月面の中央丘クレーターの特性に関する関係式の導出

[13] W3C, “HTML5: A vocabulary and associated APIs for HTML and XHTML,” W3C Working Draft 22 January 2008. https://www.w3.org/TR/2008/WD-html5-20080122/ .

[14] Wells D. C., Greisen E. W., Harten R. H., “FITS - a Flexible Image Transport System,” A&AS, 44, 1981, 363.

[15] Zapart C., Shirasaki Y., Ohishi M., Mizumoto Y., Kawasaki W., Kobayashi T., Kosugi G., et al., “ALMA- WebQL v2: a Modern Interactive Client-server Architecture for Fast Previewing of Large ALMA Datasets,”

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[17]

x86

CQ

2006

1

1

月面の中央丘クレーターの特性に関する関係式の導出

今福 拓海

* ¹

* ²

* ²

* ³

* ⁴

* ¹

Derivation of the Equation to Characterize the Lunar Central Peak Craters

IMAFUKU Takumi* ¹ , YAMAMOTO Yukio* ² , OHTAKE Makiko* ² , HIROTA Masaharu* ³ , ARAKI Tetsuya* ⁴ , ISHIKAWA Hiroshi* ¹

Abstract

There is a well-known relationship between the diameter and depth of the lunar craters. For the craters with central peaks, a non-linear relation was proposed between the diameter and the peak height. However, this relation has room for improvement since it was derived manually measuring the parameters from a small number of old crater images. Therefore, in this study, the connection between the height of the central peak and the diameter was studied using a contemporary lunar digital elevation map. As a result, it was found that there is a directly proportional relationship between the height of the central peak and the crater’s diameter.

Keywords: Regression Analysis, Digital Elevation Model, Parameter Estimation

概要

月面のクレーターの直径と深さに関する関係式は良く知られている．中央丘を持つクレーター に関しては中央丘の高さを直径から導出する関係式が存在するが，これは人手でクレーターの画 像からパラメータを計測し，導出されたものである．しかし，計測方法の不明瞭さや，用いられ ているデータの少なさ，古さなどの問題点があるため，この関係式には改善の余地があると考え られる．そこで本研究では，月面クレーターの数値標高モデルを用いて中央丘の高さのための関 係式を導出し，既存の関係式と比較した．結果として中央丘の高さとクレーターの直径には正比 例の関係があることを示した．

*

2020

12

4

Received December 4, 2020

*1 東京都立大学システムデザイン学部（

Faculty of Systems Design, Tokyo Metropolitan University

*2 宇宙航空研究開発機構宇宙科学研究所（

Institute of Space and Astronautical Science, Japan Aerospace Exploration Agency

*3 岡山理科大学総合情報学部（

Faculty of Informatics, Okayama University of Science

ٰͱΫϨʔλʔͷܗঢ়ͱͦΕΒͷαΠζͷؔ܎Λ෼ੳ͢Δݚڀ͕ߦΘΕ͍ͯΔɽ Allen Βͷݚڀ [1] Ͱ͸ɼΫ Ϩʔλʔʹର͢ΔதԝٰͷҐஔ΍޲͖ͳͲͷܗଶతಛ௃Λ౷ܭతʹ෼ੳ͍ͯ͠Δɽͦͷ݁ՌɼதԝٰͷαΠζ ͱΫϨʔλʔͷαΠζʹ͸ऑ͍૬͕ؔ͋Δ͜ͱΛࣔͨ͠ɽ·ͨɼ Friedrich Βͷݚڀ [3] ʹΑΕ͹ɼൺֱత৽͠

͍ΫϨʔλʔʹ͍ͭͯɼΫϨʔλʔͷܗঢ়͸௚ܘʹґଘ͢Δͱ͞Ε͍ͯΔɽ͜ͷݚڀ [3] Ͱࣔ͞Εͨɼ݄ͷি

ಥΫϨʔλʔͷزԿֶతಛੑΛදͨ͠ํఔࣜΛࣜʢ 1 ʣʹࣔ͢ɽ

Y = aD ^b (1)

Y ͸ΫϨʔλʔͷಛੑʢΫϨʔλʔͷਂ͞ɼதԝٰͷߴ͞ͳͲʣɼ D ͸ΫϨʔλʔͷ௚ܘɼ a ͱ b ͸ఆ਺Ͱ

͋Δɽ·ͨɼ Wood Βͷݚڀ [7] Ͱ͸݄ͷΫϨʔλʔͷதԝٰͷߴ͞͸ΫϨʔλʔͷ௚ܘʹਖ਼ൺྫ͠ɺதԝٰ

ͷߴ͕͞ΫϨʔλʔܗ੒ΤωϧΪʔͷؔ਺Ͱ͋Δ͜ͱΛ͍ࣔͯ͠Δɽ

͔͠͠ɼ͜ΕΒͷݚڀͰ͸ɼݚڀ͕ߦΘΕ͍ͯͨ౰࣌ʹར༻ՄೳͰ݄͋ͬͨ໘ͷΫϨʔλʔࣸਅ͔Β໨ࢹʹ ΑΔଌఆͰؔ܎ࣜ΍෼ੳ݁ՌΛಘ͍ͯΔɽ·ͨɼۙ೥ʹར༻Մೳͳ݄ͷྖҬͱൺֱͯ͠ɼؔ܎ࣜΛ࡞੒͢Δͨ

Ίʹ༻͍ΒΕ͍ͯΔྖҬ͕খ͍͜͞ͱ΍ɼಉ͡ΫϨʔλʔʹରͯ͠ଌఆऀʹΑͬͯଌఆ஋͕ҟͳΔ͜ͱ͕͋

Δɽͦ͜ͰɼຊݚڀͰ͸ɼதԝٰΫϨʔλʔͷதԝٰͷߴ͞Λਪఆ͢ΔͨΊͷΞϧΰϦζϜͷఏҊͱͦΕΛ༻

͍ͨճؼ෼ੳʹΑΔؔ܎ࣜΛಋग़͢Δɽ

ຊ࿦จ͸ҎԼͷߏ੒ʹै͏ɽ 2 ষͰ͸ɼఏҊख๏ʹ͍ͭͯड़΂Δɽ 3 ষͰ͸ɼதԝٰΫϨʔλʔͷσʔλΛ

༻͍ͯؔ܎ࣜΛಋग़͠ɼطଘϞσϧͱͷൺֱɼߟ࡯Λߦ͏ɽ 4 ষͰ͸ɼຊ࿦จͷ·ͱΊͱࠓޙͷ՝୊ʹ͍ͭͯ

ड़΂Δɽ

2 ఏҊख๏

ຊݚڀͰ͸ɼதԝٰͷߴ͞ͷਪఆͱɼطଘͷதԝٰͷߴ͞Λදؔ͢܎ࣜʢ 1 ʣ ( ҎԼɼطଘϞσϧͱ͢Δʣͷ

܎਺ͷߋ৽ʹऔΓ૊Ήɽதԝٰͷߴ͞ͷਪఆʹ͸ɼݪΒͷݚڀ [8] ʹ͓͍ͯɼ JAXA ͷ݄पճӴ੕ʮ͔͙΍

(SELENE) ʯʹΑͬͯऩू͞Εͨ਺஋ඪߴϞσϧ (Digital Elevation Model; DEM) [11] ͔ΒࢁຊΒͷ։ൃ͠

ͨ RPSD(Rotational Pixel Swapping for Digital Terrain Model) ๏ [9] ͱػցֶशʹΑΔதԝٰΫϨʔλʔ ͷ෼ྨʹΑͬͯɼதԝٰΛ༗͍ͯ͠Δͱ͞ΕͨΫϨʔλʔͷ 524 ݅ͷ DEM ͷϦετΛ༻͍Δɽ͜ͷ DEM

͸ɼΫϨʔλʔͷେ͖͞ʹ߹Θͤͯ੾ΓऔΒΕ͓ͯΓɼઐ໳ՈʹΑͬͯଌఆ͞Εͨਖ਼֬ͳΫϨʔλʔͷ௚ܘͷ

஋͕෇༩͞Ε͍ͯΔɽਤ 1 ʹɼ DEM σʔλͷྫΛࣔ͢ɽॎ࣠ɼԣ࣠͸ϐΫηϧ਺ɼϐΫηϧͷ৭͸ඪߴ஋Λ ද͍ͯ͠ΔɽຊݚڀͰ࢖༻ͨ͠ DEM σʔλ͸ɼ 1 ϐΫηϧ͋ͨΓॎԣ 60m ʷ 60m ͷେ͖͞Ͱ͋Δɽ·ͨɼ ඪߴ஋͸݄໘ʹ͓͚ΔҢ౓ͱܦ౓͕͍ͣΕ΋ 0 ౓ͷ஍఺Λج४ʹͨ͠஋Ͱ͋Γɼ୯Ґ͸ km Ͱ͋Δɽ

·ͨɼຊݚڀʹ͓͍ͯதԝٰͷߴ͞Λࣜʢ 2 ʣͷΑ͏ʹఆٛ͢Δɽ͜͜ͰɼϑϩΞʔͱ͸ΫϨʔλʔʹ͓͚

Δԁঢ়ʹ౔஍͕௿͘ͳ͍ͬͯΔຍ஍ͷ͜ͱΛࢦ͢ɽ

ਤ 1 தԝٰΫϨʔλʔʢΫϨʔλʔ໊ɿ Ctesibius ʣͷ DEM σʔλͷྫ

தԝٰͷߴ͞ = தԝٰͷ௖఺ͷඪߴ − ^{ϑϩΞʔͷඪߴ} (2)

தԝٰͷߴ͞Λਪఆ͢ΔͨΊɼ DEM σʔλ͔ΒΫϨʔλʔ͝ͱʹதԝٰͷ௖఺ͱϑϩΞʔɼͦΕͧΕͷඪ ߴ஋Λܾఆ͢Δɽͦͷޙɼਪఆͨ͠தԝٰͷߴ͞ͱ௚ܘͷେ͖͔͞Βճؼ෼ੳʹΑΔؔ܎ࣜͷಋग़Λߦ͏ɽ

2.1 தԝٰͷߴ͞ͷਪఆΞϧΰϦζϜ

2.1.1 ϑϩΞʔͷඪߴͷܾఆ

ΫϨʔλʔͷϑϩΞʔͷඪߴ஋Λࢉग़͢ΔͨΊʹɼ·ͣ DEM ͔ΒͦΕͧΕϐΫηϧͷඪߴ஋Λऔಘ͠ɼώ ετάϥϜΛٻΊΔɽਤ 2 ʹಘΒΕͨώετάϥϜͷྫΛࣔ͢ɽਤ 2 ͷԣ࣠͸ඪߴ஋ɼॎ࣠͸ඪߴ஋ͷҰఆͷ

۠ؒʹؚ·ΕΔϐΫηϧͷස౓Λද͢ɽຊ࿦จͰ͸ɼώετάϥϜͷϏϯͷ෯ (1 ͭͷϏϯʹؚ·ΕΔඪߴ஋

ͷൣғ ) Λ 0.1km ͱͨ͠ɽΫϨʔλʔͷ DEM ͷϐΫηϧ͔ΒώετάϥϜΛٻΊΔͱɼਤ 2 ͷΑ͏ʹɼϏ

ϯʹؚ·ΕΔඪߴͷ஋͕ߴ͍Ϗϯͱ௿͍Ϗϯͷස౓͕େ͖͘ͳΔ܏޲͕͋Δɽ

ਤ 2 ਤ 1 ͷ DEM ͷώετάϥϜ

͜ͷݪҼʹ͍ͭͯɼᯁੴিಥʹΑͬͯΫϨʔλʔ͕ੜ੒͞ΕΔࡍͷিܸʹΑͬͯɼ஍໘͕࡟ΒΕΔ͜ͱͰඪ ߴ஋͕௿͍ϑϩΞʔͱɼ੝Γ্͕ͬͨඪߴ஋ͷߴ͍ϦϜ͕Ͱ͖Δ܏޲͕͋ΔʢΫϨʔλʔͷ୺෦ͷԁ؀ঢ়ʹ౔

஍͕ߴ͘ͳ͍ͬͯΔ෦෼ͷ͜ͱΛϦϜͱݺͿʣɽͦͷͨΊɼඪߴ஋͕ߴ͘ɼස౓͕ߴ͍෦෼ʢਤ 2 ͷඪߴ஋ 1.5

ʙ 2.2 ෦෼ʣ͸ɼϦϜ͓ΑͼϦϜͷ֎ଆͰ͋Δͱߟ͑ΒΕɼඪߴ஋͕௿͘ɽͦͷස౓͕ߴ͍෦෼ʢਤ 2 ͷඪߴ

ਤ 3 ϑϩΞʔͱ൑ఆͨ͠෦෼Λ੨͘ృΓͭͿͨ͠ DEM

2.1.2 தԝٰͷ௖্ͷܾఆ

தԝٰ͸ΫϨʔλʔͷதԝʹܗ੒͞ΕΔ͜ͱ͕ଟ͍ɽ͔͠͠ɼΫϨʔλʔͷαΠζ͕େ͖͘ͳΔʹͭΕͯɼ ΫϨʔλʔͷத৺͔ΒͣΕͨҐஔʹܗ੒͞ΕΔ৔߹͕͋Δɽ·ͨɼதԝٰͷ௖্ͷඪߴ͸ϦϜͷඪߴΑΓ΋௿

͍ɽͦͷͨΊɼҎԼͷखॱͰ௖্Λܾఆ͢Δɽ

1. ΫϨʔλʔͷத৺͔ΒϦϜ·Ͱͷඪߴͷஅ໘ਤΛ DEM ͔Βෳ਺ຕ࡞੒͢Δ 2. அ໘ਤ͝ͱʹɼΫϨʔλʔͷத৺ʹ͍ۙൣғͰඪߴͷ࠷େ஋ΛٻΊΔ

3. ͦΕͧΕͷඪߴͷ࠷େ஋ͷதͰɼ࠷େ஋ΛͱΔҐஔΛԾͷதԝٰͷ௖্ͷҐஔͱ͢Δ 4. ݩͷ DEM ʹ͓͍ͯԾͷதԝٰͷ௖্ͷҐஔʹରԠ͢ΔҐஔΛٻΊΔ

5. Ծͷதԝٰͷ௖্ͷपลͰඪߴ͕࠷େ஋ΛऔΔ఺Λதԝٰͷ௖্ͱ͢Δ

্هͷखॱʹ͍ͭͯઆ໌͢Δɽஅ໘ਤ͸̍ͭͷΫϨʔλʔ DEM ʹର͠ɼ௕͞Λॎ෯ͷ൒෼Ͱݻఆ͠ɼ୺͔

Βத৺·ͰΛ 15 ˃ͣͭܭ 24 ຕʹ੾Γग़͢ɽਤ 4 ʹɼஅ໘ਤͷྫΛࣔ͢ɽԣ͕࣠ϦϜଆ͔ΒͷϐΫηϧ਺ɼॎ

͕࣠ͦͷඪߴɼ੺ઢ͕ϑϩΞʔͷඪߴ஋Λࣔ͢ɽԣ࣠ͷ஋͕ 0 ෇ۙ͸ϦϜपลͰ͋Δɽ·ͨɼ 250 ʙ 300 ෇ۙ

ͷٰঢ়ʹͳ͍ͬͯΔ෦෼͕தԝٰͰ͋Δɽ

அ໘ਤͷϦϜଆʢԣ࣠ͷ஋͕ 0 ʣ͔Βඪߴ஋Λ૸ࠪ͠ɼϑϩΞʔͷඪߴ஋ΛҰ౓Լճ͔ͬͯΒͷ࠷େ஋Λٻ ΊΔɽ͜͜ͰɼҰ౓΋ϑϩΞʔͷඪߴ஋ΛԼճΒͳ͍৔߹ɼͦͷஅ໘ਤͷ࠷େ஋͸ͳ͍΋ͷͱ͢Δɽ͜ͷૢ࡞

Λશͯͷஅ໘ਤ 24 ຕ෼ߦ͍ɼͦΕΒ࠷େ஋ͷதͰ࠷΋ߴ͍ඪߴ஋ΛऔΔϐΫηϧΛԾͷதԝٰͷ௖্ͷҐஔ ͱ͢Δɽ࣍ʹԾͷதԝٰͷ௖্ͷҐஔʹରԠ͢Δ DEM ্ͷҐஔ͔Βॎԣͷ࢛ํ޲ʢҢ౓ܦ౓ʹରͯ͠ 0 ˃ ,

90 ˃ , 180 ˃ , 270 ˃ʣ΁ɼϑϩΞʔͷඪߴ஋ΛԼճΔɼ΋͘͠͸ DEM ͷ୺·ͰϑϩΞʔͷඪߴ஋ΛԼճΒͳ

͍৔߹͸୺·ͰͷؒͰඪߴ஋͕࠷΋খ͍͞Ґஔ·Ͱͷ௕ํܗͷྖҬΛ੾Γग़͠ɼͦͷྖҬͰඪߴ஋͕࠷େ஋ͱ

ͳΔ఺Λதԝٰͷ௖্ͱ͢Δɽͨͩ͠ɼԾͷ௖্Λܾఆ͢Δࡍʹɼ͢΂ͯͷஅ໘ਤͷ࠷େ஋͕ͳ͍৔߹ɼதԝ

λΛ༻͍ͨͨΊɼ࣮ݧͰ͸தԝٰ͕ແ͍ͱਪఆ͞ΕͨΫϨʔλʔ͸ଘࡏ͠ͳ͔ͬͨɽ

ਤ 1 ͷΫϨʔλʔ͔Β੾Γग़ͨ͠௕ํܗͷྖҬΛ੨͘ృΓͭͿ͠ɼԾͷ௖্ͷҐஔΛԫ৭ͷ఺Ͱࣔͨ͠΋ͷ Λਤ 5 ʹࣔ͢ɽ·ͨɼਤ 1 Λ֦େ͠ɼ௕ํܗͷྖҬΛന͍࿮Ͱғ͍ɼதԝٰͷ௖্ͷҐஔΛ੺৭ͷ఺ɼԾͷத ԝٰͷ௖্ͷҐஔΛന৭ͷ఺Ͱࣔͨ͠΋ͷΛਤ 6 ʹࣔ͢ɽҎ্ΑΓ , தԝٰͷ௖্ͷҐஔ͕ٻ·ͬͨͷͰɼத ԝٰͷ௖্ͷඪߴͱϑϩΞʔͷඪߴ͔Βɼࣜʢ 2 ʣΛ༻͍ͯதԝٰͷߴ͞ΛٻΊΔɽ

ਤ 4 ΫϨʔλʔͷϦϜ͔Βத৺·Ͱͷஅ໘ਤ

ਤ 5 Ծͷதԝٰͷ௖্ͷҐஔ ( ԫ৭ͷ఺ ) ͱ௕ํܗͷྖҬ ਤ 6 தԝٰͷ௖্ͷҐஔ ( ੺ɿதԝٰͷ௖্ , ന : Ծͷ௖্ )

2.2 ճؼ෼ੳʹΑΔதԝٰͷߴ͞ͱΫϨʔλʔͷ௚ܘͷؔ܎ࣜͷಋग़

2.1 અͷॲཧΛద༻͢Δ͜ͱͰɼಘΒΕͨதԝٰͷߴ͞Λ༻͍ͯճؼ෼ੳʹΑͬͯؔ܎ࣜΛಋग़͢Δɽճؼ

෼ੳͱ͸໨తม਺ Y ͱಠཱม਺ D ͷؒʹؔ܎ࣜΛ౰ͯ͸ΊΔࣄͰ͋Γɼσʔλͱͷޡ͕ࠩ࠷খʹͳΔΑ͏

ʹؔ܎ࣜΛٻΊΔɽຊݚڀͰ͸ɺطଘͷϞσϧͷํఔࣜͰ͋Δࣜ (1) ʹରͯ͠ɺඇઢܗճؼ෼ੳΛ༻͍ͯΫ Ϩʔλʔͷ௚ܘͱதԝٰͷߴ͞ͷؔ܎ࣜͷಋग़Λߦͬͨɻ·ͨ , ϞσϧͷൺֱͷͨΊࣜ (3) ͷΑ͏ͳઢܗͷؔ

਺ʹରͯ͠ɺઢܗճؼ෼ੳΛ༻͍ͯΫϨʔλʔͷ௚ܘͱதԝٰͷߴ͞ͷؔ܎ࣜΛಋग़Λߦͬͨɽؔ܎ࣜͷಋग़ ʹ͓͍ͯɺઢܗճؼ෼ੳͰ͸ scikit-learn [5] ͷ LinearRegression Λ༻͍ɼඇઢܗճؼ෼ੳͰ͸ SciPy [6] ͷ curve fit Λ༻͍ͨɽ

Y = aD + b (3)

ຊݚڀʹ͓͍ͯؔ܎ࣜϞσϧͷධՁࢦඪʹ͸ܾఆ܎਺Λ༻͍Δɽࣜʢ 4 ʣʹຊݚڀʹ͓͚Δܾఆ܎਺ͷఆٛ

Λࣔ͢ɽ y ͕࣮ଌ஋ɼ f ͕ճؼϞσϧʹΑΔਪఆ஋ͱ͢Δɽ࢒ࠩ ( ࣮ଌ஋ͱ༧ଌ஋ͷࠩ ) ͷೋ৐࿨Λ࣮ଌ஋ͷฏ ۉ͔Βͷภࠩͷೋ৐࿨Ͱׂͬͨ஋͔Β̍Ҿ͍ͨ΋ͷͰ͋Δɽ ܾఆ܎਺ͷ஋͸ 1 ʹ͍ۙఔϞσϧͱͷ૬ରతͳ

࢒͕ࠩগͳ͍͜ͱΛද͠ɼσʔλͱϞσϧͷҰக౓͕ߴ͍ͱ͍͑Δɽ

R ² = 1 − Σ i (y i − f i ) ²

Σ i (y i − y) ¯ ² (4)

ද 1 ʹطଘϞσϧͱࠓճಋग़ͨ͠ඇઢܗճؼ෼ੳͷΫϨʔλʔ਺ɼ͓Αͼؔ܎ࣜʢ 1 ʣͷ܎਺ a ɼ b Λࣔ͢ɽ

ͨͩ͠ɼطଘϞσϧ͕ಋग़͞ΕΔ্Ͱ༻͍ΒΕͨσʔλ͸ɼΫϨʔλʔͷ௚ܘ͕ 17 ʙ 51km Ͱ͋ͬͨͱ͞Εͯ

͓Γɼதԝٰͷߴ͞ͷܭଌ஋΍ܭଌํ๏ͳͲ͸ࣔ͞Ε͍ͯͳ͍ɽͦͷͨΊɼܾఆ܎਺Λࢉग़͢Δ࣮ଌ஋ y ͸શ

ͯຊݚڀͰਪఆͨ͠தԝٰͷߴ͞Λ༻͍Δɽ·ͨɼද 2 ʹઢܗճؼϞσϧʹ͓͚Δճؼ܎਺ʢ܏͖ʣͱ੾ยΛ

ࣔ͢ɽ

ද 1 ΑΓɼղੳʹ࢖༻ͨ͠ΫϨʔλʔͷ਺͕طଘϞσϧͰ͸গͳ͘ɼൺ΂ͯࠓճಋग़ͨ͠ϞσϧͰ͸ଟ͍͜

ͱ͕Θ͔Δɽ·ͨɼࢦ਺ͷ஋Ͱ͋Δ b ͕طଘϞσϧʹ͓͍ͯ໿ 2 Ͱ͋Γɼؔ܎͕ࣜೋ࣍ؔ਺తͳ૿ՃΛ͢Δ͜

ͱΛ͍ࣔͯ͠ΔɽҰํͰࠓճಋग़ͨ͠Ϟσϧͷ b ͷ஋͸໿ 0.9 Ͱ͋Γɼؔ܎͕ࣜઢܗʹ͍ۙ૿ՃΛ͢Δ͜ͱΛ

͍ࣔͯ͠Δɽ

ද 3 ʹ֤ؔ܎ࣜϞσϧͷܾఆ܎਺Λࣔ͢ɽ͜͜Ͱɼܾఆ܎਺Λࢉग़͢Δࡍʹ༻͍Δ࣮ଌ஋Λɼຊ࣮ݧͰਪఆ

ͨ͠શσʔλΛର৅ͱͨ͠৔߹ͱɼΫϨʔλʔ௚ܘ͕ 17 ʙ 51km ͷ΋ͷΛର৅ʹͨ͠৔߹ʹରͯͦ͠ΕͧΕ ߦͬͨɽද 3 ΑΓɼશσʔλΛର৅ʹͨ͠΋ͷͱΫϨʔλʔ௚ܘ͕ 17 ʙ 51km ͷ΋ͷΛର৅ʹͨ͠΋ͷͲͪ

Βʹ͓͍ͯ΋ɼܾఆ܎਺͕طଘϞσϧ͸͔ͳΓ௿͘ɼࠓճಋग़ͨ͠Ϟσϧͷํ͕஋͕ 1 ʹ͍ۙ͜ͱ͕Θ͔Δɽ ࠓճಋग़ͨ͠ඇઢܗճؼϞσϧͱͦͷଞͷϞσϧΛൺֱͨ͠΋ͷΛਤ 7-9 ʹࣔ͢ɽਤ 7 ͸ඇઢܗճؼϞσϧ ʢ੺ʣɼઢܗճؼϞσϧʢԫʣɼطଘϞσϧʢ྘ʣΛ͍ࣔͯ͠Δɽਤ 8 ͸ඇઢܗճؼϞσϧʢ੺ʣͱઢܗճؼϞσ ϧʢԫʣΛ͍ࣔͯ͠Δɽਤ 9 ͸ΫϨʔλʔ௚ܘΛ 17 ʙ 51km ʹ੍ݶ֤ͨ͠Ϟσϧʢطଘɿ྘ɼඇઢܗɿ੺ɼઢ ܗɿԫʣΛ͍ࣔͯ͠Δɽ

ਤ 7 ΑΓɼطଘϞσϧ͸ԣ࣠ͷ஋͕େ͖͘ͳΔʹͭΕ࣮ͯଌ஋ͱࠓճಋग़ͨ͠Ϟσϧͱͷ͕ࠩࢦ਺ؔ਺తʹ

େ͖͘ͳ͓ͬͯΓɼΫϨʔλʔͷ௚ܘͷ஋͕େ͖͍΋ͷ͸طଘϞσϧͰ͸දݱ͖͠Εͳ͍͜ͱ͕Θ͔Δɽਤ 8 ΑΓɼࠓճಋग़ͨ͠ೋͭͷϞσϧ͕ྨࣅ͓ͯ͠Γɼσʔλ͕ਖ਼ൺྫ͍ͯ͠Δ͜ͱ͕Θ͔Δɽਤ 9 ΑΓɼطଘϞ σϧ͕શͯͷ௚ܘ͋ͨΓͷதԝٰͷߴ͞Λ্ճ͓ͬͯΓɼطଘϞσϧ͕ಋग़͞ΕΔ্Ͱ༻͍ΒΕͨσʔλͷൣ

ғͰ΋ࠓճಋग़ͨ͠ೋͭͷϞσϧͷํ͕࣮ଌ஋ͱ͍ۙ͜ͱ͕Θ͔Δɽ

ද 1 طଘϞσϧͱࠓճಋग़ͨ͠ඇઢܗϞσϧͱͷൺֱ

طଘϞσϧ ࠓճಋग़ͨ͠ඇઢܗϞσϧ ΫϨʔλʔ਺ 15 524

a 0.000589 0.011382

b 1.969 0.901

ද 2 ઢܗճؼϞσϧͷճؼ܎਺ͱ੾ย ճؼ܎਺ʢ܏͖ʣ 0.00639169

੾ย 0.06667599

ද 3 ؔ܎ࣜϞσϧͷܾఆ܎਺

طଘϞσϧ ඇઢܗϞσϧ ઢܗϞσϧ

ܾఆ܎਺ -579.59 0.48775 0.48434

ܾఆ܎਺

ʢ௚ܘ 17 ʙ 51km ʣ -20.889 -0.24754 -0.29763

ਤ 7 ֤ؔ܎ࣜϞσϧʢطଘϞσϧɿ྘ɼඇઢܗճؼϞσϧɿ੺ɼઢܗճؼϞσϧɿԫʣͱΫϨʔλʔͷ௚

ܘʹର͢Δਪఆͨ͠தԝٰͷߴ͞ʢ੨ʣͱͷൺֱ

3.3 ֤Ϟσϧͷߟ࡯

ද 1 ͷࠓճಋग़ͨ͠ඇઢܗϞσϧͷؔ܎ࣜΑΓɼΫϨʔλʔͷ௚ܘͱதԝٰͷߴ͞ʹ͸ઢܗͳؔ܎͕͋Δͱ ߟ͑ΒΕͨͨΊɼطଘͷؔ܎ࣜͷܗࣜΛجʹͨ͠ඇઢܗճؼʹՃ͑ɼઢܗճؼʹΑΔ෼ੳΛߦͬͨɽ݁Ռͱ͠

ͯɼද 3 ͓Αͼਤ 8 ΑΓɼࠓճಋग़ͨ͠ඇઢܗϞσϧͱઢܗϞσϧ͸ྨࣅ͍ͯ͠ΔͨΊɼઢܗͳؔ܎Ͱ͋Δͱ ߟ͑ΒΕΔɽ

طଘϞσϧͱͷൺֱʹ͓͍ͯɼਤ 9 ʹࣔ͢Α͏ʹطଘϞσϧ͕શͯͷ௚ܘ͋ͨΓͷதԝٰͷߴ͞Λ্ճͬͯ

͍ΔݪҼ͸ɼϑϩΞʔͷඪߴΛٻΊΔํ๏͕Өڹ͍ͯ͠Δͱߟ͑ΒΕΔɽຊݚڀͰ͸ɼඪߴͷώετάϥϜΛ

༻͍ͯϑϩΞʔͷඪߴΛܾఆ͍ͯ͠Δ͕ɼطଘϞσϧͷϑϩΞʔͷܾఆํ๏ͱҟͳΔͨΊɼطଘϞσϧΑΓ΋

ຊݚڀͷϑϩΞʔͷඪߴ͸௿͍஋Ͱ͋Δͱߟ͑ΒΕΔɽ·ͨɼܾఆ܎਺ͷൺֱͰ͸ɼܾఆ܎਺Λࢉग़͢Δ࣮ଌ

஋͕શͯຊݚڀͰநग़ͨ͠தԝٰͷߴ͞Λ༻͍͍ͯΔͨΊɼطଘͷؔ܎͕ࣜಋग़͞Εͨࡍʹ࢖༻͞Ε࣮ͨଌ஋

ͱ͸͔ͳΓҟͳΔՄೳੑ͕͋ΓɼطଘϞσϧͷܾఆ܎਺͕ඇৗʹ௿͍஋Λ͍ࣔͯ͠Δɽ

ਤ 8 ઢܗճؼϞσϧʢԫʣͱඇઢܗճؼϞσϧʢ੺ʣ ͱΫϨʔλʔͷ௚ܘʹର͢Δਪఆͨ͠தԝٰͷߴ͞

ʢ੨ʣͱͷൺֱ

ਤ 9 ΫϨʔλʔ௚ܘ 17 ʙ 51km ͷྖҬʹ͓͚Δൺ

ֱʢطଘϞσϧɿ྘ɼඇઢܗճؼϞσϧɿ੺ɼઢܗճ ؼϞσϧɿԫɼΫϨʔλʔͷ௚ܘʹର͢Δਪఆͨ͠த ԝٰͷߴ͞ɿ੨ʣ

ਤ 7 ΑΓɼطଘͷؔ܎͕ࣜಋग़͞ΕΔ্Ͱ༻͍ΒΕͳ͔ͬͨΫϨʔλʔͷ௚ܘ͕ 51km Ҏ্ͷσʔλʹؔ͠

ͯɼ໌Β͔ʹطଘϞσϧͱ࣮ଌ஋͕཭Ε͍ͯΔͨΊɼطଘͷؔ܎ࣜ͸ݟ௚͢ඞཁੑ͕͋Δͱߟ͑ΒΕΔɽ

4 ·ͱΊ

ຊݚڀͰ͸ɼதԝٰͷߴ͞ͷࣗಈਪఆͷͨΊͷΞϧΰϦζϜͷఏҊͱճؼ෼ੳʹΑͬͯΫϨʔλʔͷ௚ܘͱ தԝٰͷߴ͞ͷؔ܎ࣜϞσϧΛಋग़ͨ͠ɽதԝٰͷߴ͞ͷਪఆʹؔͯ͠ɼৄࡉͳܭଌج४΍༻͍ͨσʔλ͕ै

དྷͷݚڀʹࣔ͞Ε͍ͯͳ͔ͬͨͨΊɼͦΕΒΛࣗΒఆٛͯ͠ɼਪఆͨ͠ɽ·ͨɼճؼ෼ੳʹؔͯ͠ɼઢܗճؼ

෼ੳͱطଘͷؔ܎ࣜͷܗࣜΛجʹͨ͠ඇઢܗճؼ෼ੳΛߦͬͨɽ

࣮ݧ݁ՌΑΓɼطଘϞσϧ͕ΫϨʔλʔͷ௚ܘͱதԝٰͷߴ͞ͷඇઢܗͳؔ܎ੑΛࣔ͢ͷʹରͯ͠ɼ࣮ࡍʹ

͸ઢܗͳؔ܎Ͱ͋ΔՄೳੑ͕ߴ͍͜ͱΛࣔͨ͠ɽ

ࠓޙͷ՝୊ͱͯ͠ɼσʔλਪఆͷΞϧΰϦζϜʹ͓͚Δج४ͷݟ௚͠ɼதԝٰΫϨʔλʔ͔Βநग़͢Δಛੑ

ͷछྨͷ૿Ճɼ·ͨͦΕʹ൐͏ؔ܎ࣜͷଟ߲ԽͳͲ͕ڍ͛ΒΕΔɽ

ँࣙ

ຊݚڀ͸ɼ౦ژ౎ཱେֶ܏ࣼతݚڀඅ ( શֶ෼ ) ֶ௕ࡋྔ࿮ࠃࡍݚڀ؀ࢧԉٴͼ JSPS Պݚඅ 20K12081 ʹ ΑΔɽ

ࢀߟจݙ

[1] Allen, C. C. Central peaks in lunar craters. The moon 12, 4 (1975), 463–474.

[2] Hale, W., and Head, J. Central peaks in lunar craters-morphology and morphometry. In Lunar and planetary science conference Proceedings (1979), vol. 10, pp. 2623–2633.

[3] H¨ orz, F., Grieve, R., Heiken, G., Spudis, P., and Binder, A. Lunar surface processes. Lunar sourcebook (1991), 61–120.

[4] Matsunaga, T., Ohtake, M., Haruyama, J., Ogawa, Y., Nakamura, R., Yokota, Y.,

Morota, T., Honda, C., Torii, M., and Abe, M. Discoveries on the lithology of lunar crater central peaks by selene spectral profiler. Geophysical Research Letters 35, 23 (2008).

[5] Pedregosa, F., Varoquaux, G., Gramfort, A., Michel, V., Thirion, B., Grisel, O., Blondel, M., Prettenhofer, P., Weiss, R., and Dubourg, V. Scikit-learn: Machine learning in python. Journal of machine learning research 12, Oct (2011), 2825–2830.

[6] Virtanen, P., Gommers, R., Oliphant, T. E., Haberland, M., Reddy, T., Cournapeau, D., Burovski, E., Peterson, P., Weckesser, W., Bright, J., et al. Scipy 1.0: fundamental algorithms for scientific computing in python. Nature methods 17, 3 (2020), 261–272.

[7] Wood, C. A. Moon: Central peak heights and crater origins. Icarus 20, 4 (1973), 503–506.

[8] ݪ૱ࢤ , ࢁຊ޾ੜ , ߥ໦ప໵ , ኍాխय़ , and ੴ઒ത . ͔͙΍ DEM Λ༻͍ͨ , ػցֶशʹΑΔதԝٰΫ Ϩʔλʔࣝผ . Ӊ஦Պֶ৘ใղੳ࿦จࢽୈ 8 ߸ (2019), 1–10.

[9] ࢁຊ૱ , দӬ߃༤ , தଜྑհ , ؔࠜ߁ਓ , ฏా੒ , and ࢁޱ༃ . ճసϐΫηϧεϫοϐϯά๏Λ࢖ͬͨΫ Ϩʔλʔ೥୅ֶ . ೔ຊ࿭੕Պֶձࢽ༡੕ਓ 24, 1 (2015), 20–32.

[10] ௶Ҫ௚ , ࠤ౻ণࢬ , ߴڮਖ਼޾ , and ࠤഢ࿨ਓ . ݄ΫϨʔλதԝٰද໘ؠ૬ͷݕূ . ೔ຊϦϞʔτηϯγϯ άֶձࢽ 23, 4 (2003), 340–354.

[11] ௶಺࠼Ի , ࣰాྰಸ , ֲ఩໵ , ޙ౻༞ل , य़ࢁ७Ұ , and ࡾ୐࿰ . Selene ( ͔͙΍ ) ౥ࡌ஍ܗΧϝϥεςϨ ΦϖΞσʔλ͔ΒಘΒΕͨ਺஋஍ܗϞσϧ (DTM) ͳΒͼʹ਺஋ඪߴϞσϧ (DEM) ϓϩμΫτͷඪߴ

஋ͷݕূใࠂ . Ӊ஦ߤۭݚڀ։ൃػߏݚڀ։ൃࢿྉ (2016), 1–36.