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在深部地震测深调查中,超过临界角的广角地震反射已被广泛应用于地壳结构的成象。层速度和层厚度的计算通常是基于Dix的双曲线方程,该方程需要零偏移距旅行时和均方根速度的先验数据。由于广角反射时间是用非双曲的泰勒和Koehler级数表示的,使其强行与双曲方程确立的那套数据相匹配,在层速度估算中就会引起很大的误差。我们提出一种快速而简便的方法来确定广角反射时的层速度。它是运用阻尼最小二乘技术使观测旅行时和正响应之间的均方根误差最小来实现的。通过切比雪夫(正交的)多项式近似计算,可计算出正响应,这种响应中含有高次项的反射级数。针对给定的含有某些随机误差的速度模型,可用这一方法反演合成反射时,它由不同的初始模型开始,最后产生一个与真实模型相吻合的模型。模拟结果证实了估算参数的可靠性。此外,利用该方法还可测量估算参数的不确定性和分辨率。
In the deep seismic sounding survey, the wide-angle seismic reflection beyond the critical angle has been widely used in the imaging of the crustal structure. The calculation of layer velocity and layer thickness is usually based on the hyperbolic equation of Dix, which requires prior knowledge of travel time and root mean square velocity at zero offset. Since the wide-angle reflection time is represented by a non-hyperbolic Taylor and Koehler series, which is forced to match the set of data established by the hyperbolic equation, a large error is caused in the estimation of the layer velocity. We propose a quick and easy way to determine the layer velocity at wide-angle reflections. It is achieved using damped least square techniques to minimize the root mean square error between observed travel and positive responses. By the Chebyshev (orthogonal) polynomial approximation calculation, a positive response can be calculated which contains the order of reflection of the higher order term. For a given velocity model with some random errors, this method can be used to invert the synthetic reflection, starting with a different initial model and finally producing a model that fits the real model. The simulation results confirm the reliability of the estimated parameters. In addition, the method can be used to measure the uncertainty and resolution of estimated parameters.