposed into a source function a receiver response a normal incidence reflectivity term and an offsetrelated component that is laterally shift invariant as a result the performance of existing surface consistent deconvolution techniques is best when applied to primary reflection data only since the offset dependency of ground roll and multiples varies laterally in media with lateral variations we have developed an alternative method for surfaceconsistent deconvolution that is applicable to the entire seismic trace and is therefore essentially a raw data preprocessing step the method is based on reciprocity of the medium response assuming that conditions for applicability of reciprocity are met we can attribute differences between normal and reciprocal recordings to the source and receiver perturbations contrary to existing surfaceconsistent deconvolution methods this approach uses the full description of the wavefield and is therefore ideally suited for prestack processing we have applied this technique to single sensor data acquired in manistee county michigan at this site nearsurface conditions vary and this significantly affects data quality the application of the new deconvolution procedure substantially improves s n ratio on both prestack and poststack data and these results compare favorably to those obtained using existing surface consistent deconvolution techniques since they require subjective data scaling to obtain acceptable results the obtained source corrections are correlated to changes in near surface conditions in this case to changes in water saturation levels we do not observe such a correlation for the receiver corrections which vary rapidly along the spread finally the receiver response does not agree with the generally accepted damped harmonic oscillator model for frequencies below 100 hz the retrieved receiver variations are larger than predicted by this model and we cannot explain the receiver response using a single resonant frequency for the geophone ground coupling

standard monomial bases and degenerations of som c representations we study explicit weight bases for the finite dimensional representations of so m using a flat degeneration technique we describe the representation spaces via a lattice cone associated with the gelfand tsetlin patterns for gl m combinatorial descriptions of the weight bases for so m relative to those for gl m will be given

okounkov bodies and toric degenerations let vardelta be the okounkov body of a divisor d on a projective variety x we describe a geometric criterion for vardelta to be a lattice polytope and show that in this situation x admits a flat degeneration to the corresponding toric variety this degeneration is functorial in an appropriate sense

toric degenerations of grassmannians and schubert varieties from matching field tableaux abstract we study grobner degenerations of grassmannians and the schubert varieties inside them we provide a family of binomial ideals whose combinatorics is governed by matching field tableaux in the sense of sturmfels and zelevinsky in 31 we prove that these ideals are all quadratically generated and they yield a sagbi basis of the plucker algebra this leads to a new family of toric degenerations of grassmannians moreover we apply our results to construct a family of grobner degenerations of schubert varieties inside grassmannians we provide a complete characterization of toric ideals among these degenerations in terms of the combinatorics of matching fields permutations and semi standard tableaux