Interferometry basics in practice: Exercises

The following exercises aim to learn the link between the object intensity distribution and the corresponding visibility curves of a long-baseline optical interferometer. They are also intended to show the additional constraints on observability that an interferometer has.This practical session is meant to be carried out with the ASPRO software, from the Jean-Marie Mariotti Center, but can also be done using other observation preparation software, such as viscalc from ESO.There are two main parts with series of exercises and the exercises corrections. The first one aims at understanding the visibility and its properties by practicing with simple examples, and the second one is about UV coverage.     

All you ever wanted to know about optical long baseline stellar interferometry, but were too shy to ask your adviser

I try to present a small view of the properties and issues related to astronomical interferometry observations. I recall a bit of history of the technique, give some basic assessments to the principle of interferometry, and finally, describe physical processes and limitations that affect optical long baseline interferometry and which are, in general, very useful for everyday work. Therefore, this text is not intended to perform strong demonstrations and show accurate results, but rather to transmit the general “feeling” one needs to have to not be destabilised by the first contact to real world interferometry.     

Imaging pre‐existing natural fractures using microseismic data

In hydraulic fracturing treatments, locating not only hydraulic fractures but also any pre‐existing natural fractures and faults in a subsurface reservoir is very important. Hydraulic fractures can be tracked by locating microseismic events, but to identify the locations of natural fractures, an additional technique is required. In this paper, we present a method to image pre‐existing fractures and faults near a borehole with virtual reverse vertical seismic profiling data or virtual single‐well profiling data (limited to seismic reflection data) created from microseismic monitoring using seismic interferometry. The virtual source data contain reflections from natural fractures and faults, and these features can be imaged by applying migration to the virtual source data. However, the imaging zone of fractures in the proposed method is strongly dependent on the geographic extent of the microseismic events and the location and direction of the fracture. To verify our method, we produced virtual reverse vertical seismic profiling and single‐well profiling data from synthetic microseismic data and compared them with data from real sources in the same relative position as the virtual sources. The results show that the reflection travel times from the fractures in the virtual source data agree well with travel times in the real‐source data. By applying pre‐stack depth migration to the virtual source data, images of the natural fractures were obtained with accurate locations. However, the migrated section of the single‐well profiling data with both real and virtual sources contained spurious fracture images on the opposite side of the borehole. In the case of virtual single‐well profiling data, we could produce correct migration images of fractures by adopting directional redatuming for which the occurrence region of microseismic events is divided into several subdivisions, and fractures located only on the opposite side of the borehole are imaged for each subdivision.     

Wave dispersion in high‐rise buildings due to soil–structure interaction

Nonparametric techniques for estimation of wave dispersion in buildings by seismic interferometry are applied to a simple model of a soil–structure interaction (SSI) system with coupled horizontal and rocking response. The system consists of a viscously damped shear beam, representing a building, on a rigid foundation embedded in a half‐space. The analysis shows that (i) wave propagation through the system is dispersive. The dispersion is characterized by lower phase velocity (softening) in the band containing the fundamental system mode of vibration, and little change in the higher frequency bands, relative to the building shear wave velocity. This mirrors its well‐known effect on the frequencies of vibration, i.e. reduction for the fundamental mode and no significant change for the higher modes of vibration, in agreement with the duality of the wave and vibrational nature of structural response. Nevertheless, the phase velocity identified from broader band impulse response functions is very close to the superstructure shear wave velocity, as found by an earlier study of the same model. The analysis reveals that (ii) the reason for this apparent paradox is that the latter estimates are biased towards the higher values, representative of the higher frequencies in the band, where the response is less affected by SSI. It is also discussed that (iii) bending flexibility and soil flexibility produce similar effects on the phase velocities and frequencies of vibration of a building. Copyright © 2014 John Wiley & Sons, Ltd.     

基于逆虚折射干涉法有效提取近地表弱地震信号

在地震勘探中,地形起伏和近地表速度的剧烈变化会导致地震波旅行时的扰动,通常会通过折射波信息来估算和消除这些扰动.本文在虚折射的基础上提出了逆虚折射干涉法,通过虚折射波场和原始折射波场的互相关,并对所有位于固定相位点上的检波点进行叠加,重构出逆虚折射波场.通过逆虚折射与超级虚折射的叠加,保证了不同偏移距下折射波振幅恢复的一致性,显著提高折射波的信噪比,有效提取弱信号.同时,本文采用反褶积干涉法来压制由于互相关和褶积产生的子波旁瓣的影响,弥补低频和高频能量的损失,改善恢复的折射波场的稳定性和分辨率.该新方法不需要知道近地表复杂速度模型的信息,可以将虚折射的勘探孔径恢复到原始地震记录的最大孔径.合成资料和实际资料的计算结果表明,基于反褶积的逆虚折射干涉法能够从低信噪比的资料中,有效恢复出折射波信息.     

Walkaway VSP数据的联合相干成像(英文)

本文将相干成像用于WVSP数据的一次反射波和下行地表多次波的成像中,通过对叠加次数分布的分析,发现一次反射波相干成像的成像范围小但在井位置处的叠加次数高;下行地表多次波相干成像的成像范围大而在井位置处的叠加次数少。基于此,本文尝试利用一种WVSP的联合相干成像方法来解决这一问题。该方法利用WVSP的直达波与下行地表多次波和直达波与一次反射波来进行联合相干成像。这种联合相干成像方法在有效拓宽成像面积的同时增加了覆盖次数(特别是在井旁),使干涉记录中的虚假同相轴得到了有效地压制,提高了成像剖面的信噪比,使成像结果更加可靠。正演模拟得到的WVSP合成记录和野外实际采集到的WVSP数据处理结果均表明这种方法的有效性。     

Equipartitioning is not sufficient for Green's function extraction

The extraction of the Earth's Green's function from field fluctuations is a rapidly growing area of research.The principle of Green's function extraction is often related to the requirement of equipartitioning,which stipulates that the energy of field fluctuations is distributed evenly in some sense.We show the meaning of equipartitioning for a variety of different formulations for Green's function retrieval.We show that equipartitioning is not a sufficient condition,and provide several examples that illustrate this point.We discuss the implications of lack of equipartitioning for various schemes for the reconstruction of the Green's function in seismology.The theory for Green's function extraction is usually based on a statistical theory that relies on ensemble averages.Since there is only one Earth,one usually replaces the ensemble average with a time average.We show that such a replacement only makes sense when attenuation is taken into account,and show how the theory for Green's function extraction for oscillating systems can be extended to incorporate attenuation.     

Deformation patterns associated with the M5.9 Athens (Greece) earthquake of 7 September 1999

The static displacement field of the Athens 1999 earthquake has been numerically modeled by a BEM method and analysed from SAR interferometry images with compatible results: (a) for a fault that reaches the surface the subsidence field coincides with the hangingwall domain of the Fili neotectonic normal fault with maximum amplitude, d _max, 5.5–7 cm, which is consistent with the possibly co-seismic displacement of 6–10 cm observed in the field, the average fault dislocation of 5–8 cm found by the application of circular source models, and the displacement up to 6 cm predicted by empirical relations between magnitude and displacement; the field of uplift covers the footwall domain of the fault with d _max1.5 cm;d gradually decreases with distance from the fault at a gradient of 0.4 cm/km, (b) for a blind fault d _max is only 1.8 and 0.3 cm in the hangingwall and footwall, respectively, and the decay gradient becomes 0.15 cm/km, (c) the total deformation area is 15 km × 15 km and the Fili fault, with a preferred mean dip of 60°, constitutes the natural boundary between the subsidence and uplift areas. The macroseismic field pattern is similar with that of the static ground deformation. The majority of intensity values VI (MM and EMS-98 scales), are distributed within the hangingwall of the Fili fault, while the highest intensities (VIII and IX) concentrate very close to the Fili fault within its hangingwall domain. A gradual decrease of the intensities with the distance from the Fili fault is evident. Because of the similarity between the intensity distribution pattern and the static ground deformation pattern, we make the hypothesis that the latter predicts well enough the main characteristics of the former although the ground displacement is dominated by relatively low frequency as compared to the ground acceleration.     

Evidences for extended sources and temporal modulations in molecular observations of C/1995 O1 (Hale-Bopp) at the IRAM interferometer

Comet C/1995 O1 (Hale-Bopp) has been observed on October 5 and 25, 1996 and from March 6 to March 22, 1997 with the Institut de Radioastronomie Millimétrique (IRAM) interferometer at Plateau de Bure (France). Millimetre lines of HCN,HNC, CO, H₂CO, CH₃OH, H₂S, CS and SO were mapped with spatial resolutions of 1.5–3.5 arc sec. These observations allow us to investigate whether these species are released by the nucleus or produced in the coma by extended sources or photo-processes. The brightness distribution of the HCN J (1-0) line is consistent with release from the nucleus. The HNC J (1-0) distribution deviates from that of HCN in the innermost coma, and indicates production of HNC in the coma. This is in agreement with the heliocentric variation of the HNC/HCN ratio (Biver et al., 1997, Science 275, 1915; Irvine et al., 1998, this issue) and formation by chemical reactions (Rodgers and Charnley, 1998, Ap. J. 501, L227; Irvine et al., 1998, Nature 393, 547). There is clear evidence that SO is a photo dissociation product. The observations also confirm that H₂CO is mainly produced by an extended source, as first evidenced in comet P/Halley. The contribution of the nucleus to the total H₂CO production rate does not exceed 6%. The molecular lines have also been monitored hourly with the five antennas of the interferometer in single-dish mode. The line velocity shifts show aperiodic modulation linked to the nucleus rotation. The amplitude of the modulation differs from one species to another. The periodic modulation seen for the CO J (2-1) line on March 11 suggests that a significant fraction of CO is released continuously night and day by an active source situated at equatorial latitudes on the nucleus surface. This revised version was published online in July 2006 with corrections to the Cover Date.     

Monitoring vertical deformation due to water pumping in the city of Paris (France) with differential interferometry

The Saint-Lazare area in Paris (France) has undergone important water pumping for the construction of the underground Haussmann–Saint-Lazare station for the EOLE subway line. This paper presents the monitoring of the small surface displacements related to this pumping activity, by classical SAR interferometry. Piezometric measurements provided on 87 piezometers by SNCF and IGC as well as precise levelling data acquired on 626 points by SNCF are also examined. Their comparison with interferometric results shows their good agreement and complementarity, as well as the potential ‘operationality’ of SAR interferometric approach in such a study. To cite this article: B. Fruneau et al., C. R. Geoscience 337 (2005).