Normalized impedance function and the straightforward inversion scheme for magnetotelluric data

This paper investigates the performance of normalized response function obtained by normalizing the Cagniard impedance function by a suitable factor and then rotating the phase by 45‡ to make it purely real for homogeneous half-space and equal to the square root of the half-space resistivity. Two apparent resistivity functions based on respectively the real and imaginary parts of this response function are proposed. The apparent resistivity function using the real part contains almost the same information as that yielded by the Cagniard expression while the one using the imaginary part qualitatively works as an indicator of the number of interfaces in the earth model. The linear straightforward inversion scheme (SIS), developed by the authors employing the concept of equal penetration layers, has been used to validate the proposed apparent resistivity functions. For this purpose, several synthetic and field models have been examined. Five synthetic models are studied to establish the veracity of the new functions and two well-studied published field data sets are inverted through SIS for comparison. We noticed that the new function and SIS compliment each other and lead to better understanding of the data information and model resolution.     

Estimation of Vertical Continuous Stochastic Parameters from Seismic Reflection Data

This paper presents a scheme to invert reflected seismic wave fields for vertical spatial statistics of the Earth’s continuous stochastic velocity distribution. The forward model is based on a single scattering theory, where a seismogram is modeled as a convolution of a source wavelet and stochastic reflectivity, which obeys a von Kármán autocorrelation function. Tests with synthetic data indicate that the method presented here recovers vertical characteristic length from seismic reflection data that is similar to that of the original velocity model; however, the inversion does not reliably recover the Hurst exponent, ν. The input wavelet’s power spectrum is a free parameter in the inversion and is estimated as well, but is band-limited relative to the original source wavelet. Noise degrades the quality of the estimates of the stochastic parameters such that the recovered stochastic parameters are biased according to the power spectrum of the noise.     

影响薄互层地震反射波特征因素分析

通过对楔状模型,两层,多层介质等厚或不等厚模型和实际井中反射系数序列的频谱分析,和对用不同主频不同类型,不同衰减系数子波的合成记录剖面的波形分析以及合成记录的频谱分析,初步认为,薄互层的单层时间厚度,子结构厚度是决定反射波特征,频谱特征的基础,薄互层的互层数,入射子波是重要的影响因素;在目前的常规地震勘探中,薄互层地震反射波多以时间不可分辨的面貌出现,因此为了得到特定薄互层结构的可分辨的最佳图像,     

An integrated multi-scale 3D seismic model of the Archaean Yilgarn Craton, Australia

The collection of a range of different seismic data types has greatly improved our understanding of the crustal architecture of Australia's Archaean Yilgarn Craton over the last few years. These seismic data include broadband seismic studies, seismic receiver functions, wide-angle recordings and mine-scale to deep seismic reflection transects. Each data set provides information on the three-dimensional (3D) tectonic model of the Yilgarn Craton from the craton scale through to the mine scale. This paper demonstrates that the integration and rationalisation of these different seismic data sets into a multi-scale 3D geological/seismic model, that can be visualised at once in a single software package, and incorporating all available data sets, significantly enhances this understanding. This enhanced understanding occurred because the integrated 3D model allowed easy and accurate comparison of one result against another, and facilitated the integrated questioning and interrogation across scales and seismic method. As a result, there are feedback questions regarding understanding of the individual seismic data sets themselves, as well as the Yilgarn Craton as a whole.The methodology used, including all the data sets in the model range, had to allow for the wide range of data sets, frequencies and seismic modes. At the craton scale, P-wave, S-wave and surface wave variations constrained the 3D lithospheric velocity model, revealing noticeable large-scale velocity variations within and across the craton. An interesting feature of the data, easily identified in 3D, is the presence of a fast S-wave velocity anomaly (> 4.8 km s^− 1) within the upper mantle. This velocity anomaly dips east and has a series of step-down offsets that coincide approximately with province and terrane boundaries of the Yilgarn Craton.One-dimensional receiver function profiles show variations in their crustal velocity across the craton. These crustal velocity variations are consistent with the larger-scale geological subdivision of the craton, and provide characteristic profiles for provinces and terranes. The receiver function results and the deep seismic reflection data both agree on the depth to the Moho, and both indicate an increase in Moho depth to the east. The 2D seismic refraction results in the south-west of the craton provide crustal thickness information, an indication of middle and lower crustal compositions, and information regarding the broad-scale architectural framework.At the province- and terrane-scale, the deep seismic reflection data and the mine-scale seismic data provide geometric constraints on crustal architecture, in particular the orientation of the region's fault systems as well as variations in the thickness of the granite–greenstone succession. Integration of the results from wide-angle seismic refraction data coincident with the deep seismic reflection data provided additional constraints on likely upper crustal lithologies.The integrated 3D seismic model implies the dominant geodynamic process involved the development of an orogenic belt that developed with a series of contractional (folding and thrusting) events, separated by equally important extensional events. The seismic reflection data in particular suggests that extensional movement on many shear zones was more common than previously thought.The seismic reflection data suggest that the dominant mineral systems involved deeply sourced fluid flowing up crustal-penetrating shear zones. These deeply sourced fluids were further focussed into sites located above fault-breached domal regions in the upper crust.     

基于A- CGAN的深反射地震数据随机噪声压制方法研究

基于深度学习的地震数据噪声压制方法是当前地震数据去噪处理的重要方向。深度学习方法突破了传统滤波处理的局限,在对常规地震数据的噪声压制中表现出效率高、信噪分离效果好的特点。但针对深部弱有效反射数据,当前的深度学习方法特征提取能力有限,难以取得较好的去噪效果。笔者等结合深反射地震数据特点,针对当前深度学习噪声压制方法在特征提取及对数据集依赖上的局限,提出了基于注意力循环生成对抗网络(Attention Cycle- Consistent Generative Adversarial Networks,A- CGAN)的深反射地震数据随机噪声压制方法。借助循环一致生成对抗网络(Cycle- Consistent Generative Adversarial Networks,Cycle- GAN)的域映射思想,降低对数据集的要求。为了构建适用于深反射地震数据的去噪网络,从3个方面对Cycle- GAN进行改进：在Cycle- GAN的生成器（去噪器）中加入残差结构和注意力机制,用于加深网络深度和提高其特征提取能力;在Cycle- GAN的鉴别器中使用块判决,提高鉴别精度和准确度;在损失函数部分加入感知一致性损失函数,提升网络模型恢复纹理细节信息的能力。通过合成地震数据和实际深反射地震数据测试,验证了优化算法的有效性,体现了良好的应用价值。     

基于A- CGAN的深反射地震数据随机噪声压制方法研究

基于深度学习的地震数据噪声压制方法是当前地震数据去噪处理的重要方向。深度学习方法突破了传统滤波处理的局限,在对常规地震数据的噪声压制中表现出效率高、信噪分离效果好的特点。但针对深部弱有效反射数据,当前的深度学习方法特征提取能力有限,难以取得较好的去噪效果。笔者等结合深反射地震数据特点,针对当前深度学习噪声压制方法在特征提取及对数据集依赖上的局限,提出了基于注意力循环生成对抗网络(Attention Cycle- Consistent Generative Adversarial Networks,A- CGAN)的深反射地震数据随机噪声压制方法。借助循环一致生成对抗网络(Cycle- Consistent Generative Adversarial Networks,Cycle- GAN)的域映射思想,降低对数据集的要求。为了构建适用于深反射地震数据的去噪网络,从3个方面对Cycle- GAN进行改进：在Cycle- GAN的生成器（去噪器）中加入残差结构和注意力机制,用于加深网络深度和提高其特征提取能力;在Cycle- GAN的鉴别器中使用块判决,提高鉴别精度和准确度;在损失函数部分加入感知一致性损失函数,提升网络模型恢复纹理细节信息的能力。通过合成地震数据和实际深反射地震数据测试,验证了优化算法的有效性,体现了良好的应用价值。     

Estimating the number of casualties in earthquakes from early field reports and improving the estimate with time

We investigate the time dependence of the number of deaths reported through Internet after earthquakes and/or earthquake-generated tsunami. An approximate relation N(t) = N ₀ [1 − exp(−αt)] is used to describe such temporal variation, in which N(t) is the number of deaths reported at time t, N ₀ is the final number of deaths, and α is the coefficient reflecting the rescue process. We considered 12 earthquake cases since 2001 using the information from the web, which shows that the N-t relation approximates the data, and the logarithm of α is reversely proportional to the magnitude of earthquake, albeit with significant uncertainties. Quick and rough estimate of the final death toll can be made using this simple and approximate relation, with the empirical α-M relation as a reference. For the 12 cases under consideration, quick and rough estimate of fatalities can be obtained 2 days after the earthquake, fitting the real situation in the order of magnitudes. Although being very rough, this estimate can assist the emergency decision-making and can be revised as time lapses. When more and more data becomes available, curve fitting can provide both N ₀ and α at the same time. The method is tested against the data of the recent Yushu earthquake on April 14, 2010.     

Benford’s Law in Time Series Analysis of Seismic Clusters

Benford’s analysis is applied to the recurrence times of approximately 17,000 seismic events in different geological contexts of Italy over the last 6 years, including the Mt. Etna volcanic area and the seismic series associated with the destructive M _w 6.3, 2009 L’Aquila earthquake. A close conformity to Benford’s law and a power-law probability distribution for the recurrence times of consecutive events is found, as typical of random multiplicative processes. The application of Benford’s law to the recurrence event times in seismic series of specific seismogenic regions represents a novel approach, which enlarges the occurrence and relevance of Benford-like asymmetries, with implications on the physics of natural systems approaching a power law behaviour. Moreover, we propose that the shift from a close conformity of Benford’s law to Brownian dynamics, observed for time separations among non-consecutive events in the study seismic series, may be ruled by a periodical noise factor, such as the effects of Earth tides on seismicity tuning.     

Methods and applications of 3-D wave equation common-azimuth prestack migration

To tackle the difficulties of a 3-D full volume prestack migration based on the double-square-root (DSR) one-way wave equation in practical applications, the common-azimuth migration approach is first discussed using dual-domain wave propagators under the theoretical frame of crossline common-offset migration. Through coordinate transforming, a common-azimuth prestack tau migration technology that recursively continues the source and receiver wavefields and picks up the migrated results in the two-way vertical traveltime (tau) direction is developed. The migrations of synthetic data sets of SEG/EAGE salt model prove that our common-azimuth migration approaches are effective in both depth and tau domains. Two real data examples show the advantages of wave-theory based prestack migration methods in accuracy and imaging resolution over the conventional Kirchhoff integral methods. Translated from Oil Geophysical Prospecting, 2006, 41(6): 629–634 [译自: 石油地球物理勘探]     

On the Validity of Commonly Used Covariance and Variogram Functions on the Sphere

Covariance and variogram functions have been extensively studied in Euclidean space. In this article, we investigate the validity of commonly used covariance and variogram functions on the sphere. In particular, we show that the spherical and exponential models, as well as power variograms with 0<α≤1, are valid on the sphere. However, two Radon transforms of the exponential model, Cauchy model, the hole-effect model and power variograms with 1<α≤2 are not valid on the sphere. A table that summarizes the validity of commonly used covariance and variogram functions on the sphere is provided.     

Pressure-induced phase transition in synthetic trioctahedral Rb-mica

 The crystal structure of a synthetic Rb analog of tetra-ferri-annite (Rb–TFA) 1M with the composition Rb_0.99Fe²⁺ _3.03(Fe³⁺ _1.04 Si_2.96)O_10.0(OH)_2.0 was determined by the single-crystal X-ray diffraction method. The structure is homooctahedral (space group C2/m) with M1 and M2 occupied by divalent iron. Its unit cell is larger than that of the common potassium trioctahedral mica, and similar lateral dimensions of the tetrahedral and octahedral sheets allow a small tetrahedral rotation angle α=2.23(6)°. Structure refinements at 0.0001, 1.76, 2.81, 4.75, and 7.2 GPa indicate that in some respects the Rb–TFA behaves like all other micas when pressure increases: the octahedra are more compressible than the tetrahedra and the interlayer is four times more compressible than the 2:1 layer. However, there is a peculiar behavior of the tetrahedral rotation angle α: at lower pressures (0.0001, 1.76, 2.81 GPa), it has positive values that increase with pressure [from 2.23(6)° to 6.3(4)°] as in other micas, but negative values −7.5(5)° and −8.5(9)° appear at higher pressures, 4.75 and 7.2 GPa, respectively. This structural evidence, together with electrostatic energy calculations, shows that Rb–TFA has a Franzini A-type 2:1 layer up to at least 2.81 GPa that at higher pressure yields to a Franzini B-type layer, as shown by the refinements at 4.75 and 7.2 GPa. The inversion of the α angle is interpreted as a consequence of an isosymmetric displacive phase transition from A-type to B-type structure between 2.81 and 4.75 GPa. The compressibility of the Rb–TFA was also investigated by single-crystal X-ray diffraction up to a maximum pressure of 10 GPa. The lattice parameters reveal a sharp discontinuity between 3.36 and 3.84 GPa, which was associated with the phase transition from Franzini-A to Franzini-B structure. Received: 21 October 2002 / Accepted: 25 February 2003     

Effect of interface characteristics on the influence coefficients of an embedded circular footing under horizontal and moment loading

By means of a semi-analytical FE approach an embedded circular footing under monotonic horizontal and moment loading is studied. In a non-homogeneous soil whose shear modulus is characterized by a power law variation with depth, horizontal, rocking and coupled modes of displacement, expressed in terms of influence factors are thoroughly examined. The exponent α that controls the shape of the stiffness variation with depth is termed shear modulus factor. Surface influence coefficients are considered for the situations where the interface between the soil and the footing is either perfectly rough or perfectly smooth. First, results of semi-analytical FE analysis in the case of rough footing are established and compared with those of another numerical method. Results of comparison show good agreement. Then, for different values of α the surface influence coefficients are presented for an embedded footing in perfect smooth contact with soil. The metacentre is referred to as the depth at which there is no coupling between the sliding and the rocking modes of footing deformations. Expressions for location and horizontal influence coefficient corresponding to this particular depth are developed and their variations with α examined. The paper finishes by showing the effect of interface conditions on the soil normal stresses developed beneath the embedded circular footing for the case of loading applied at the footing top.     

Numerical modeling of the development of a preferentially leached layer on feldspar surfaces

Compositional depth profiles in the leached layer of feldspar surfaces are usually interpreted by using analytical solutions which introduce oversimplifying assumptions. Here we present a general multicomponent interdiffusion numerical model for simulating cation release from a preferentially leached layer on feldspar surfaces in acid solutions. The numerical model takes into account interdiffusion, dissolution of the solid phase (represented by a moving boundary problem), and adsorption in the leached layer. Effective diffusion coefficients of ions vary with concentration along the leached layer. Governing equations of ions diffusion in the leached layer are solved numerically with a finite element method implemented in a multicomponent reactive transport code, CORE^3D, previously verified against analytical solutions of compositional depth profiles. The numerical model is tested with published X-ray photoelectron spectroscopy (XPS) data on early development of compositional profiles of labradorite leached in pH 2 HCl solutions. Model parameters are estimated by fitting depth profiles of Ca and Al measured at 12, 26, 48, 72, and 143 h. The best fit is achieved with tracer diffusion coefficients of 4 × 10⁻¹⁸, 8 × 10⁻¹⁷, 3.4 × 10⁻¹⁷, and 7 × 10⁻¹⁸ cm²/s for H, Na, Ca, and Al, respectively, which fall within the range of values reported in the literature. Our estimate of the retreat velocity corresponding to the dissolution rate is 3 × 10⁻¹³ cm/s. Results of sensitivity runs show that computed compositional profiles are sensitive to most model parameters.     

High-temperature thermal expansion of lime, periclase, corundum and spinel

The high-temperature cell parameters of lime (CaO), periclase (MgO), corundum (Al₂O₃), and spinel (MgAl₂O₄) have been determined from 300 up to 3000 K through X-ray diffraction experiments with synchrotron radiation. The good agreement found with dilatometric results suggests that vacancy-type defects do not make a large contribution to thermal expansion for these oxides, even near the melting point, justifying the use of X-ray diffraction for determining volume properties up to very high temperatures. Thermal expansion coefficients were determined from the measured cell volumes with equations of the form α=α₀ + α₁ T + α₂/T ². Along with available isobaric heat capacity and compressibility data, these derived coefficients clearly show that anharmonic effects contribute little to the isochoric heat capacities (C _v ) of CaO, MgO, and Al₂O₃, which do not depart appreciably from the 3nR Dulong and Petit limit. Received: 31 March 1999 / Revised, accepted: 23 June 1999     

An investigation of upper mantle heterogeneity beneath the Archaean and Proterozoic crust of western Canada from Lithoprobe controlled-source seismic experiments

Observations of upper mantle reflectivity at numerous locations around the world have been linked to the presence of a heterogeneous distribution of rock types within a broad layer of the upper mantle. This phenomenon is observed in wide-angle reflection data from Lithoprobe's Alberta Basement Transect [the SAREX and Deep Probe experiments of 1995] and Trans-Hudson Orogen Transect [the THoRE experiment of 1993]. SAREX and Deep Probe image the Archaean lithosphere of the Hearne and Wyoming Provinces, whereas THoRE images the Archaean and Proterozoic lithosphere of the Trans-Hudson Orogen and neighbouring areas.Finite-difference synthetic seismograms are used to constrain the position and physical properties of the reflective layer. SAREX/Deep Probe modelling uses a 2-D visco-elastic finite-difference routine; THoRE modelling uses a pseudospectral algorithm. In both cases, the upper mantle is parameterized in terms of two media. One medium is the background matrix; the other is statistically distributed within the first as a series of elliptical bodies. Such a scheme is suitable for modelling: (1) variations in lithology (e.g., a peridotite matrix with eclogite lenses) or (2) variations in rheology (e.g., lenses of increased strain within a less strained background).The synthetic seismograms show that the properties of heterogeneities in the upper mantle do not change significantly between the two Lithoprobe transects. Beneath the Trans-Hudson Orogen in Saskatchewan, the layer is best modelled to lie at depths between 80 and 150 km. Based on observations from perpendicular profiles, anisotropy of the heterogeneities is inferred. Beneath the Precambrian domains of Alberta, 400 km to the west, upper mantle heterogeneities are modelled to occur between depths of 90 and 140 km. In both cases the heterogeneous bodies within the model have cross-sectional lengths of tens of kilometers, vertical thicknesses less than 1 km, and velocity contrasts from the background of − 0.3 to − 0.4 km/s. Based on consistency with complementary data and other results, the heterogeneous layer is inferred to be part of the continental lithosphere and may have formed through lateral flow or deformation within the upper mantle.     

Structural thermal behavior of paragonite and its dehydroxylate: a high-temperature single-crystal study

 The lattice constants of paragonite-2M₁, NaAl₂(AlSi₃)O₁₀(OH)₂, were determined to 800 °C by the single-crystal diffraction method. Mean thermal expansion coefficients, in the range 25–600 °C, were: α_a = 1.51(8) × 10⁻⁵, α_b = 1.94(6) × 10⁻⁵, α_c = 2.15(7) ×  10⁻⁵ °C⁻¹, and α_V = 5.9(2) × 10⁻⁵ °C⁻¹. At T higher than 600 °C, cell parameters showed a change in expansion rate due to a dehydroxylation process. The structural refinements of natural paragonite, carried out at 25, 210, 450 and 600 °C, before dehydroxylation, showed that the larger thermal expansion along the c parameter was mainly due to interlayer thickness dilatation. In the 25–600 °C range, Si,Al tetrahedra remained quite unchanged, whereas the other polyhedra expanded linearly with expansion rate proportional to their volume. The polyhedron around the interlayer cation Na became more regular with temperature. Tetrahedral rotation angle α changed from 16.2 to 12.9°. The structure of the new phase, nominally NaAl₂ (AlSi₃)O₁₁, obtained as a consequence of dehydroxylation, had a cell volume 4.2% larger than that of paragonite. It was refined at room temperature and its expansion coefficients determined in the range 25–800 °C. The most significant structural difference from paragonite was the presence of Al in fivefold coordination, according to a distorted trigonal bipyramid. Results confirm the structural effects of the dehydration mechanism of micas and dioctahedral 2:1 layer silicates. By combining thermal expansion and compressibility data, the following approximate equation of state in the PTV space was obtained for paragonite: V/V ₀ = 1 + 5.9(2) × 10⁻⁵ T(°C) − 0.00153(4) P(kbar). Received: 12 July 1999 / Revised, accepted: 7 December 1999     

Three-dimensional visualization of orbital forcing and climatic repsonse: Interactively exploring the pacemaker of the ice ages

 Recent developments in continuous core-logging techniques now permit us to recover the high-resolution time series necessary for the detailed spectral analyses of paleoclimatic proxy records. When applied to long records recovered by scientific drilling (5–10 Ma) they enable us to look at the long-term history and evolution of the ocean's response to orbital forcing. A serious limitation in these studies is the need to display the complex, multidimensional spatial and temporal interactions of the ocean-climate system in an easily comprehensible manner. We have addressed this issue by developing a series 3D visualization tools which permit visualization of the role of the orbital parameters in determining the latitudinal variation of insolation as well as the interactive exploration of multidimensional data sets. The ORBITS tool allows us to visualize the effect of orbital eccentricity, precession, and tilt on the latitudinal distribution of insolation on the earth at the solstices and the equinoxes for any time over the past 5 Ma (for Berger's orbital model) or 10 Ma (for Laskar's orbital model). The effect of the orbital parameters on insolation can be viewed individually, in pairs, or all three together. By moving the model steadily through time, the rate at which orbitally induced changes in insolation occur can also be visualized. To look at the ocean's response to orbital forcing we take the long time series generated from our paleoclimatic proxies and calculate their spectrum over a fixed, but sliding, time window. To view the complex multidimensional relationships found in these evolutionary spectral analyses, we use another interactive 3D data exploration tool developed at the University of New Brunswick (Canada). This tool (FLEDERMAUS) uses a six-degrees-of-freedom input device (BAT) and a series of software modules for color coding, shading, and rendering complex data sets, to allow the user to interactively "fly" through the multidimensional data. Through the use of color, texture, and 3D position, as many as six or seven variables can be explored in a simple and intuitive manner. With special liquid-crystal-display glasses, the scene can be viewed in true "stereo." We use these tools to explore the relationship between orbital forcing and the response of the benthic isotope and calcium carbonate record at ODP Site 846 (90°W and 5°S) This analysis shows an equatorial Pacific carbonate record which has a large component of linear response to tilt, but little linear response to precession. There is a major shift in response, from a carbonate-dominated response to an isotope (ice volume)-dominated response at approximately 4.5 Ma, and as expected, there is a large nonlinear response at the lower frequencies (400 and 100 kyr) during the past 800 kyr to 1 Ma Received: 22 June 1995 / Accepted: 29 January 1996     

弹性层系的反射系数正演

应用层系位移和应力递推公式，针对固体多层介质，导出了纵、横波反射、透射系数公式，并对新疆某油田模型进行了试算，探讨了反射系数与入射角之间的变化规律。结果表明，该区含气砂岩易于检测。通过zoeppritz方程和垂直入射的反射系数解析式分别对单界面和本文模型进行了检验，结果是完全一致的。     

Impact of modification of initial cyclonic structure on the prediction of a cyclone over the Arabian Sea

Most tropical cyclones have very few observations in their vicinity. Hence either they go undetected in standard analyses or are analyzed very poorly, with ill defined centres and locations. Such initial errors obviously have major impact on the forecast of cyclone tracks using numerical models. One way of overcoming the above difficulty is to remove the weak initial vortex and replace it with a synthetic vortex (with the correct size, intensity and location) in the initial analysis. The objective of this study is to investigate the impact of introducing NCAR–AFWA synthetic vortex scheme in the regional model MM5 on the simulation of a tropical cyclone formed over the Arabian Sea during November 2003. Two sets of numerical experiments are conducted in this study. While the first set utilizes the NCEP reanalysis as the initial and lateral boundary conditions, the second set utilizes the NCAR–AFWA synthetic vortex scheme. The results of the two sets of MM5 simulations are compared with one another as well as with the observations and the NCEP reanalysis. It is found that inclusion of the synthetic vortex has resulted in improvements in the simulation of wind asymmetries, warm temperature anomalies, stronger vertical velocity fields and consequently in the overall structure of the tropical cyclone. The time series of the minimum sea level pressure and maximum wind speed reveal that the model simulations are closer to observations when synthetic vortex was introduced in the model. The central minimum pressure reduces by 17 hPa while the maximum wind speed associated with the tropical cyclone enhances by 17 m s ⁻¹ with the introduction of the synthetic vortex. While the lowest central pressure estimated from the satellite image is 988 hPa, the corresponding value in the synthetic vortex simulated cyclone is 993 hPa. Improvements in the overall structure and initial location of the center of the system have contributed to considerable reduction in the vector track prediction errors ie. 642 km in 24 h, 788 km in 48 h and 1145 km in 72 h. Further, simulation with the synthetic vortex shows realistic spatial distribution of the precipitation associated with the tropical cyclone.