Wave Equation Distributed Acoustic Sensing Data Inversion

Distributed Acoustic Sensing(DAS)is a new seismic observation system that has developed rapidly.The DAS technology senses the fiber deformation caused by external vibration in real-time based on the Rayleigh scattering effect in the fiber.By extracting the backscattered signals at different times and demodulating the phase and strain changes,the axial strain measurement of the fiber is realized.Each small section of the optical fiber can be equivalent to a single-component strain gauge to realize distributed measurement.Compared with traditional geophones,DAS is resistant to harsh environments and easy to achieve high-density observations in large areas.Imaging and velocity inversion.Regarding velocity structure inversion imaging,since DAS technology only receives the axial strain rate response from the optical fiber,the data signal-to-noise ratio is low.Reliable,high-precision velocity imaging results are challenging to obtain.In addition,the theoretical basis of fiber signal propagation mechanism,response sensitivity,gauge length,and scattering directionality is still lacking incomplete analysis.Given the above problems,this paper first analyzes the DAS signal amplitude and sensitivity response based on the plane wave-particle displacement-velocity formula and the relationship between velocity and strain rate,compares traditional geophones’ response,and analyses the response gauge length,wavelength,and different azimuth angles.It provides theoretical guidance for the acquisition and processing of measured DAS data.Then,based on the finite-difference numerical simulation method of the wave equation,combined with the relationship between velocity and strain rate,the DAS signal’s elastic wave finite-difference numerical simulation is realized.Taking the traditional geophone simulation results as a reference,comparing the DAS and geophone data’s waveform and surface wave dispersion difference provides a theoretical basis for subsequent inversion imaging.Finally,the DAS wave equation inversion theory directly based on the strain rate is deduced and realized.The DAS fullwaveform inversion(FWI)method and wave-equation dispersion inversion are studied.The typical model and measured DAS data are used to verify this paper.The proposed method can obtain the S-wave velocity structure imaging at different scales,providing a reliable image method for applying DAS technology.