## Abstract

Based on the mathematical equivalence between the crack field and the continuous dislocation field, we briefly review continuum theory of defects from the view point of differential geometry. Then we derive a new differential geometric equation of static gravity change for anelastic effect due to the fault (dislocation) density. This equation shows that high gradient of dilatancy caused by the concentration of fault (dislocation) density accompanies high gradient of gravity change near the boundary between positive and negative gravity anomalies. This agrees with the characteristic distribution patterns; the distribution of short-wavelength gravity anomaly, active faults and shallow seismic activities overlap one another in the northeast Japan. Moreover, we discuss: (I) dynamic gravity anomaly related to earthquakes; (II) local gravity anomaly near the edges of an active fault; (III) differential geometric interpretation of gravity anomaly caused by the dislocation density; (IV) differential geometric relationship between gravity anomaly and magnetic anomaly (Poisson's relation).

Original language | English |
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Pages (from-to) | 239-257 |

Number of pages | 19 |

Journal | Acta Geophysica Polonica |

Volume | 47 |

Issue number | 3 |

Publication status | Published - 1999 |

## Keywords

- Active fault
- Differential geometry
- Dislocation density
- Earthquake
- Gravity anomaly