International Journal of Geosciences, 2013, 4, 283-289 http://dx.doi.org/10.4236/ijg.2013.42026 Published Online March 2013 (http://www.scirp.org/journal/ijg) The Application of Joint Inversion in Geophysical Exploration Ákos Gyulai, Mátyás Krisztián Baracza, Éva Eszter Tolnai Department of Geophysics, Faculty of Earth Science and Engineering, University of Miskolc, Miskolc, Hungary Email: gfgyulai@uni-miskolc.hu, baracza@uni-miskolc.hu, evaeszter.tolnai@gmail.com Received October 15, 2012; revised December 9, 2012; accepted January 18, 2013 ABSTRACT The paper presents a short overview about the application of joint inversion in geophysics. It gives also an alternative explanation for the term of “different data sets” and discusses what types of inversion procedures can be considered as joint inversion. Nowadays there are no standard standpoints using the appellation joint inversion. What is joint inver- sion? Based on the information matrix an answer could be given for this question what could be regarded as various types of data sets that are inverted simultaneously. We would like to expand the explanation—that is professed by many researchers—of the method that regards only the simultaneous inversion of data sets based on different physical pa- rameters as joint inversion. Keywords: Joint Inversion; Simultaneous Inversion; Geophysical; Serious Expansion 1. Introduction The adaptation of joint inversion is the straightforward consequence of the applied complex interpretation me- thods in geophysics together with the development of inversion methods. The first phrasing and application of joint inversion were given by Vozoff in 1975 as “invert- ing several different kinds of geophysical measurements”. He realized the simultaneous inversion of DC (Direct Current) resistivity and magnetotelluric measured data sets [1]. This method could be regarded as the basis of joint inversion methods. Vozoff as the first researcher and author of joint inversion method developed the si- multaneous inversion of different measured electric con- ductivity data. We could put a question about why do we consider two data sets as different data sets? Is it because one is gained from DC measurement and the other one is from electromagnetic measurement or because the dif- ference is in the deeper physical content through the data about the geological structure? Perhaps it is not so diffi- cult question to answer. Furthermore the term of joint inversion was applied in literature for the inversion of data measured by different physical principles. For instance, in near-surface explora- tion it generally represents the joint inversion of seismic and geoelectric data. Distinguishing inversion methods based on different data combinations researchers have tried to introduce different appellation e.g. cooperative inversion, simultaneous inversion, combined inversion etc. However, most of them remained with the term “joint inversion” for naming the method that gives the solution of various types of data sets inverted simultane- ously. In most cases the complex geophysical exploration means the application of physically different methods hence these methods appeared more frequently as joint inversion. 2. The Method of Joint Inversion The scheme overview of joint inversion by [2] demon- strates the joint inversion of diverse subsurface electrical soundings and VSP (Vertical Seismic Profiling) meas- urements. The seismic model parameter vector is (the first and the fifth layers are considered to be half-spaces)   T 2 3 4 1 2 3 4 5 , , , , , , , s h h h v v v v v  P   T 2 3 4 1 2 3 4 5 , , , , , , , e h h h , (1) where h i denotes the layer-thicknesses and v i denotes the seismic propagation velocities. The geoelectric model parameter vector is  P , (2)      where ρ i denotes the resistivities. The joint parameter vector   P is the combination of vectors s P e P   T 2 3 4 1 5 1 5 , , , , , , , , h h h v v and    P     calculated , i i Y Y S  P . (3) The common elements in the joint parameter vector in this example are the layer thicknesses as Equation (3) shows. The direct problem is , (4) Copyright © 2013 SciRes. IJG