Frequency-Bessel Transform Method For Extracting Dispersion Information From Seismic Records

Surface wave dispersion is an inherent physical phenomenon related to the un-derground structure of the earth's surface,and the dispersion characteristics of surface waves are widely used in the detection of the shear wave velocity structures.An impor-tant method to detect the velocity structure through the characteristics of surface wave dispersion is to extract the dispersion curves from the seismic waves or noise cross cor-relation functions,and to invert for the underground structure through the dispersion curves.A large amount of information of crust and mantle has been provided through the dispersion curve inversion.The traditional methods of extracting the dispersion curve mainly depends on nar-row band filtering and measuring the phase velocities of different frequencies.The ad-vantage of this approach is that it is stable and easy to operate,but the disadvantages are also obvious:the limited resolution of the dispersion curve measured and the difficulty to measure the dispersion curve in higher modes.Many studies have proved that the overtone dispersion curves contain a large amount of information about the structure,which can effectively reduce the uncertainty in the inversion of dispersion curves.In order to extract overtone dispersion information from seismic signals,some scholars have improved and proposed some new methods.These methods can be divided into the following categories:the method of domain change;extracting dispersion through the inversion method;the method of extracting dispersion information through specific distribution of stations.The above methods can effectively extract the high-modes to a certain extent,but most of these methods have requirements for the epicenter distance and the frequency of the extracted dispersion curves are often below 0.1 Hz.Based on these method,Chen Xiaofei Research Group(Wang et al.,2019;Wu et al.,2020)has proposed an new array-based method named Freqeuncy-Bessel Transform method to extract higher modes from ambient noise data.This method is based on the thoery of the solution of elastic dy-namic equation in 3-dimensional layered media.Compared with the traditional method,the dispersion curves extracted by this method have higher resolution,wider frequency range.The focus of this paper is to extend this method from the application of ambient noise data to the application of earthquake events data.The Frequency-Bessel Trans-form Method has a basic theoretical hypothesis in the application of ambient noise data,that is,the cross correlation function is equivalent to the imaginary part of Green's func-tion of isotropic source.However,the main source of natural earthquakes are double couple sources,which is obviously non-isotropic.The major difference between the two kind of sources is that there are differences between the items contained:the ver-tical component green function of isotropic source contains only the item containing the 0th-order Bessel function k-integral,while the green function of the double-couple source contains the k-integral items of the Oth-,1st-and 2nd-order Bessel functions.At the same time,the records of isotropic sources have nothing to do with the azimuth,while the radiation patterns of each items for double couple source are different.According to the differences mentioned above,in this paper,we first prove that each item of Green's function of double couple source can be applied to the Frequency-Bessel Transform method,if all of the radiation patterns are constants.Then,on this basis,we find that controlling the azimuth range can control the influence of radiation patterns.Thus we can promote the Frequency-Bessel Transform method to the applica-tion of earthquake events.In this paper,we take the records from USArray of several earthquakes as exam-ples.In practice,we found that data from most earthquake events can only extract the fundamental dispersion curve.Through the analysis of actual and synthetic seismic records,we found that the reason of this phenomenon is that the energy of fundamental surface wave is so strong that,in the Fourier transform,it can mask the other wave-form's energy.To solve this problem,we calculated time windows by given group velocity interval,which separates the energy in the waveform.In this way,we success-fully extracted the overtone dispersion curves.We call this process as the Multi-Window F-J method.Comparing the dispersion curves extracted from ambient noise with the dispersion curve extracted from earthquake events,we found that there is a strong complementary relationship between the two datasets.We believe,in future imaging work,combining the different characteristics of the two to provide better constraints on the structure is the focus.In addition to the Rayleigh wave and Love wave dispersion curves,we extracted the PL wave dispersion curve from the actual data by the Frequency-Bessel Transform method.In actual operation,we intercepted the waveform before the first arrival of the S wave through the time windows and extracted the dispersion curve with the phase velocity higher than 5km/s.Traditional seismological theory believes that the dispersion before the initial S wave can be explained by the leaking mode,and in ocean exploration,this phenomenon is also called guided-P wave dispersion.In our research on the extracted PL wave dis-persion curve,we found that the so-called leaking mode and guided-P wave dispersion are not simple equivalence relations,and the difference between the two structures may differ greatly for different structures..Through careful study of the theoretical dispersion spectrum,we found that when the difference between the maximum S wave velocity and the minimum P wave ve-locity in the main layer is not large,there will be a very obvious coupling of leaking modes and Guided-P dispersion,in which the leaking modes dominate,and the figure of these two is "twisted";when the difference between the maximum S wave velocity and the minimum P wave velocity in the main structure is large,the "twisted" is almost invisible and the Guided-P wave dispersion dominates.In classical theories,these two are considere the same thing.However,the examples we have observed from the actual data can obtain the region where the leaking mode is dominant and the region where the Guided-P wave dispersion is dominant,at the same time.Furthermore,we found that the leaking mode is sensitive to both P wave velocity and S wave velocity,and the Guided-P wave dispersion curve is only sensitive to the P-wave velocity structure.This provides an important basis for us to classify the two in the future and effectively retrieve the P wave velocity structure from surface wave data.