A comparative analysis of two-dimensional multi-valued ray tracing techniques
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ORIGINAL PAPER
A comparative analysis of two-dimensional multi-valued ray tracing techniques Bin Li 1 & Chao-ying Bai 1,2 & Qing-lin Wang 3 & Stewart Greenhalgh 4
Received: 31 August 2015 / Accepted: 2 November 2017 # Saudi Society for Geosciences 2017
Abstract Seismic wavefront self-intersection (or multivalued seismic rays) is a natural phenomenon when a seismic wave propagates through a complex medium, which is commonly ignored in most previous studies. The later arrivals not only contain useful information regarding low velocity anomalous zones and/or irregular reflecting interfaces, but also have the potential to improve the ray coverage in subsequent seismic imaging. Due to the relative immaturity of this field of research, it is instructive to compare different algorithms and therefore develop more advanced, efficient, and practical schemes for tracing multi-valued arrivals between the source and the receivers when the medium is heterogeneous and incorporates irregular or curved interfaces. For these reasons, we first modify the so-called reduced phase space method, in which a continuous wavefront mapping method is implemented for efficient and accurate consideration, and then compare it with two newly developed grid-based algorithms for tracing multi-valued direct arrivals in heterogeneous media and multivalued reflected arrivals when undulating interfaces are pres-
* Chao-ying Bai [email protected]
1
School of Geology Engineering and Geomatics, Chang’an University, Xi’an 710054, China
2
Institute of Computational Geophysics, Chang’an University, Xi’an 710054, China
3
Earthquake Administration of Shandong Province, Jinan 250014, China
4
Department of Geosciences, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia
ent. The results show that the modified reduced phase space method is a potent and useful algorithm for tracking both multi-valued direct and reflected arrivals. The first-order Braylet^ method is simple in principle but is unable to trace all possible later arrivals. Under such circumstances, the extremal solution method is a good choice to trace the multivalued reflected arrivals; it is comparable to the modified reduced phase space method in practical application. Keywords Wavefront self intersection . Multi-valued ray tracing . The modified reduced phase space method . The Braylet^ method . An extremal solution method
Introduction The development of advanced and efficient practical schemes for tracing multi-valued wave arrivals between the source and the receivers within complex media would allow the prediction of many more observable phases, which in turn has the potential to benefit many areas of seismology, such as traveltime tomography, receiver function analysis, and seismic migration. The complex behavior of seismic rays for the two-point ray tracing problem is often referred to as the multi-pathing problem (e.g., Červeny 2001). This means that a multiplicity of raypaths must be considered between source and receiver. It is well known that either low
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