In this study, a new finite-difference technique is designed to reduce the number of grid points needed in frequency-space domain modeling. The new algorithm uses optimal nine-point operators for the approximation of the Laplacian and the mass acceleration terms. The coefficients can be found by using the steepest descent method so that the best normalized phase curves can be obtained. ABSTRACTThis method reduces the number of grid points per wavelength to 4 or less, with consequent reductions of computer memory and CPU time that are factors of tens less than those involved in the conventional secondorder approximation formula when a band type solver is used on a scalar machine.

S U M M A R YFor the last 30 yr, since Tarantola's pioneering theoretical study of waveform inversion, geophysicists and applied mathematicians have utilized a waveform inversion to delineate the earth's structures. However, successful applications of waveform inversion to real data are nominal. The failures are mainly caused by the high non-linearity of the waveform inversion and the real data containing insufficient low-frequency components.We propose a waveform inversion algorithm that is robust and is not sensitive to the initial model by exploiting the wavefield in the Laplace domain and the adjoint property of the wave equation. The wavefield in the Laplace domain is equivalent to the zero frequency component of the damped wavefield. Therefore, the inversion of Poisson's equation in electrical prospecting can be viewed as a waveform inversion problem, exploiting the zero frequency component of an undamped wavefield. Since our inversion algorithm in the Laplace domain is strongly associated with the nature of DC inversion for Poisson's equation in electrical prospecting, our algorithm can generate a velocity model that is equivalent to a long-wavelength velocity model (a smooth velocity model).Through numerical tests, we found that the Laplace-transformed wavefields for optimally low Laplace damping constants are critically needed in our algorithm as the low-frequency components are necessary in the waveform inversion of the frequency domain. We note that the objective function by l 2 norm of the logarithmic wavefield in the Laplace domain behaves as if it has no local minimum points in low and high Laplace damping constants. Moreover, we note that the forward modelling in the Laplace domain could be accurately calculated by using a coarser grid of several hundreds of metres than that of the frequency domain.Numerical tests of the salt dome model with high-velocity contrast demonstrate the robustness of our algorithm to both synthetic and real data. To apply our algorithm to real data more successfully, we need to improve the accuracy of the Laplace transformation for the wavefields in the time domain. However, our waveform inversion in the Laplace domain can be successfully applied to real data since our algorithm has more advantages in forward modelling and inversion than those in the frequency domain.

Although waveform inversion has been studied extensively since its beginning 20 years ago, applications to seismic field data have been limited, and most of those applications have been for global-seismology-or engineering-seismology-scale problems, not for exploration-scale data. As an alternative to classical waveform inversion, we propose the use of a new, objective function constructed by taking the logarithm of wavefields, allowing consideration of three types of objective function, namely, amplitude only, phase only, or both. In our waveform inversion, we estimate the source signature as well as the velocity structure by including functions of amplitudes and phases of the source signature in the objective function. We compute the steepest-descent directions by using a matrix formalism derived from a frequency-domain, finite-element/finite-difference modeling technique. Our numerical algorithms are similar to those of reverse-time migration and waveform inversion based on the adjoint state of the wave equation. In order to demonstrate the practical applicability of our algorithm, we use a synthetic data set from the Marmousi model and seismic data collected from the Korean continental shelf. For noisefree synthetic data, the velocity structure produced by our inversion algorithm is closer to the true velocity structure than that obtained with conventional waveform inversion. When random noise is added, the inverted velocity model is also close to the true Marmousi model, but when frequencies below 5 Hz are removed from the data, the velocity structure is not as good as those for the noise-free and noisy data. For field data, we compare the time-domain synthetic seismograms generated for the velocity model inverted by our algorithm with real seismograms and find that the results show that our inversion algorithm reveals short-period features of the subsurface. Although we use wrapped phases in our examples, we still obtain reasonable results. We expect that if we were to use correctly unwrapped phases in the inversion algorithm, we would obtain better results.

A prestack reverse time‐migration image is not properly scaled with increasing depth. The main reason for the image being unscaled is the geometric spreading of the wavefield arising during the back‐propagation of the measured data and the generation of the forward‐modelled wavefields. This unscaled image can be enhanced by multiplying the inverse of the approximate Hessian appearing in the Gauss–Newton optimization technique. However, since the approximate Hessian is usually too expensive to compute for the general geological model, it can be used only for the simple background velocity model.We show that the pseudo‐Hessian matrix can be used as a substitute for the approximate Hessian to enhance the faint images appearing at a later time in the 2D prestack reverse time‐migration sections. We can construct the pseudo‐Hessian matrix using the forward‐modelled wavefields (which are used as virtual sources in the reverse time migration), by exploiting the uncorrelated structure of the forward‐modelled wavefields and the impulse response function for the estimated diagonal of the approximate Hessian. Although it is also impossible to calculate directly the inverse of the pseudo‐Hessian, when using the reciprocal of the pseudo‐Hessian we can easily obtain the inverse of the pseudo‐Hessian. As examples supporting our assertion, we present the results obtained by applying our method to 2D synthetic and real data collected on the Korean continental shelf.

Summary By specifying a discrete matrix formulation for the frequency–space modelling problem for linear partial differential equations (‘FDM’ methods), it is possible to derive a matrix formalism for standard iterative non‐linear inverse methods, such as the gradient (steepest descent) method, the Gauss–Newton method and the full Newton method. We obtain expressions for each of these methods directly from the discrete FDM method, and we refer to this approach as frequency‐domain inversion (FDI). The FDI methods are based on simple notions of matrix algebra, but are nevertheless very general. The FDI methods only require that the original partial differential equations can be expressed as a discrete boundary‐value problem (that is as a matrix problem). Simple algebraic manipulation of the FDI expressions allows us to compute the gradient of the misfit function using only three forward modelling steps (one to compute the residuals, one to backpropagate the residuals, and a final computation to compute a step length). This result is exactly analogous to earlier backpropagation methods derived using methods of functional analysis for continuous problems. Following from the simplicity of this result, we give FDI expressions for the approximate Hessian matrix used in the Gauss–Newton method, and the full Hessian matrix used in the full Newton method. In a new development, we show that the additional term in the exact Hessian, ignored in the Gauss–Newton method, can be efficiently computed using a backpropagation approach similar to that used to compute the gradient vector. The additional term in the Hessian predicts the degradation of linearized inversions due to the presence of first‐order multiples (such as free‐surface multiples in seismic data). Another interpretation is that this term predicts changes in the gradient vector due to second‐order non‐linear effects. In a numerical test, the Gauss–Newton and full Newton methods prove effective in helping to solve the difficult non‐linear problem of extracting a smooth background velocity model from surface seismic‐reflection data.

Various pigment colors were produced by Monascus fermentations with separate addition of 20 amino acids. The color characteristics and structures of the pigment derivatives were investigated. When each amino acid was added to the fermentation broth as a precursor, pigment extracts with different hue and chroma values were obtained depending on the content ratios of yellow, orange, and red colors in the fermentation broth. The yellow and orange pigments were identical regardless of amino acid addition. The red compounds varied on the basis of the type of amino acid added. LC-MS and (1)H and (13)C NMR structural analyses confirmed that the derivative pigments contained the moieties of the added amino acids. L, a, and b values of the CIELAB color system for the derivative pigments were measured. Values of hue and chroma were then calculated. The colors of the derivative pigments were in the range of orangish red to violet red. The hydrophilicities/hydrophobicities of the derivative pigments could be predicted from their log P values, which were estimated using computer programs.

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Ghrelin, a newly identified gut hormone, has been implicated in the regulation of food intake and energy homeostasis. This study was undertaken to investigate changes in expression levels of stomach ghrelin as well as of ghrelin receptor in the hypothalamus and pituitary glands according to feeding state. Stomach ghrelin mRNA levels were increased by 48 h fasting but decreased by re-feeding. The ghrelin receptor mRNA levels of 48 h fasted rats were 8 times higher in the hypothalamus and 3 times higher in the anterior pituitary gland than levels in fed rats. In summary, not only stomach ghrelin, but also hypothalamic ghrelin receptor mRNA expression, increased during a fast. Such as enhanced ghrelin receptor expression could contribute to the amplification of ghrelin action in a negative-energy balance state.