An efficient, probabilistic neural network approach to solving inverse problems: Inverting surface wave velocities for Eurasian crustal thickness

Abstract

Abstract. Nonlinear inverse problems usually have no analytical solution and may be solved by Monte Carlo methods that create a set of samples, representative of the a posterJori distribution. We show how neural networks can be trained on these samples to give a continuous approximation to the inverse relation in a compact and computationally efficient form. We examine the strengths and weaknesses of this approach and use it to determine the full a posterJori distribution of crustal thickness from surface wave velocities. The solution to this inverse problem shows significant asymmetry and large uncertainties due to trade-off with shear velocity structure around the Moho. We produce maps of maximum likelihood crustal thickness across Eurasia which are in agreement with current knowledge about the crust; thus we provide an independent confirmation of these models. In this application, characterized by repeated inversion of similar data, the neural network algorithm proves to be very efficient.

Fast probabilistic petrophysical mapping of reservoirs from 3D seismic data

“…Notice that these plots are different from plots that represent the theoretical uncertainty alone, as might be found in other papers (e.g., Tarantola and Valette, 1982). This is because in the MDN inversion methodology, data measurement uncertainties are also added to the theoretical forward equations uncertainties (Devilee et al, 1999;Meier et al, 2007b;Shahraeeni and Curtis, 2011). Figure 6b shows I P as a function of porosity for the constant values of clay content and water saturation given above, but when the confounding parameters (i.e., effective pressure, bulk modulus, and density of hydrocarbon) are varied according to their a priori distributions.…”

“…Maiti et al (2007) and Maiti and Tiwari (2009) apply neural networks to identify lithofacies boundaries using density, neutron porosity, and gamma ray logs of the German Continental Deep Drilling Project (KTB). However, these two papers did not address the problem of inverting data for the joint PDF of a continuous multidimensional model vector, as in Devilee et al (1999), Meier et al (2007aMeier et al ( , 2007b, and Curtis (2009, 2011). Hampson et al (2001) and Schultz et al (1994) also apply neural networks to predict log properties from seismic data.…”

“…The MDN provides a solution to the time and the memory problems associated with the MC sampling method. Previously, Devilee et al (1999) and Meier et al (2007aMeier et al ( , 2007b show other geophysical applications of the MDN for solving 1D inverse problems. The latter papers invert global seismological data sets for the global distribution of various rock properties and structures in the crust and upper mantle, showing that large, seismic-like data sets can be inverted efficiently and probabilistically for 3D earth models.…”

Inversion of Schlumberger resistivity sounding data from the critically dynamic Koyna region using the Hybrid Monte Carlo-based neural network approach

“…For example: (1) for seismic event classification (Dystart and Pulli, 1990), (2) well log analysis (Aristodemou et al, 2005;Maiti et al, 2007;Maiti and Tiwari, 2007, 2010b, (3) first arrival picking (Murat and Rudman, 1992), (4) earthquake prediction (Feng et al, 1997), (5) inversion (Raiche, 1991;Devilee et al, 1999), (6) parameter estimation in geophysics (Macias et al, 2000), (7) prediction of aquifer water level (Coppola Jr. et al, 2005), (8) magneto-telluric data inversion (Spichak and Popova, 2000), (9) magnetic interpretations (Bescoby et al, 2006), (10) signal discrimination (Maiti and Tiwari, 2010a), (11) modeling (Sri Lakshmi and Tiwari, 2009), (12) DC resistivity inversion (Qady and Ushijima, 2001;Lampinen and Vehtari, 2001;Singh et al, 2005Singh et al, , 2006Singh et al, , 2010.…”

Inverting Rayleigh surface wave velocities for eastern Tibet and western Yangtze craton crustal thickness based on deep learning neural networks

“…Devilee et al(1999) were the first to use a neural network to invert surface wave velocities for Eurasian crustal thickness in a fully non-15 linear and probabilistic manner. Ueli Meier et al(2007) further develop the methods of Devilee et al (1999), then invert surface wave data for global crustal thickness on a 2• × 2• grid globally using a neural network. Although traditional shallow neural network can present nonlinear inverse function, it maybe cannot learn or approximate the real inverse function well when the real inverse function is too complicated.…”