Crustal Gravitational Potential Energy Change and Subduction Earthquakes

Abstract

Crustal gravitational potential energy (GPE) change induced by earthquakes is an important subject in geophysics and seismology. For the past forty years the research on this subject stayed in the stage of qualitative estimate. In recent few years the 3D dynamic faulting theory provided a quantitative solution of this subject. The theory deduced a quantitative calculating formula for the crustal GPE change using the mathematic method of tensor analysis under the principal stresses system. This formula contains only the vertical principal stress, rupture area, slip, dip, and rake; it does not include the horizontal principal stresses. It is just involved in simple mathematical operations and does not hold complicated surface or volume integrals. Moreover, the hanging wall vertical moving (up or down) height has a very simple expression containing only slip, dip, and rake. The above results are significant to investigate crustal GPE change. Commonly, the vertical principal stress is related to the gravitational field, substituting the relationship between the vertical principal stress and gravitational force into the above formula yields an alternative formula of crustal GPE change. The alternative formula indicates that even with lack of in situ borehole measured stress data, scientists can still quantitatively calculate crustal GPE change. The 3D dynamic faulting theory can be used for research on continental fault earthquakes; it also can be applied to investigate subduction earthquakes between oceanic and continental plates. Subduction earthquakes hold three types: (a) crust only on the vertical up side of the rupture area; (b) crust and seawater both on the vertical up side of the rupture area; (c) crust only on the vertical up side of the partial rupture area, and crust and seawater both on the vertical up side of the remaining rupture area. For each type we provide its quantitative formula of the crustal GPE change. We also establish a simplified model (called CRW Model) as follows: for Type B and Type C subduction earthquakes, if the seawater average depth on the vertical up side of the rupture area is less than a tenth of the hypocenter depth, then take the approximation that the seawater above the continental plate is replaced by the upper crustal material of the continental plate. The formula of quantitative calculating the crustal GPE change is also provided for this model. Finally, for 16 September 2015 Mw 8.3 Illapel Chile earthquake, we apply CRW Model and obtain the following results: the crustal GPE change is equal to 1.8 × 1019 J, and the hanging wall vertical moving-up height is 1.9 m with respect to the footwall. We believe this paper might be the first report on the quantitative solution of the crustal GPE change for this subduction earthquake; our results and related method will be helpful in research into the earthquakes in Peru–Chile subduction zone and the Andean orogeny. In short, this study expounds a new method for quantitative determining the crustal GPE change caused by subduction earthquakes, which is different from other existing methods.