A study about a dome near Yerkes: observations, measurements and classification

Transcription

1 A study about a dome near Yerkes: observations, measurements and classification By Raffaello Lena, Cristian Fattinnanzi, Jim Phillips and Christian Wöhler GLR group 1) Introduction The study of domes provides lunar observers with an opportunity for systematic observations of the Moon. Our activity has shown both the elusive nature of these volcanic structures and the utility of CCD imaging and digital image analysis in the elucidation of their character [1]. The Crisium basin is located just northeast of Mare Tranquillitatis. The basin is of Nectarian epoch, while the mare material is of the Upper Imbrian epoch [2]. On the western rim of the Mare Crisium lies the ghost crater Yerkes, at longitude 51.7 east and latitude 14.6 north (Xi Eta 0.252). Many observers have studied the dome field near the crater Yerkes and the ALPO Lunar Dome list reports several domes (Table 1). The region near Yerkes was very well monitored by the GLR group. In this study we report measurements and include CCD images of the lunar dome located at E and N (Xi Eta 0.256). This has made it possible to extract additional information (slope and height) for its classification and interpretation in geologic terms. Finally we report also an overview about the last published ALPO catalogue (1992). The ALPO have tried over the years to eliminate errors and duplication, but some duplicate sightings of the dome remain in the catalogue. 2) Instruments and measurements Table 1 summarizes the domes, extracted from the ALPO catalogue, located near the crater Yerkes. Table 2 lists the 5 observers who supplied a total of 9 observations. For each of the observations, the local lunar altitude of the Sun (H) and the Sun's selenographic colongitude (C) were calculated using the Lunar Observer's Tool kit by H. D. Jamieson (ALPO) [3]. Table 3 reports the diameter and the position of the dome. The image of Fig. 2 was computer resampled in order to minimize the E-W perspective distortion and it was superimposed onto LAC s

2 map (chart #62). Furthermore, the scale of the image was obtained (0.370 km per pixel) which allowed the diameter to be expressed in km. The images reported in Figs. 1-5 are oriented with north at the top and west (IAU) at the left. A 3D reconstruction was performed using the raw images taken with a webcam Vesta Pro (Figs. 1 and 2) and a ToUCam (Fig. 3). An actual gamma calibration was carried out for these images (γ = 0.8 for images shown in Figs. 1 and 2, and γ = 1.0 for the image shown in Fig. 3). Table 4 reports the measured values of height and slope. 3) Digital elevation map of the dome near Yerkes Generating an elevation map of a part of the lunar surface requires its three-dimensional (3D) reconstruction. The Clementine spacecraft entirely mapped the lunar surface in 3D at a resolution on the ground of 0.25 degrees in longitude and latitude, i. e. better than 7.5 km, by means of laser altimetry. Although the obtained profiles nicely show large-scale features such as the huge South Pole Aitken Basin on the lunar far side, they do not reveal the 3D structure of the lunar surface on small, such as kilometre, scales [4]. Parts of the lunar surface have been mapped in 3D based on a stereoscopic analysis of image pairs acquired by the Clementine spacecraft and from the Apollo command modules orbiting the Moon [5]. The resolution of the obtained surface profiles is 1 km on the ground, while the accuracy of the derived elevation values is not better than 100 m, which is not sufficient for measuring the height of lunar domes. We will therefore generate an elevation map of the dome near Yerkes based on our telescopic CCD images. A well-known image-based method for three-dimensional surface reconstruction is shape from shading (SFS). It makes use of the fact that surface parts inclined towards the light source appear brighter than surface parts inclined away from it apart from binocular vision, shading is one of the most important cues on which human vision is based. The SFS approach aims at deriving the orientation of the surface at each image location by using a model of the reflectance properties of the surface and knowledge about the illumination conditions, finally leading to an elevation value for each image pixel [6]. In this paper we make use of the algorithm described in detail in section 5.1 of Ref. [6]. The shape from shading method requires accurate knowledge of the scattering properties of the surface in terms of the bidirectional reflectance distribution function (BRDF). A very simple model, the so-called Lambert model, assumes perfectly diffuse scattering, implying an intensity R L of scattered light according to R L (ρ, θ i ) = ρ cos θ i with ρ as the surface albedo and θ i as the angle between the surface normal and the direction of incident light. But the Lambert model does not correspond very well to the true scattering behaviour of the lunar surface. A much more appropriate relation is the physically motivated BRDF by Hapke [7] which is based on the theory of radiative transfer. It allows conclusions about certain surface properties such as average particle size, particle density, albedo of the surface material, or macroscopic surface roughness. Sets of Hapke parameters valid for the lunar regolith are given e. g. in [8]. It is not straightforward, however, to directly employ the Hapke model for 3D reconstruction purposes. Therefore, in many astrogeologic applications the simple, empirical Lunar-Lambert law is used:

3 R LL (ρ, θ i, θ e, α) = ρ [2 L(α) cos θ i / (cos θ i + cos θ e ) + (1 L(α)) cos θ i ] with θ e as the angle between the surface normal and the viewing direction and the Lunar-Lambert parameter L(α) as an empirical value depending on the phase angle α. This model is a weighted sum of the Lommel-Seeliger and the Lambert BRDF. Given a suitable choice of L(α), the Lunar- Lambert law fits the true scattering behaviour of a planetary surface equally well as the Hapke model. Values for L(α) have been tabulated in [9] for planetary surfaces with a wide range of regolith properties. For oblique illumination and perpendicular view we have cos θ i << cos θ e 1, such that R LL shows essentially the same behaviour as R L. The dome near Yerkes regarded in this paper, however, is situated far from the centre of the Moon' s apparent disk (θ e 50 ), where the Lunar-Lambert BRDF strongly differs from the Lambert model. The CCD images presented in this paper have been acquired under phase angles around 30, where Ref. [9] yields L(α) = 0.95 for a low-albedo surface with the Hapke parameters of the lunar regolith. For 3D reconstruction by means of SFS, it is necessary that the greyvalue G of a pixel is proportional to the intensity I of incident light. For many CCD cameras and especially webcams, this is not necessarily the case because it is often possible to adjust the gamma value manually from within the camera control software, such that the relation between greyvalue and intensity is governed by G ~ I γ. For the Philips webcams used for the images presented here, we performed a calibration of the gamma scale in the camera control software, relying on flatfield frames of varying intensities acquired with different neutral density filters. We estimate the remaining uncertainty of γ to ±0.1, which is taken into account for the confidence intervals of the derived height values for the dome. Table 1: Domes in Yerkes region reported in ALPO list. Dome Entry # Lunar orthographic coordinate Longitude ( ) Latitude ( ) Diameter (km) Remarks ξ η A Dumbbell shaped-2 domes (?) B No data C No data D Bisected by a cleft

4 Table 2: Contributing observers and instruments, where (M) and (E) refer to morning and evening illumination respectively. Observers telescope D and F/D type Number of submitted reports Fattinnanzi C. Newton webcam 2 (E) 250 mm f/5 Lena R. SC 200 mm f/10 and visual 2 (M) Refractor 100 mm f/15 Phillips J. Refractor 203 mm f/9 webcam 2 (E) Shaw B. Newton 250 mm f/6 webcam 2 (E) Wöhler C. Newton 200 mm f/6 webcam 1 (E) Table 3: Position and remarks of the dome described in the text. Lunar orthographic coordinate ξ η Longitude ( ) Latitude ( ) Diameter (km) Remarks Hemispherical with a summit depression Table 4: Measurements of the dome located at E and N. Date Hour (UT) H ( ) C ( ) Figure Scale Height Slope ( ) (km per pixel) (m) September 2, ± ± :12 UT December 29, ± ± :55 UT August 3, :22 UT ± ± 0.30

5 4) Observations Fig. 1 displays the dome under an evening illumination. This image was taken by C. Fattinnanzi on September 2, 2004, at 00:12 UT. Another image, here proposed as Fig. 2, was made by C. Fattinnanzi on December 29, 2004 at 00:55 UT. Fig. 3 shows an image taken by C. Wöhler on August 3, 2004, at 00:22 UT. Fig. 4 reports the dome under a lower solar altitude. This image was taken on October 31, 2004 at 11:15 UT by J. Phillips (H 4.70, C ). The dome s eastern flank does not show a black shadow on the raw image, but a dark grey shading (penumbra) of the dome s flank which represents grazing illumination by sunlight. In addition, Fig. 5 shows the dome as drawn by R. Lena. This observation was carried out on January 21, 1999 at 18:05 UT with a 250 mm f/10 Schmidt-Cassegrain telescope (H 14.27, C ). The dome appears to be hemispherical with the presence of a small darkish area on the top that could suggest a craterlet or a depression. Close inspection, particularly of Fattinnanzi' s frames (Figs. 1 and 2) shows this summit feature. It shows a penumbra on the western flank. 5) Results and discussion With a solar altitude of the dome was estimated to have a base diameter of 8.5±0.4 km. The height values reported in Table 4 were obtained by determining elevation differences between the summit of the dome and its surrounding on the corresponding 3D profiles derived by SFS analysis. The dome height on the images shown in Figs. 1 and 2 was measured as 90±20 m and 110±20 m, respectively. These height values are consistent with the measurement carried out on the image shown in Fig. 3, estimated as 110±30 m. From Table 4 it follows that the average slope angle is smaller than 2, corresponding to a hemispherical circular dome having a gentle slope (see Fig. 4). Moreover a central depression on the dome summit was detected. Fig. 6 shows the 3D reconstruction results obtained by means of the SFS method as described in Section 3, making use of the Lunar-Lambert BRDF model with L(α) = Fig. 6a displays a 3D view of the complete dome derived from the image in Fig. 3, while Fig. 6b shows the northern half of the dome based on an evaluation of the image in Fig. 2. The reconstruction results are presented as a mesh (left) and as a rendered view (right), viewed approximately from the north-west, respectively. In the rendered views, the z axis is 20 times exaggerated. From the data in Tables 1 and 3 we see that this dome ( ) is situated close to the ALPO dome reported under the entry #C ( ) in Table 1. As a note of interest ALPO does not show any classification for The last published ALPO catalogue (1992) probably contains numerous errors and missing or incomplete data. When ALPO and the BAA first began their dome catalogue in the 1960s, the observers were using different maps. This led to the fact that some of the domes in the catalogue are actually multiple observations of the same dome, and likely different and wrong coordinates are given. We may categorize the present dome as of Class 1 using the Head and Gifford Scheme [10], and as DW/2a/6f/7j using the Westfall scheme [11].

6 It is a clear example of a classical dome. Domes probably formed in the later stages of volcanism on the moon. Early stage lavas were very fluid, due to their high temperature, massive volumes, and mineralogy. Over time, the erupting lavas cooled, decreased in flow rate, and began to crystallize. This changed the characteristics of the lava, decreasing its fluidity so that it began to ' pile up' around its vent, forming low shield-like volcanoes. This is the possible source of the present lunar dome. References [1] Pau K.C, Lena R., A Study about an unlisted dome near the Valentine dome, Strolling Astronomer, 46 (4), pp , [2] Wilhelms, D., The Geologic History of the Moon, USGS Prof. Paper Washington: GPO, [3] Jamieson, H. D., The Lunar Dome Survey Fall, Strolling Astronomer, 1992 Progress Report, 37 (1), pp , [4] Bussey, B., Spudis, P., The Clementine Atlas of the Moon, Cambridge University Press, Cambridge, UK, [5] Cook, A. C., Spudis, P. D., Robinson, M. S., Watters, T. R., Bussey, D. B. J., The topography of the lunar poles from digital stereo analysis, Proc. 30th Lunar and Planetary Science Conference, Houston, USA, 1999, abstract #1154. [6] Horn, B. K. P., Height and Gradient from Shading, MIT technical report, AI memo no. 1105A, [7] Hapke, B., Theory of reflectance and emittance spectroscopy, Cambridge University Press, Cambridge, UK, [8] Warell, J., Properties of the Hermean regolith: IV. Photometric parameters of Mercury and the Moon contrasted with Hapke modelling, Icarus, vol. 167, no. 2, pp , [9] McEwen, A. S., Photometric Functions for Photoclinometry and Other Applications, Icarus 92 (1991) [10] Head, J., Gifford, A., Lunar mare domes: classification and modes of origin, The Moon and Planets, 22, [11] Westfall, J., A Generic Classification of Lunar Domes, Strolling Astronomer, Vol. 18, no. 1-2, pp.15-20, 1964.

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