The influence of sea water velocity variation on seismic traveltimes,ray paths,and amplitude

The main factors affecting seismic exploration is the propagation velocity of seismic waves in the medium. In the past, during marine seismic data processing, the propagation velocity of sea water was generally taken as a constant 1500 m/s. However, for deep water exploration, the sound velocity varies with the season, time, location, water depth, ocean currents, and etc.. It also results in a layered velocity distribution, so there is a difference of seismic traveltime, ray paths, and amplitude, which affect the migration imaging results if sea water propagation velocity is still taken as constant for the propagation wavefield. In this paper, we will start from an empirical equation of seismic wave velocity in seawater with changes of temperature, salinity, and depth, consider the variation of their values, build a seawater velocity model, and quantitatively analyze the impact of seawater velocity variation on seismic traveltime, ray paths, and amplitude in the seawater velocity model.

Ray path of head waves with irregular interfaces

Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity.However,the path that the rays travel along in media with irregular interfaces is not clear.Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements（SEMO） that can accurately evaluate waves traveling along an irregular interface.Consequently,the head waves are separated from interface waves by a time window.Thus,their energy and arrival time changes can be analyzed independently.These analyses demonstrate that,contrary to the case for head waves propagating along a flat interface,there are two mechanisms for head waves traveling along an irregular interface：a refraction mechanism and transmission mechanism.That is,the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media.Such knowledge will be helpful in constructing a more accurate inversion method,such as head wave travel-time tomography,and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas,such as the Tibetan Plateau.

A Comparison of the Radar Ray Path Equations and Approximations for Use in Radar Data Assimilation

The radar ray path equations are used to determine the physical location of each radar measurement. These equations are necessary for mapping radar data to computational grids for diagnosis, display and numerical weather prediction （NWP）. They are also used to determine the forward operators for assimilation of radar data into forecast models. In this paper, a stepwise ray tracing method is developed. The influence of the atmospheric refractive index on the ray path equations at different locations related to an intense cold front is examined against the ray path derived from the new tracing method. It is shown that the radar ray path is not very sensitive to sharp vertical gradients of refractive index caused by the strong temperature inversion and large moisture gradient in this case. In the paper, the errors caused by using the simplified straight ray path equations are also examined. It is found that there will be significant errors in the physical location of radar measurements if the earth＇s curvature is not considered, especially at lower elevation angles. A reduced form of the equation for beam height calculation is derived using Taylor series expansion. It is computationally more efficient and also avoids the need to use double precision variables to mitigate the small difference between two large terms in the original form. The accuracy of this reduced form is found to be sufficient for modeling use.

Variation of Radio Refractivity with Respect to Moisture and Temperature and Influence on Radar Ray Path

In this study, the variation of radio refractivity with respect to temperature and moisture is analyzed. Also, the effects of vertical gradients in temperature and moisture on the propagation paths of electromagnetic waves of weather radar are examined for several sites across the United States using several years of sounding data from the National Weather Service. The ray path is important for identifying storm characteristics and for properly using the radar data in initializing numerical weather prediction models. It is found that during the warm season the radio refractivity gradient is more sensitive to moisture gradients than to temperature gradients. Ray paths from the commonly accepted vertical ray path model are compared to a ray path computed from a stepwise ray tracing algorithm using data from actual soundings. For the sample of about 16 000 soundings examined, we find that only a small fraction of the ray paths diverge significantly from those calculated using a ray path model based on the US Standard Atmosphere. While the problem of ray dueting in the presence of a temperature inversion is fairly well known, we identify the presence of a strong vertical moisture gradient as the culprit in the majority of the cases where significant deviations occurred.

The Effect of Spatial Structure Character of Heat Source on the Ray Path and the Evolution of Wave Energy of Meridional Wave Train

This paper studies correlations between the spatial structure character of thermal forcing and deformation and the amplitude of rays of meridional wave train. It is shown that if thermal forcing appears a meridional linear variation the rays of quasi-stationary planetary wave may propagate along oblique lines and if the meridional variability of heat source has second order term the rays show distinct deformation as a great circular route. Additionally, the inhomogeneous distribution may cause lower frequency oscillations in mid- and low-latitudes. The combination of zonal and meridional wave numbers and distributive character of heat source may form an inverse mechanism of variational trend of generized wave energy, reflecting in some degree the physical process of transition between meridional and zonal flow patterns.

Fast ray tracing method in 3-D structure and its proof of positive definiteness

Based on Fermat’s principle, two-point ray tracing method was studied in three-dimensional structure. By means of first order Taylor’s incomplete series expansion (i.e. no expansion to the length of the ray), a symmetry block tridiagonal matrix equation set was deduced. Further, the positive definiteness of coefficient matrix was discussed, and the positive definiteness was accurately proved in a mathematical way. It assured that the algorithm was well-posed. Associated with iterative method, the solution to ray tracing can be got through step-by-step linearized iteration of the nonlinear problem. An algorithm of the whole path iterative ray tracing method in three-dimensional velocity structure was obtained. This method shows a clear and simple as well as explicit computation formula, which makes ray tracing computation easily applicable in practice. The correction vector is obtained through finding the solution to the positive definite block tridiagonal equation set, which ensures the method is robust convergence. This study offers a new kind of feasible and efficient ray tracing method for three dimensional seismic migration and tomography. Meanwhile, it also provides the prerequisite guarantee to design a fast algorithm.

Analysis and evaluation of band-limited ray tracing method

From the analysis and the contrast of band-limited ray tracing method based on Kirchhoff integral, it was found that the method performs many approximations in the derivation process and omits the derivative term of the phase factor in the Kirchhoff integral. Numerical calculations and analysis show that the omission of cor-relation terms in Kirchhoff integrals has a non-negligible effect on the calculation results, and the different terms in the Kirchhoff integral have different effects on different frequency ranges. The method can be applied to ve-locity models containing complex interfaces without changing waves and continuous media. the velocity model and can be extended to elastic waves and continuous media.

Quantitative Investigation of Tomographic Effects in Abnormal Regions of Complex Structures

The detection of abnormal regions in complex structures is one of the most challenging targets for underground space engineering.Natural or artificial geologic variations reduce the effectiveness of conventional exploration methods.With the emergence of real-time monitoring,seismic wave velocity tomography allows the detection and imaging of abnormal regions to be accurate,intuitive,and quantitative.Since tomographic results are affected by multiple factors in practical small-scale applications,it is necessary to quantitatively investigate those influences.We adopted an improved three-dimensional(3D)tomography method combining passive acoustic emission acquisition and active ultrasonic measurements.By varying individual parameters(i.e.,prior model,sensor configuration,ray coverage,event distributions,and event location errors),37 comparative tests were conducted.The quantitative impact of different factors was obtained.Synthetic experiments showed that the method could effectively adapt to complex structures.The optimal input parameters based on quantization results can significantly improve the detection reliability in abnormal regions.