Recent advances in optimized geophysical survey design

Surveydesignultimatelydictatesthequalityofsubsurface information provided by practical implementations of geophysicalmethods.Itisthereforecriticaltodesignexperimental procedures that cost effectively produce those data that maximize the desired information. This review cites recent advances in statistical experimental design techniques applied in the earth sciences. Examples from geoelectrical, crosswell and surface seismic, and microseismic monitoring methodsareincluded.Usingoverdetermined1Dand2Dgeoelectrical examples, a minor subset of judiciously chosen measurementsprovidesalargepercentageoftheinformation content theoretically offered by the geoelectrical method. In contrast, an underdetermined 2D seismic traveltime tomography design study indicates that the information content increases almost linearly with the amount of traveltime data source-receiver pairs considered until the underdeterminancyisreducedsubstantially.Anexperimentaldesignstudy of frequency-domain seismic-waveform inversion experiments reveals that a few optimally chosen frequencies offer asmuchsubsurfaceinformationasthefullbandwidth.Anonlinear experimental design for a seismic amplitude-versusangle survey identifies those incidence angles most important for characterizing a reservoir.Anonlinear design example shows that designing microseismic monitoring surveys based on array aperture is a poor strategy that almost certainlyleadstosuboptimaldesigns.

[1]  Andrew Curtis,et al.  Optimal design of focused experiments and surveys , 1999 .

[2]  Öz Yilmaz,et al.  Seismic data processing , 1987 .

[3]  Jonathan B. Ajo-Franklin,et al.  Optimal experiment design for time-lapse traveltime tomography , 2009 .

[4]  Stanley H. Ward,et al.  Statistical evaluation of electrical sounding methods; Part I, Experiment design , 1976 .

[5]  R. Barker,et al.  Practical techniques for 3D resistivity surveys and data inversion1 , 1996 .

[6]  W. J. Studden,et al.  Theory Of Optimal Experiments , 1972 .

[7]  Jeannot Trampert,et al.  Optimal nonlinear Bayesian experimental design: an application to amplitude versus offset experiments , 2003 .

[8]  Hansruedi Maurer,et al.  Frequency and spatial sampling strategies for crosshole seismic waveform spectral inversion experiments , 2009 .

[9]  Andrew Curtis,et al.  Geological Prior Information: Informing Science and Engineering , 2005 .

[10]  A. Curtis,et al.  Optimal elicitation of probabilistic information from experts , 2004, Geological Society, London, Special Publications.

[11]  Hansruedi Maurer,et al.  Optimized design of geophysical experiments , 1997 .

[12]  Frank Scherbaum,et al.  The design of optimum networks for aftershock recordings , 1994 .

[13]  Alan G. Jones,et al.  An objective real-time data-adaptive technique for efficient model resolution improvement in magnetotelluric studies , 1986 .

[14]  Naoshi Hirata,et al.  Generalized least-squares solutions to quasi-linear inverse problems with a priori information. , 1982 .

[15]  M. H. Loke,et al.  Rapid parallel computation of optimised arrays for electrical imaging surveys [extended abstract] , 2009 .

[16]  Hansruedi Maurer,et al.  Optimizing the design of geophysical experiments: Is it worthwhile? , 2000 .

[17]  A. Curtis Optimal experiment design: cross-borehole tomographic examples , 1999 .

[18]  Christopher L. Liner,et al.  3-D seismic survey design as an optimization problem , 1999 .

[19]  Stuart Crampin,et al.  Microcracks in the Earth's crust , 1985 .

[20]  David M. Steinberg,et al.  Configuring a seismographic network for optimal monitoring of fault lines and multiple sources , 1995, Bulletin of the Seismological Society of America.

[21]  W. Menke Geophysical data analysis : discrete inverse theory , 1984 .

[22]  David R. Cox Planning of Experiments , 1958 .

[23]  Roel Snieder,et al.  Reconditioning inverse problems using the genetic algorithm and revised parameterization , 1997 .

[24]  Anthony Lomax,et al.  Earthquake location, direct, global-search methods , 2009 .

[25]  Anthony Lomax,et al.  A deterministic algorithm for experimental design applied to tomographic and microseismic monitoring surveys , 2004 .

[26]  P. Bird Stress and temperature in subduction shear zones: Tonga and Mariana , 1978 .

[27]  Thomas Hennig,et al.  Object orientated focussing of geoelectrical multielectrode measurements , 2008 .

[28]  Hansruedi Maurer,et al.  Design strategies for electromagnetic geophysical surveys , 2000 .

[29]  Hansruedi Maurer,et al.  Optimizing the design of geophysical experiments: Is it worthwhile? , 2000 .

[30]  David H. Wolpert,et al.  No free lunch theorems for optimization , 1997, IEEE Trans. Evol. Comput..

[31]  A. Curtis,et al.  Prior information, sampling distributions, and the curse of dimensionality , 2001 .

[32]  Douglas W. Oldenburg,et al.  Optimal Survey Design Using the Point Spread Function Measure of Resolution , 2005 .

[33]  Toby J. Mitchell,et al.  An Algorithm for the Construction of “D-Optimal” Experimental Designs , 2000, Technometrics.

[34]  Carl Wunsch,et al.  Oceanographic Experiment Design by Simulated Annealing , 1990 .

[35]  D. Oldenburg,et al.  THE INTERPRETATION OF DIRECT CURRENT RESISTIVITY MEASUREMENTS , 1978 .

[36]  R. G. Pratt,et al.  Efficient waveform tomography for lithospheric imaging: implications for realistic, two-dimensional acquisition geometries and low-frequency data , 2007 .

[37]  Albert Tarantola,et al.  Inverse problem theory - and methods for model parameter estimation , 2004 .

[38]  Alan G. Green,et al.  Experimental design: Electrical resistivity data sets that provide optimum subsurface information , 2004 .

[39]  Hansruedi Maurer,et al.  Optimized and robust experimental design: a non-linear application to EM sounding , 1998 .

[40]  Emanuel Winterfors,et al.  Numerical detection and reduction of non-uniqueness in nonlinear inverse problems , 2008 .

[41]  Boris Gurevich,et al.  A semi‐empirical velocity‐porosity‐clay model for petrophysical interpretation of P‐ and S‐velocities , 1998 .

[42]  Henry P. Wynn,et al.  Maximum entropy sampling , 1987 .

[43]  C. E. SHANNON,et al.  A mathematical theory of communication , 1948, MOCO.

[44]  A. Tarantola,et al.  Generalized Nonlinear Inverse Problems Solved Using the Least Squares Criterion (Paper 1R1855) , 1982 .

[45]  David M. Steinberg,et al.  Optimal configuration of a seismographic network: A statistical approach , 1990, Bulletin of the Seismological Society of America.

[46]  Partha S. Routh,et al.  The point-spread function measure of resolution for the 3-D electrical resistivity experiment , 2009 .

[47]  Hansruedi Maurer,et al.  Optimization of DC resistivity data acquisition: real-time experimental design and a new multielectrode system , 2002, IEEE Trans. Geosci. Remote. Sens..

[48]  R. Pratt Seismic waveform inversion in the frequency domain; Part 1, Theory and verification in a physical scale model , 1999 .

[49]  Andrzej Kijko,et al.  An algorithm for the optimum distribution of a regional seismic network—I , 1977 .

[50]  R. Gerhard Pratt,et al.  Efficient waveform inversion and imaging: A strategy for selecting temporal frequencies , 2004 .

[51]  D. H. Griffiths,et al.  A MULTI-ELECTRODE ARRAY FOR RESISTIVITY SURVEYING , 1985 .

[52]  Toby J. Mitchell,et al.  An algorithm for the construction of “ D -optimal” experimental designs , 2000 .

[53]  W. Press,et al.  Numerical Recipes: The Art of Scientific Computing , 1987 .

[54]  Andrew Curtis,et al.  Theory of model-based geophysical survey and experimental design , 2012 .

[55]  Jonathan Chambers,et al.  Improved strategies for the automatic selection of optimized sets of electrical resistivity tomography measurement configurations , 2006 .

[56]  Gail Heath,et al.  Spatial focusing of electrical resistivity surveys considering geologic and hydrologic layering , 2007 .

[57]  Darrell Coles,et al.  A method of fast, sequential experimental design for linearized geophysical inverse problems , 2009 .

[58]  Andrew Curtis,et al.  Iteratively constructive sequential design of experiments and surveys with nonlinear parameter-data relationships , 2009 .

[59]  Andrew Curtis,et al.  Theory of model-based geophysical survey and experimental design: Part 2—nonlinear problems , 2004 .

[60]  P. Laycock,et al.  Optimum Experimental Designs , 1995 .

[61]  E. Haber,et al.  Numerical methods for experimental design of large-scale linear ill-posed inverse problems , 2008 .