Reverse time migration (RTM) artifacts usually start to appear in large refection angles which include a wide-angle range. On the other hand, the only proposed starting refection angle for RTM artifacts is 60 degrees which is not based on a proven investigation and it seems to be just a suggestion based on trial and error. As an important issue, we determine a predominant starting refection angle (PSRA) for RTM artifacts which enables us to suppress artifacts properly. Therefore, frst we try to open and discuss some issues from a new fundamentally perspective about the number of cross-correlations (NOCC) and its relationship with RTM amplitude and artifacts at refection and nonrefection points. Second, the cross-correlation and its related NOCC at each subsurface position form a new approach to determine PSRA for RTM artifacts. Using NOCC values, the refection angle of 55 degrees was determined as PSAR at which the RTM artifacts often start to appear. Finally, a new imaging condition based on the down- and upgoing wave felds and a new weighting function were proposed to suppress RTM artifacts. The new imaging condition can maintain the desired information and suppress artifacts properly for the angle domain of 55° to 90°. A key point in the suppressing process is the direct relationship between refection angle and artifact production where each refection angle in the domain of 55° to 90° can produce a diferent amount of artifacts. Therefore, the proposed imaging condition is able to designate a suitable weight for each refection angle to properly maintain the desired amplitude and suppress artifacts.
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Relative locations of recurrent earthquakes can be recovered from values of cross-correlation coefficients between their waveforms at a single station, provided that an idea of Menke (1999) that the values depend inversely exponentially from separation between the sources is true. An algorithm developed in Gnyp (2013) based on this idea was applied here for recovering relative locations of the two groups of the 2005-2006 recurrent earthquakes in Mukacheve, Ukraine, from the sets of crosscorrelation coefficients between their records at the four local network stations to find out whether the locations were in principle reproducible independently at each of the stations, at epicentral distances from about 6 to 64 km. The resulting sets of locations occurred in good agreement with each other, which may be considered as an experimental evidence for validity of the Menke’s dependence over the corresponding range of distances. The reproducibility of relative locations has been analyzed in terms of existence and uniqueness of the inverse problem’s solution, and in connection with data completeness and the influence of noise on it.
Due to the increasingly complex market situation characterized by the growing variability of its determinants, making accurate decisions is riddled with an increasing risk of error. Widely used economic methods for analyzing market phenomena with a trajectory of time series has proved insufficient in many cases. Hence, it becomes necessary to seek more precise analytic methods, based on which it is be possible to obtain more precise mapping and relations in real-life activities. The goal of the present study is to apply the time-frequency analysis in the domain of real estate. Based on the application of, among others, Savitzky-Golay filtering, spectral density analysis, or cross-correlation, the time-frequency analysis will render it possible to precisely identify the parameters that selectively determine the housing market. The obtained results will make it possible to decrease the informational gap in the investment decision-making process in the housing market.
PL
Ze względu na coraz bardziej złożoną sytuację rynkową, charakteryzującą się rosnącą zmiennością determinantów ją określających, podejmowanie trafnych decyzji jest obarczone zwiększającym się ryzykiem popełnienia błędu. Metody stosowane w naukach ekonomicznych do analizy zjawisk rynkowych mających przebiegi szeregów czasowych stają się niewystarczające do poprawnego modelowania zjawisk rynkowych. Konieczne staje się poszukiwanie precyzyjniejszych metod analitycznych, pozwalających uzyskać dokładniejsze odwzorowania i zależności występujące w sferze działań realnych. Celem badań jest zastosowanie analizy czasowo-częstotliwościowej w sektorze nieruchomości. Analiza ta, bazująca na wykorzystaniu m.in. filtracji Savitky̕ego-Golaya, analizy widmowej czy korelacji krzyżowej, pozwoli możliwie precyzyjnie sparametryzować wybrane determinanty wpływające na rynek nieruchomości mieszkaniowych. Otrzymane wyniki pozwolą na zmniejszenie luki informacyjnej w podejmowaniu decyzji inwestycyjnych na rynku nieruchomości mieszkaniowych.
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The aim of the study was to establish the strength and direction of the relationship between daily temperature of river water and air with the use of selected estimation methods. The relationship was assessed for the River Noteć and its tributaries (Western Poland), using the cross-correlation function and Granger causality. The study established cause-and-effect relations for “water–air” and “air–water” directions of influence. It was confirmed that forecasting the pattern of flowing water temperature from changes in air temperature yields better results when done based on data from the previous day. Results of modelling the relationship between data series with the use of the linear and natural cubic splines models confirmed the presence of a nonlinear relation. It was also established that there is a statistically significant correlation of random fluctuations for both temperature series on the same days. This made it possible to confirm the occurrence of short-term connections between water and air temperature. The results can be used to determine the qualities of thermal regimes and to predict temperature of river waters in the conditions of climate change.
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