In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed poin...In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.展开更多
The undulation and characteristics of the Lehmann discontinuity at the base of the Low Velocity Zone in the upper mantle are significant for understanding the coupling between the lithosphere and asthenosphere, and co...The undulation and characteristics of the Lehmann discontinuity at the base of the Low Velocity Zone in the upper mantle are significant for understanding the coupling between the lithosphere and asthenosphere, and corresponding geodynamic processes. Vertical waveform data from six earthquakes with focal depths between 75 and 150 km and magnitudes Mb 5.0–6.0 since 2004 were collected from the short-period Hi-net array. Selected waveform data were processed for each event network pair using the Nth-root slant stack method to retrieve the SdP conversion phases from the possible 220 km(Lehmann) discontinuity. The conversion points related to the SdP phases show that there is a clear and flat velocity interface around 230 km, suggesting that there is a sinking of the Lehmann discontinuity beneath Tonga with no obvious undulation. The 230 km depth of the Lehmann discontinuity in this location could be explained by an hypothesis of transition in the deformation mechanism from dislocation creep to diffusion creep.展开更多
The existence of discontinuities, the topographies of the 410 km and 660 km discontinuities, and the penetrations of subducting slabs near the 660 km discontinuities beneath the Sea of Okhotsk were studied using Nth r...The existence of discontinuities, the topographies of the 410 km and 660 km discontinuities, and the penetrations of subducting slabs near the 660 km discontinuities beneath the Sea of Okhotsk were studied using Nth root slant stack and digital records from networks in Germany and the western United States. Results show the obvious evidence for reflected and refractive phases associated with the 410 km and 660 km discontinuities. There may be discontinuities at other depths such as 150 km, 220 km and 520 km. The 410 km discontinuity is elevated and the 660 km discontinuity is depressed respectively, consistent with the expected thermal signature of the phase transitions. The subducting slab has penetrated into the lower mantle in the northern part of the Sea of Okhotsk, while it is stagnant on the 660 km discontinuity in the southern part.展开更多
The SdP, pdP and sdP phases are picked up with the Nth root slant stack method from the digital waveform data recorded by the networks and arrays in USA, Germany and Switzerland for the earthquakes occurring beneath I...The SdP, pdP and sdP phases are picked up with the Nth root slant stack method from the digital waveform data recorded by the networks and arrays in USA, Germany and Switzerland for the earthquakes occurring beneath Izu-Bonin and Japan Sea. The mantle discontinuities and the effects of subducting slab on the 660 km and 410 km discontinuities are studied. It is found that there are mantle discontinuities existing at the depths of 170, 220, 300, 410, 660, 850 and 1150 km. Beneath Izu-Bonin, the 410 km discontinuity is elevated, while the 660 km discontinuity is depressed; for both discontinuities, there are regionalized differences. Beneath Japan Sea, however, there is no depth variation of the 410 km discontinuity, and the 660 km discontinuity is depressed without obvious effect of the subducting slab.展开更多
文摘In this paper we propose two original iterated maps to numerically approximate the nth root of a real number. Comparisons between the new maps and the famous Newton-Raphson method are carried out, including fixed point determination, stability analysis and measure of the mean convergence time, which is confirmed by our analytical convergence time model. Stability of solutions is confirmed by measuring the Lyapunov exponent over the parameter space of each map. A generalization of the second map is proposed, giving rise to a family of new maps to address the same problem. This work is developed within the language of discrete dynamical systems.
基金sponsored by the National Natural Science Foundation of China (Grant No. 41074065)SinoProbe-Deep Exploration in China (Grant No. SinoProbe-07-04)
文摘The undulation and characteristics of the Lehmann discontinuity at the base of the Low Velocity Zone in the upper mantle are significant for understanding the coupling between the lithosphere and asthenosphere, and corresponding geodynamic processes. Vertical waveform data from six earthquakes with focal depths between 75 and 150 km and magnitudes Mb 5.0–6.0 since 2004 were collected from the short-period Hi-net array. Selected waveform data were processed for each event network pair using the Nth-root slant stack method to retrieve the SdP conversion phases from the possible 220 km(Lehmann) discontinuity. The conversion points related to the SdP phases show that there is a clear and flat velocity interface around 230 km, suggesting that there is a sinking of the Lehmann discontinuity beneath Tonga with no obvious undulation. The 230 km depth of the Lehmann discontinuity in this location could be explained by an hypothesis of transition in the deformation mechanism from dislocation creep to diffusion creep.
基金This work was supported by the Special Funds for the State Major Basic Research of China (Grant No. 95-13-04-06)the National Natural Science Foundation of China (Grant No. 49874020)the Ph.D. Programs Foundation of the Ministry of Education of Chi
文摘The existence of discontinuities, the topographies of the 410 km and 660 km discontinuities, and the penetrations of subducting slabs near the 660 km discontinuities beneath the Sea of Okhotsk were studied using Nth root slant stack and digital records from networks in Germany and the western United States. Results show the obvious evidence for reflected and refractive phases associated with the 410 km and 660 km discontinuities. There may be discontinuities at other depths such as 150 km, 220 km and 520 km. The 410 km discontinuity is elevated and the 660 km discontinuity is depressed respectively, consistent with the expected thermal signature of the phase transitions. The subducting slab has penetrated into the lower mantle in the northern part of the Sea of Okhotsk, while it is stagnant on the 660 km discontinuity in the southern part.
基金the National Natural Science Foundation of China(Grant No.49874020) the Ph D Programs Foundation of Ministry of Education of China(Grant No.99000108).
文摘The SdP, pdP and sdP phases are picked up with the Nth root slant stack method from the digital waveform data recorded by the networks and arrays in USA, Germany and Switzerland for the earthquakes occurring beneath Izu-Bonin and Japan Sea. The mantle discontinuities and the effects of subducting slab on the 660 km and 410 km discontinuities are studied. It is found that there are mantle discontinuities existing at the depths of 170, 220, 300, 410, 660, 850 and 1150 km. Beneath Izu-Bonin, the 410 km discontinuity is elevated, while the 660 km discontinuity is depressed; for both discontinuities, there are regionalized differences. Beneath Japan Sea, however, there is no depth variation of the 410 km discontinuity, and the 660 km discontinuity is depressed without obvious effect of the subducting slab.
