Laplace-domain waveform inversion using a single damping constant

Abstract

(3) conventionally used multiple damping constants make the LWI algorithm computationally intensive.

LWI using a single damping constant (single-damping LWI), which is the main topic of this study, is motivated by the similar appearances of the inversion results obtained from LWI using different damping constants. Through the numerical experiment, the trends of inverted velocity model using different damping constants are identified, and the potential issues caused by extremely small and large damping constants, when the time-domain seismic data are used, are analyzed. Using the result of numerical experiment, range of proper damping constant for single-damping LWI is suggested. By inverting the Laplace-domain wave field with respect to the selected representative damping constant, the computing efficiency is dramatically enhanced (up to 6 times faster) while maintaining the quality of the inversion result (model misfit is smaller than 3). New scaling method using a depth weighting function is proposed in this study, and it provides the better convergence rate for single-damping LWI. Finally, real towed streamer data are used to verify the feasibility of single-damping LWI algorithm by comparing the result with that of the conventional LWI.

Laplace-domain waveform inversion (LWI) produces long-wavelength velocity models of the earth by using the Laplace transformed wave field. LWI is recognized as an efficient method for building long-wavelength velocity models because real data, which lacks low frequency information, can be inverted with minimal pre-processing stages such as band-pass filtering and first-arrival picking. Originally, the LWI algorithm was developed for 2-D acoustic media, but it has recently been extended for more realistic environments, such as acoustic and elastic media with irregular topography and 3-D acoustic, elastic and acoustic-elastic coupled media. In addition, the computing efficiency is significantly enhanced by exploiting the explicit time-domain modeling algorithm or implicit Laplace-domain modeling using an iterative matrix solver. Conventional LWI using various damping constants produces promising results. However, there remain several issues to be addressed: (1) the role of each damping constant is not clearly identified, so the combination of the optimal damping constants is empirically decided without a theoretical background

(2) there has not been any study to assess the potential issues caused by extremely small and large damping constants