3-D Reverse-Time Migration Of Teleseismic Receiver Functions And Its Applications

Seismic velocity discontinuities of the Earth are important parts of the Earth interior structure.Their depths and undulations provide much-needed information on Earth's composition,temperature and pressure states,and dynamic processes.The active-source seismology is used mainly for research of shallow structures of the earth because of its limited penetration depth and enormous costs.With abundant earthquakes and seismic stations around the globe,the passive-source seismology is widespreadly used for imaging the Earth interior structures.In the passive-source seismology,one often-used data analysis technique is the teleseismic P-wave receiver function(RF)method,which has been used for imaging various crustal and mantle discontinuities in different regions.The reverse-time migration(RTM)method is a wave equation-based migration method first developed in the active-source seismology and can produce more accurate images in complex velocity models.It has several attractive features including flexibility,numerical stability,image fidelity and relatively easy implementation.In recent years,RTM has been adopted for passive-source seismic waveform data.The traditional RF imaging methods have the following shortcomings: 1)methods like the common-conversion-point(CCP)stacking could not handle strong velocity lateral variations,2)those using a full wave-equation numerical solver require expensive computation and memory storage and often demand using high-performance computers,3)the current teleseismic RTM methods need to remove the source time function(STF)of each earthquake from the waveform data first and to separate the P and S waves in the reconstructed wavefield before an imaging condition can be applied.These additional steps in the procedure increase the complexity of data processing that may affect the imaging results.Here,we develope a prestack RTM method that is applied to teleseismic RFs directly.We call the method RF-RTM,which can image using the primary P-to-S converted wave Ps and the secondary P-to-S converted wave PpPs.1)Similar to RTM,this method can image structures with strong velocity lateral variations.2)Instead of using a full wave-equation solver as in other passive-source RTM methods,we use the phase-shift-plus-interpolation(PSPI)wavefield propagator.The PSPI method,though an approximate solution to the 3-D wave equation,has been shown to be computationally efficient with satisfactory accuracy and be unconditionally stable.Its cost and complexity do not depend significantly on the size of the data.3)The RF method removes effects of the earthquake source in recorded three-component P-wave waveforms by deconvolving the vertical component from the radial component.In addition to the direct P arrival,RFs mainly contain a series of P-to-S converted phases from different seismic discontinuities beneath the stations.Thus the RF-RTM method does not need to remove the source time function and to separate the P and S waves.4)Most passive seismology experiments suffer from sparse,incomplete,and irregular spatial sampling,resulting in distorted images and artifacts.However,high-resolution teleseismic RF imaging techniques utilize the coherent signals of a seismic array to map the subsurface structure and require the seismic records to be spatially sampled densely and regularly.In order to satisfy this requirement,we develop a nonlinear stretching-and-squeezing method to interpolate RFs.5)Finally,we apply the methods to RFs of a 300-km-long linear seismic array in the Wabash Valley Seismic Zone(WBSZ)in the central US and a 100-km-long linear array through the Western Junggar(WJ)basin in northwest China.We can have the following conclusions:1.Tests using synthetic data in various crustal models demonstrate the effectiveness of the RF-RTM method and its superiority over the CCP stacking method.1)The method handles diffraction caused by strong lateral structural variation correctly and there is no limitation on the maximum dip of interface.2)In the presence of diffractions caused by strong lateral structural variations,the RF-RTM method can delineate clearly the interfaces while the CCP image is heavily contaminated by noise caused by the diffraction energies.2.We discuss the factors related to the quality of imaging results and conclude: 1)We suggest station spacing <5 km to be used for crustal-scale imaging using RFs.A 2-D seismic array is desired.If it is not feasible,a linear array should be oriented perpendicular to the strike of structure.Higher frequency RFs and smaller station spacing are needed in the presence of noise in the real data and regions of strong lateral variation.2)We test the sensitivity of RF-RTM on velocity model,and the results demonstrate a severe trade-off between interface depth and seismic velocities,particularly the Vp/Vs ratio,above the interface.An accurate crustal model of P-and S-wave velocities is essential for both RF-RTM and CCP to produce correct structural images.3)Our RF-RTM method can use the surface-reflected multiple PpPs for imaging.Being able to image using both Ps and PpPs data in RFs offers several benefits,including increasing the amount of data available for imaging,recognizing ‘ghost' interfaces in the image caused by the multiples and adjusting the model average Vp/Vs ratio above the interface by comparing the Ps image and PpPs image.4)Ambient noise affects the imaging results,especially with strong lateral variations.To get accurate imaging,high signal-noise-ratio is necessary.5)To compare the accuracy and efficiency of our RF-RTM using PSPI with RTM using finite-difference(FD)method,we can see RF-RTM is better than FD-RTM.3.We calculate synthetic RFs for several models to validate the efficacy of RF with the nonlinear interpolation method,and conclude that 1)Synthetic experiments show that this method is able to properly interpolate and regularize unevenly distributed RFs,even if the assumptions are not strictly satisfied;2)our method can work for some extreme cases,but some traces with strong diffraction waves from the corners cannot be fully recovered;3)this method has the advantage of being able to mitigate stair-step artifacts.4.We get useful information from the imaging results of the seismic array in the WBSZ as following.1)The shallowest interface depth varies from 1 to 3 km,with the deepest part near the centre of the profile.We interpreted it as the bottom of Phanerozoic Illinois basin.The interface between 10 and 20 km is most likely the boundary between the upper and lower crust.The strong and deep interface is the Moho that deepens from 50 km beneath the southeastern end to 60 km beneath the northwestern end.There is also an intermittent interface at about 40 km depth which we interpreted as the top of a lower crustal basal layer.Its impedance contrast is strongest near the centre of the profile and was interpreted as the top of a ‘rift pillow'.2)Compared with the CCP image that is horizontally smoothed due to its use of locally 1-D velocity models,the RF-RTM image reveals a little bit more details of structural lateral variations.5.From the RF-RTM results of the linear array through the Western Junggar basin in northwest China,we can see that: 1)The thickness of the Western Junggar basin basement is about 3 km,with apparent lateral undulation.2)Between the Zaire Mountain and the western Junggar basin a dip mid-crust interface can be observed.3)the Moho depth along the profile increases from about 42 km to 50 km.Beneath the Zaire mountian the Moho is flat at a depth of 42 km.In the transition zone of the Zaire moutain and the western Junggar basin,the Moho deepens clearly to the Western Junggar basin and reaches the deepest of approximately 50 km.4)Compared with CCP,the RF-RTM method reveal more lateral variation details.