Application of Factor Analysis in Seismic Profiling
Zhenhai Wang, Chi Hau Chen · 2007
CONTENTS 6.1 Introduction to Seismic Signal Processing.................................................................... 102 6.1.1 Data Acquisition ................................................................................................... 102 6.1.2 Data Processing..................................................................................................... 103 6.1.2.1 Deconvolution........................................................................................ 103 6.1.2.2 Normal Moveout ................................................................................... 103 6.1.2.3 Velocity Analysis ................................................................................... 104 6.1.2.4 NMO Stretching..................................................................................... 104 6.1.2.5 Stacking ................................................................................................... 104 6.1.2.6 Migration ................................................................................................ 104 6.1.3 Interpretation......................................................................................................... 105 6.2 Factor Analysis Framework ............................................................................................ 105 6.2.1 General Model....................................................................................................... 105 6.2.2 Within the Framework......................................................................................... 107 6.2.2.1 Principal Component Analysis ........................................................... 107 6.2.2.2 Independent Component Analysis..................................................... 108 6.2.2.3 Independent Factor Analysis............................................................... 109 6.3 FA Application in Seismic Signal Processing .............................................................. 109 6.3.1 Marmousi Data Set ............................................................................................... 109 6.3.2 Velocity Analysis, NMO Correction, and Stacking ........................................ 110 6.3.3 The Advantage of Stacking................................................................................. 112 6.3.4 Factor Analysis vs. Stacking ............................................................................... 112 6.3.5 Application of Factor Analysis........................................................................... 114 6.3.5.1 Factor Analysis Scheme No. 1............................................................. 114 6.3.5.2 Factor Analysis Scheme No. 2............................................................. 114 6.3.5.3 Factor Analysis Scheme No. 3............................................................. 116 6.3.5.4 Factor Analysis Scheme No. 4............................................................. 116 6.3.6 Factor Analysis vs. PCA and ICA ..................................................................... 118 6.4 Conclusions........................................................................................................................ 120 References ................................................................................................................................... 120 Appendices ................................................................................................................................. 122 6.A Upper Bound of the Number of Common Factors.................................................... 122 6.B Maximum Likelihood Algorithm.................................................................................. 123 Formed millions of years ago from plants and animals that died and decomposed beneath soil and rock, fossil fuels, namely, coal and petroleum, due to their low cost availability, will remain the most important energy resource for at least another few decades. Ongoing petroleum research continues to focus on science and technology needs for increased petroleum exploration and production. The petroleum industry relies heavily on subsurface imaging techniques for the location of these hydrocarbons.