2005博士生专业英文复习内容.docVIP

Characterization of geological boundaries using 1-D wavelet（微波） transform on gravity data One of the most common problems encountered in geophysical(地球物理，地球物理学) studies is how to determine the geometry of geological（地质的，地质学的） contacts at depth. To address this problem, we use the wavelet transform applied to gravity, an operator recently introduced in the potential-fields domain by Moreau (1995). The use of the wavelet operator, as first defined by Grossman and Morlet (1984) allows wavelength-adaptive convolution operators that vary with the wavelength of the studied portion of signal. The wavelet operator can focus on individual objects. The special class of wavelets we use in this study lets us analyze the scaling properties of the source via upward continuation. Here, we discuss the wavelet technique capabilities for gravity data. We briefly recall the basic principles of wavelet transform theory. Then we derive analytic expressions of the wavelet coefficients（系数） for simple-shaped gravity sources and test the method on several synthetic examples. We show that horizontal and vertical location of the source as well as its shape, vertical extension, and dip can be estimated. Finally, analytic results also allow determination of the dipping angle of the source from the phase term of the complex wavelet transform. Synthetic tests show that the computed inclination of the source is generally good even if slightly underestimated. Convolution（褶合，褶积；卷积） It can be shown that the convolution of two functions in the time domain is mathematically equivalent to multiplication of their amplitude（振幅，幅度，幅值） spectra（频谱；波谱；能谱；质谱；范围） and addition of their phase spectra in the frequency domain. The operation of convolution can thus be performed by transforming the time functions into the frequency domain, multiplying their amplitude spectra, summing their phase spectra and taking the inverse transform of the resultant frequency spectrum. Thus, digital filtering can be enacted in e