No abstract

Summary The accurate numerical modelling of 3-D seismic wave propagation is essential in understanding details to seismic wavefields which are, observed on regional and global scales on the Earth’s surface. The diffusive-viscous wave (DVW) equation was proposed to study the connection between fluid saturation and frequency dependence of reflections and to characterise the attenuation property of the seismic wave in a fluid-saturated medium. The attenuation of DVW is primarily described by the Active Attenuation Parameters (AAP) in the equation. It is, therefore, imperative to acquire these parameters and to additionally specify the characteristics of the DVW. In this paper, Quality Factor, Q is used to obtain the AAP, and they are compared to those of the visco-acoustic wave. We further derive the 3-D numerical schemes based on a second order accurate finite volume scheme with a second order Runger-Kutta approximation for the time discretisation and a fourth order accurate finite difference scheme with a fourth order Runger-Kutta approximation for the time discretisation. We then simulate the propagation of seismic waves in a 3-D fluid-saturated medium based on the derived schemes. The numerical results indicate stronger attenuation when compared to the visco-acoustic case.

whose continuous interest, encouragement, contributions and support during my PhD journey I greatly appreciate. Prof. Arturo Hidalgo-Lopez, I say thank you for your guidance throughout every phase of this research; for the knowledge shared in all aspects related to numerical methods and FORTRAN programming; as well as your great sense of humour. I am also indebted to my former co-supervisor Prof. Rafael Medina Ferro from whom I have learned so much, and who played a vital role in the successful publication of our first article. Prof. Rafael Medina Ferro, kindly take a bow for your remarkable contributions. My PhD journey would not have been possible without the financial support from my dearest parents, Mr. Victor Mensah and Mrs. Ethel Mensah. Dad, Mom, I say thank you for giving me the necessary tools to succeed in life and God richly bless you. The financial support is greatly acknowledged.I am grateful to my lovely and supportive brothers for all their sacrifices and support throughout these years. I ask the Almighty God to make you my siblings in the next life.God richly bless you all.Lastly, I wish to deeply thank and dedicate this research to my pretty wife, Wilhelmina, my adorable kids, Ethel, Victor, Jason, and Jaden, for all their sacrifices and support. My darling Wilhelmina, I love you and forever will. My adorable angels, I love you all and forever remain indebted to you for your sacrifices.