Imaging Of Source Rupture Process By Multi-array Separation Variables Back-projection Method

Starting from the basic principle of array back-projection,we deeply analyze the problems existing in the present back-projection method,and propose a new method of multi-array back-projection named multi-array separation variables back-projection method.According to the fact that the back projection method is essentially the coherent superposition of seismic waves,and the Rayleigh criterion in optics and the spatial sampling theorem in information theory are introduced,the resolution of seismic array and the highest effective frequency of spatial sampling are analyzed quantitatively in theory.The response function distribution characteristics of the generalized array are tested in detail.It is found that there is a big difference between the generalized array response function and the classical array response function: even for a circular array,the distribution of the generalized array response function is not circular,and the same generalized array has different distribution of the generalized array response function to earthquakes in different directions.The concepts of elevation compression effect and equivalent aperture of array are proposed.The distribution of generalized array response function is explained in physics.The response function distribution of the generalized array with ellipse indicates that the discrimination ability of the generalized array in azimuth and epicentre distance is quite different.The new method separates the azimuth information with higher precision from the back projection result of a single array and combines two or more arrays to determine the source rupture process.This method eliminates the information of epicentral distance with low accuracy,eliminates the influence of the difference between the one-dimensional velocity structure model and the actual earth to the greatest extent,and overcomes the epicentral distance error introduced by the assumption of constant source depth in the classical inverse projection.The new method uses several arrays with different orientations,each with a smaller aperture,which can avoid the influence of radiation pattern and Doppler effect.We use the non-negative least square method to eliminate the smoothing effect of the sliding time window on the high-frequency energy,and the obtained energy release time function is closer to the high-frequency energy release process of the seismic source.We have designed two typical source models,one is a thrust fault with a small dip angle,the other is a strike-slip fault with a large dip angle.The depth of the input source changes significantly.We have calculated the synthetic seismograms and tested the new method in detail.Theoretical test results show that this method can eliminate the difference between the array imaging results of different azimuths,and when the focal depth changes significantly,the new method can ensure that the back projection results are still accurate.At the location far away from the initial rupture point,the location result is still of high accuracy without aftershock correction.Finally,we applied the new method to the Nepal earthquake in 2015 and the Indonesia earthquake in 2018,and obtained the imaging results consistent with the geodetic measurements such as GPS and In SAR.