arXiv subjects

Xuehua Chen

Publications and source records attributed to Xuehua Chen.

4 recordsLinked to original sources

arXiv2026

Seismic P-wave attenuation estimation based on frequency-dependent AVO using Kramers-Kronig relations for gas reservoir prediction

Estimation of seismic attenuation (inverse quality factor) is important for gas reservoir prediction. Two key issues in seismic attenuation estimation are the development of a physically consistent reflection coefficient equation and stable estimation of seismic attenuation from seismic data. To address these issues, this study, within the framework of isotropic linear viscoelastic media, starts from the Kramers-Kronig relations and expresses the viscoelastic stiffness matrix as a function of seismic attenuation. Under the assumptions of weak attenuation and small elastic and attenuation contrasts across the interface, a frequency-dependent PP-wave reflection coefficient equation explicitly containing seismic attenuation terms is derived using scattering theory. The derived reflection coefficient equation not only satisfies the causality constraint, but also preserves a compact mathematical form. Based on this reflection coefficient equation, seismic attenuation is estimated within the framework of frequency-dependent AVO inversion. Synthetic seismic data tests show that the estimated P-wave attenuation attribute is sensitive to variations in reservoir gas saturation, with reservoirs of higher gas saturation exhibiting stronger P-wave attenuation anomalies. Application to field seismic data further demonstrates that the P-wave attenuation anomalies agree well with the gas saturation log and effectively identify high gas saturation reservoirs. This study provides a new approach for extracting P-wave attenuation information from seismic data and achieving high resolution prediction of gas reservoirs.

physics.geo-ph↗

arXiv2013

A few endpoint geodesic restriction estimates for eigenfunctions

We prove a couple of new endpoint geodesic restriction estimates for eigenfunctions. In the case of general 3-dimensional compact manifolds, after a $TT^*$ argument, simply by using the $L^2$-boundedness of the Hilbert transform on $\R$, we are able to improve the corresponding $L^2$-restriction bounds of Burq, Gérard and Tzvetkov and Hu. Also, in the case of 2-dimensional compact manifolds with nonpositive curvature, we obtain improved $L^4$-estimates for restrictions to geodesics, which, by Hölder's inequality and interpolation, implies improved $L^p$-bounds for all exponents $p\ge 2$. We do this by using oscillatory integral theorems of Hörmander, Greenleaf and Seeger, and Phong and Stein, along with a simple geometric lemma (Lemma \ref{lemma3.2}) about properties of the mixed-Hessian of the Riemannian distance function restricted to pairs of geodesics in Riemannian surfaces. We are also able to get further improvements beyond our new results in three dimensions under the assumption of constant nonpositive curvature by exploiting the fact that in this case there are many totally geodesic submanifolds.

math.AP↗

arXiv2013

On integrals of eigenfunctions over geodesics

If $(M,g)$ is a compact Riemannian surface then the integrals of $L^2(M)$-normalized eigenfunctions $e_j$ over geodesic segments of fixed length are uniformly bounded. Also, if $(M,g)$ has negative curvature and $γ(t)$ is a geodesic parameterized by arc length, the measures $e_j(γ(t))\, dt$ on $\R$ tend to zero in the sense of distributions as the eigenvalue $\la_j\to \infty$, and so integrals of eigenfunctions over periodic geodesics tend to zero as $\la_j\to \infty$. The assumption of negative curvature is necessary for the latter result.

math.AP↗

arXiv2012

An improvement on eigenfunction restriction estimates for compact boundaryless Riemannian manifolds with nonpositive sectional curvature

Let $(M,g)$ be an $n$-dimensional compact boudaryless Riemannian manifold with nonpositive sectional curvature, then our conclusion is that we can give improved estimates for the $L^p$ norms of the restrictions of eigenfunctions to smooth submanifolds of dimension $k$, for $p>\dfrac{2n}{n-1}$ when $k=n-1$ and $p>2$ when $k\leq n-2$, compared to the general results of Burq, Gérard and Tzvetkov \cite{burq}. Earlier, Bérard \cite{Berard} gave the same improvement for the case when $p=\infty$, for compact Riemannian manifolds without conjugate points for $n=2$, or with nonpositive sectional curvature for $n\geq3$ and $k=n-1$. In this paper, we give the improved estimates for $n=2$, the $L^p$ norms of the restrictions of eigenfunctions to geodesics. Our proof uses the fact that, the exponential map from any point in $x\in M$ is a universal covering map from $\mathbb{R}^2\backsimeq T_{x}M$ to $M$, which allows us to lift the calculations up to the universal cover $(\mathbb{R}^2,\tilde{g})$, where $\tilde{g}$ is the pullback of $g$ via the exponential map. Then we prove the main estimates by using the Hadamard parametrix for the wave equation on $(\mathbb{R}^2,\tilde{g})$, the stationary phase estimates, and the fact that the principal coefficient of the Hadamard parametrix is bounded, by observations of Sogge and Zelditch in \cite{SZ}. The improved estimates also work for $n\geq 3$, with $p>\frac{4k}{n-1}$. We can then get the full result by interpolation.

math.AP↗