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First the linear relationship between magnetization and stress is obtained for a general 3dimensional stress state. It is deduced by applying the principle of superposition to experimental results of uniaxial compression tests. The isotropic piezomagnetic law thus obtained has two independent parameters, which is equivalent to the law proposed by ZLOTNICKI et al. (1981). The ordinary piezomagnetic law (STACEY, 1964; NAGATA, 1970a) with a single parameter, i.e. the stress sensitivity, is a particular case of this extended formula. Because of its simplicity and validity as an average for aggregates of various rocks, the single parameter formula is applied in the following calculations. The basic equation is derived by connecting the Gaussian law for the magnetic field and the CauchyNavier equation for static elastic equilibrium through constitutive relationships, i.e. the piezomagnetic law and the Hooke law for isotropic elasticity. It is a Poisson\u0027s equation with a source term expressed in terms of the displacement. The representation theorem is obtained for the solution : the tectonomagnetic field is given by surface integrals of the displacement and its normal derivatives over the strained body. Applying the theorem to a medium including a dislocation surface within it, we find that the dislocation surface behaves as a magnetic sheet. For Volterra dislocations, the magnetic sheet becomes simply a double layer, of which the moment is given by the inner product of the displacement discontinuity and the magnetization vector. The seismomagnetic moment thus defined is useful to intuitively realize coseismic magnetic changes. In the following calculations, the model earth considered is the simplest one: a homogeneous and isotropic elastic halfspace having a uniformly magnetized top layer with a constant stress sensitivity. The piezomagnetic field associated with the Mogi model is investigated in detail. Two mathematical techniques are introduced, which are frequently used throughout this study: i.e. the double Fourier (or Hankel) transforms and the LipschitzHankel type integrals. The piezomagnetic field associated with the inflation of a finite spherical pressure source is solved with the aid of these two methods. The point source solution is also obtained, and subsequently used as a Green\u0027s function for the multiple Mogi model in Chapter 5. The way we obtained the point source solution becomes the prototype of constructing Green\u0027s functions in the following chapters. In the case of integrals containing a singular point of the stress field, we must take a limit in a special way: i.e. to enclose the singular point with a closed surface which satisfies the boundary conditions and then to shrink the surface to that point. A variety of tectonic models can be formed by superposing the displacement field solutions of single forces acting at points in an elastic halfspace. Piezomagnetic changes associated with the same models are given as well by the linear combination of fundamental piezomagnetic potentials, which arise from stressinduced magnetization produced by unit single forces acting at points. The method is adaptable to surface load and volume source problems. As an application example, piezomagnetic change is calculated for a uniform circular load. Comparing the calculations with some observations of the dammagnetic effect, we suggest that the in situ value of the stress sensitivity of the upper crust is an order of magnitude greater than that of stiff rocks which are usually tested in rockmagnetic experiments. Finally the dislocation problems are considered. The same integral representation as the Volterra formula for the elastic field is derived for the piezomagnetic field. The elementary piezomagnetic potentials are defined as the potentials produced by a point dislocation. The effect of divergent stresses around a point dislocation is evaluated as follows: we enclose the point dislocation with a small thin disk parallel to the infinitesimal dislocation surface, diminish the thickness of the disk and then its radius. Elementary potentials consits of dipoles and multipoles at the position of point dislocation and their mirror images with respect to the Curie depth. However, some types of strain nuclei lack magnetic source equivalents at the dislocation position. Hence the seismomagnetic effect accompanying some kinds of fault motion becomes much weaker than that anticipated from the seismomagnetic moment. An important application of the theory is the multiple tensioncrack model, which is a versatile model for crustal dilatancy or crustal deformation of volcanic origin. Another application is the piezomagnetic change associated with faulting. Formulas for a vertical rectangular fault with shearing as well as tensile fault motion are presented.", "subitem_description_type": "Abstract"}, {"subitem_description": "\u5730\u9707\u3084\u706b\u5c71\u6d3b\u52d5,\u3042\u308b\u3044\u306f\u3086\u308b\u3084\u304b\u306a\u5730\u6bbb\u5909\u52d5\u306b\u3088\u308b\u5730\u6bbb\u5fdc\u529b\u306b\u4f34\u3063\u3066,\u5730\u78c1\u6c17\u304c\u5909\u5316\u3059\u308b.\u3053\u308c\u306f\u5ca9\u77f3\u304c\u5fdc\u529b\u306b\u3088\u3063\u3066\u78c1\u5316\u3092\u5909\u3048\u308b\u30d4\u30a8\u30be\u78c1\u6c17\u52b9\u679c\u3092,\u305d\u306e\u539f\u56e0\u3068\u3057\u3066\u3044\u308b.\u672c\u8ad6\u6587\u3067\u306f\u69d8\u3005\u306a\u5730\u6bbb\u6d3b\u52d5\u306b\u4f34\u3046\u30d4\u30a8\u30be\u78c1\u6c17\u5909\u5316\u3092\u7d71\u4e00\u7684\u306b\u6271\u3046\u65b9\u6cd5\u3092\u5b9a\u5f0f\u5316\u3059\u308b.\u3053\u306e\u7406\u8ad6\u306f\u57fa\u672c\u7684\u306b\u306f, STACEY (1964)\u304c\uff62\u5730\u9707\u5730\u78c1\u6c17\u52b9\u679c\uff63\u3092\u898b\u7a4d\u308b\u8a08\u7b97\u3067\u884c\u3063\u305f\u3084\u308a\u65b9\u3092\u4e00\u822c\u5316\u3057\u305f\u3082\u306e\u3067\u3042\u308b.", "subitem_description_type": "Abstract"}]}, "item_4_full_name_3": {"attribute_name": "\u8457\u8005\u5225\u540d", "attribute_value_mlt": [{"nameIdentifiers": [{"nameIdentifier": "127200", "nameIdentifierScheme": "WEKO"}], "names": [{"name": "\u7b39\u4e95, \u6d0b\u4e00"}]}]}, "item_4_identifier_registration": {"attribute_name": "ID\u767b\u9332", "attribute_value_mlt": [{"subitem_identifier_reg_text": "10.15083/0000032742", "subitem_identifier_reg_type": "JaLC"}]}, "item_4_publisher_20": {"attribute_name": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "\u6771\u4eac\u5927\u5b66\u5730\u9707\u7814\u7a76\u6240"}]}, "item_4_source_id_10": {"attribute_name": "\u66f8\u8a8c\u30ec\u30b3\u30fc\u30c9ID", "attribute_value_mlt": [{"subitem_source_identifier": "AN00162258", "subitem_source_identifier_type": "NCID"}]}, "item_4_source_id_8": {"attribute_name": "ISSN", "attribute_value_mlt": [{"subitem_source_identifier": "00408972", "subitem_source_identifier_type": "ISSN"}]}, "item_4_subject_15": {"attribute_name": "\u65e5\u672c\u5341\u9032\u5206\u985e\u6cd5", "attribute_value_mlt": [{"subitem_subject": "453", "subitem_subject_scheme": "NDC"}]}, "item_4_text_21": {"attribute_name": "\u51fa\u7248\u8005\u5225\u540d", "attribute_value_mlt": [{"subitem_text_value": "Earthquake Research Institute, University of Tokyo"}]}, "item_4_text_34": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"subitem_text_value": "Departmental Bulletin Paper"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "attribute_type": "creator", "attribute_value_mlt": [{"creatorNames": [{"creatorName": "Sasai, Yoichi"}], "nameIdentifiers": [{"nameIdentifier": "127199", "nameIdentifierScheme": "WEKO"}]}]}, "item_files": {"attribute_name": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "20170626"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "ji0664001.pdf", "filesize": [{"value": "7.9 MB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 7900000.0, "url": {"label": "ji0664001.pdf", "url": "https://repository.dl.itc.utokyo.ac.jp/record/32742/files/ji0664001.pdf"}, "version_id": "02fb1505ed664dad89e499d0794c5196"}]}, "item_language": {"attribute_name": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"resourcetype": "departmental bulletin paper", "resourceuri": "http://purl.org/coar/resource_type/c_6501"}]}, "item_title": "Tectonomagnetic Modeling on the Bases of the Linear Piezomagnetic Effect", "item_titles": {"attribute_name": "\u30bf\u30a4\u30c8\u30eb", "attribute_value_mlt": [{"subitem_title": "Tectonomagnetic Modeling on the Bases of the Linear Piezomagnetic Effect", "subitem_title_language": "en"}]}, "item_type_id": "4", "owner": "1", "path": ["80/4535/4717/4718", "9/504/4538/4719/4720"], "permalink_uri": "https://doi.org/10.15083/0000032742", "pubdate": {"attribute_name": "PubDate", "attribute_value": "20080530"}, "publish_date": "20080530", "publish_status": "0", "recid": "32742", "relation": {}, "relation_version_is_last": true, "title": ["Tectonomagnetic Modeling on the Bases of the Linear Piezomagnetic Effect"], "weko_shared_id": 1}
Tectonomagnetic Modeling on the Bases of the Linear Piezomagnetic Effect
https://doi.org/10.15083/0000032742
704441145304421a80e7fe5ebcae0e5b
名前 / ファイル  ライセンス  アクション  

ji0664001.pdf (7.9 MB)


Item type  紀要論文 / Departmental Bulletin Paper(1)  

公開日  20080530  
タイトル  
タイトル  Tectonomagnetic Modeling on the Bases of the Linear Piezomagnetic Effect  
言語  en  
言語  
言語  eng  
資源タイプ  
資源  http://purl.org/coar/resource_type/c_6501  
タイプ  departmental bulletin paper  
ID登録  
ID登録  10.15083/0000032742  
ID登録タイプ  JaLC  
その他のタイトル  
その他のタイトル  線形ピエゾ磁気効果に基づく地殻活動磁場のモデル化  
著者 
Sasai, Yoichi
× Sasai, Yoichi 

著者別名  
識別子  
識別子  127200  
識別子Scheme  WEKO  
姓名  
姓名  笹井, 洋一  
抄録  
内容記述タイプ  Abstract  
内容記述  Modeling of tectonomagnetic changes is formulated in a unified way. First the linear relationship between magnetization and stress is obtained for a general 3dimensional stress state. It is deduced by applying the principle of superposition to experimental results of uniaxial compression tests. The isotropic piezomagnetic law thus obtained has two independent parameters, which is equivalent to the law proposed by ZLOTNICKI et al. (1981). The ordinary piezomagnetic law (STACEY, 1964; NAGATA, 1970a) with a single parameter, i.e. the stress sensitivity, is a particular case of this extended formula. Because of its simplicity and validity as an average for aggregates of various rocks, the single parameter formula is applied in the following calculations. The basic equation is derived by connecting the Gaussian law for the magnetic field and the CauchyNavier equation for static elastic equilibrium through constitutive relationships, i.e. the piezomagnetic law and the Hooke law for isotropic elasticity. It is a Poisson's equation with a source term expressed in terms of the displacement. The representation theorem is obtained for the solution : the tectonomagnetic field is given by surface integrals of the displacement and its normal derivatives over the strained body. Applying the theorem to a medium including a dislocation surface within it, we find that the dislocation surface behaves as a magnetic sheet. For Volterra dislocations, the magnetic sheet becomes simply a double layer, of which the moment is given by the inner product of the displacement discontinuity and the magnetization vector. The seismomagnetic moment thus defined is useful to intuitively realize coseismic magnetic changes. In the following calculations, the model earth considered is the simplest one: a homogeneous and isotropic elastic halfspace having a uniformly magnetized top layer with a constant stress sensitivity. The piezomagnetic field associated with the Mogi model is investigated in detail. Two mathematical techniques are introduced, which are frequently used throughout this study: i.e. the double Fourier (or Hankel) transforms and the LipschitzHankel type integrals. The piezomagnetic field associated with the inflation of a finite spherical pressure source is solved with the aid of these two methods. The point source solution is also obtained, and subsequently used as a Green's function for the multiple Mogi model in Chapter 5. The way we obtained the point source solution becomes the prototype of constructing Green's functions in the following chapters. In the case of integrals containing a singular point of the stress field, we must take a limit in a special way: i.e. to enclose the singular point with a closed surface which satisfies the boundary conditions and then to shrink the surface to that point. A variety of tectonic models can be formed by superposing the displacement field solutions of single forces acting at points in an elastic halfspace. Piezomagnetic changes associated with the same models are given as well by the linear combination of fundamental piezomagnetic potentials, which arise from stressinduced magnetization produced by unit single forces acting at points. The method is adaptable to surface load and volume source problems. As an application example, piezomagnetic change is calculated for a uniform circular load. Comparing the calculations with some observations of the dammagnetic effect, we suggest that the in situ value of the stress sensitivity of the upper crust is an order of magnitude greater than that of stiff rocks which are usually tested in rockmagnetic experiments. Finally the dislocation problems are considered. The same integral representation as the Volterra formula for the elastic field is derived for the piezomagnetic field. The elementary piezomagnetic potentials are defined as the potentials produced by a point dislocation. The effect of divergent stresses around a point dislocation is evaluated as follows: we enclose the point dislocation with a small thin disk parallel to the infinitesimal dislocation surface, diminish the thickness of the disk and then its radius. Elementary potentials consits of dipoles and multipoles at the position of point dislocation and their mirror images with respect to the Curie depth. However, some types of strain nuclei lack magnetic source equivalents at the dislocation position. Hence the seismomagnetic effect accompanying some kinds of fault motion becomes much weaker than that anticipated from the seismomagnetic moment. An important application of the theory is the multiple tensioncrack model, which is a versatile model for crustal dilatancy or crustal deformation of volcanic origin. Another application is the piezomagnetic change associated with faulting. Formulas for a vertical rectangular fault with shearing as well as tensile fault motion are presented.  
抄録  
内容記述タイプ  Abstract  
内容記述  地震や火山活動,あるいはゆるやかな地殻変動による地殻応力に伴って,地磁気が変化する.これは岩石が応力によって磁化を変えるピエゾ磁気効果を,その原因としている.本論文では様々な地殻活動に伴うピエゾ磁気変化を統一的に扱う方法を定式化する.この理論は基本的には, STACEY (1964)が｢地震地磁気効果｣を見積る計算で行ったやり方を一般化したものである.  
書誌情報 
東京大學地震研究所彙報 = Bulletin of the Earthquake Research Institute, University of Tokyo 巻 66, 号 4, p. 585722, 発行日 19920325 

ISSN  
収録物識別子タイプ  ISSN  
収録物識別子  00408972  
書誌レコードID  
収録物識別子タイプ  NCID  
収録物識別子  AN00162258  
フォーマット  
内容記述タイプ  Other  
内容記述  application/pdf  
日本十進分類法  
主題  453  
主題Scheme  NDC  
出版者  
出版者  東京大学地震研究所  
出版者別名  
Earthquake Research Institute, University of Tokyo 