Occam Inversion Research Articles

Rayleigh wave tomography of China and adjacent regions

This paper presents a tomographic study on the S wave velocity structure of China and adjacent regions. Group velocity dispersions of fundamental Rayleigh waves along more than 4000 paths were determined with frequency‐time analysis. The study region was divided into a 1° × 1° grid, and velocities in between grid nodes were calculated by bilinear interpolation. The Occam's inversion scheme was adopted to invert for group velocity distributions. This method is robust and allows us to use a fine grid in model parameterization and thus helps to restore a more realistic velocity pattern. Checkerboard tests were carried out, and the lateral resolution was estimated to be 4°–6° in China and its eastern continental shelves. The resulting group velocity maps from 10 to 184 s showed good correlation with known geological and tectonic features. The pure path dispersion curves at each node were inverted for shear wave velocity structures. The three‐dimensional velocity model indicates thick lithospheres in the Yangtze and Tarim platforms and hot upper mantles in Baikal and western Mongolia, coastal area and continental shelves of eastern China, and Indochina and South China Sea regions. The Tibetan Plateau has a very thick crust with a low‐velocity zone in its middle. Beneath the crust a north dipping high‐velocity zone, mimicking a subducting plate, reaches to 200 km in depth and reaches to the Kunlun Mountains northward. In northern Tibet a low‐velocity zone immediately below the Moho extends eastward then turns southward along the eastern edge of the plateau until it connects to the vast low‐velocity area in Indochina and the South China Sea.

Love Wave Seismic Tomography of China and Vicinal Sea Areas

AbstractWe assembled the surface wave data recorded by 33 digital seismic stations in China and vicinal areas, and extracted group velocity dispersion curves of fundamentalmode Love wave along approximately 4 000 paths by means of multiple‐filter techniques. The study area was divided into a grid of 1° × 1°, and 43 group velocity distribution maps were obtained between 7.3 s and 184 s by means of Occam's inversion, afterwards the shear wave velocity structures were inverted at each node. The lateral resolution is about 3°–5° which is tested with checkerboard method. The results show that: the difference of the crust and upper mantle structure in the area is very significant, the correlation of the interior structure and surface character is down to 100–150 km. China continent can be divided into several different blocks, and the block boundary is comparatively clear.

Magnetotelluric image of the crust and upper mantle in the backarc of the northwestern Argentinean Andes

Magnetotelluric data from the backarc of the Central Andes in NW Argentinawere re-examined by employing impedance tensor decomposition and 2-D inversion and modelling techniques. The data in the period range of 50–15 000 s were collected on a profile of 220 km length reaching from the Eastern Cordillera across the Santa Barbara System to the Andean foreland of the Argentinean Chaco. After a dimensionality analysis, data from most sites were treated as regional 2-D. The exception was the eastern section of the profile, where the magnetotelluric transfer functions for periods ≤ 1000 s reflect a 3-D earth. Application of two tensor decomposition schemes yielded a regional strike direction of N–S, which is the azimuth of the Central Andean mountain chains. Several 2-D models were obtained by pseudo- and full 2-D Occam inversion schemes. Special emphasis was placed on the inversion of phase data to reduce the influence of static shifts in the apparent resistivity data. The smooth inversion models all show a good conductor at depth. A final model was then calculated using a finite element forward algorithm. The most prominent feature of the resulting model is a conductor which rises from depths of 180 km below the Chaco region to 80 km beneath the Santa Barbara System and the Eastern Cordillera. Its interpretation as a rise of the electrical asthenosphere is supported by seismic attenuation studies. Magnetotelluric results, surface heat-flow distribution in the area, and the electrical properties of crustal and mantle rocks suggest that the upper mantle is predominantly ductile beneath the Eastern Cordillera and the western Santa Barbara System. This generally agrees with anelastic seismic attenuation models of the area and is useful in discriminating between models of Q quality factor distribution.

Rayleigh Wave Velocity and Structure of Crust and Upper Mantle Beneath the Seas in Eastern China

AbstractThis paper is to reveal the velocity structure of crust and upper mantle under the seas in eastern China by studying the surface wave dispersion. High quality Rayleigh wave data from thirty‐one stations was used in this paper. A new grid inversion method (Occam's inversion method) was adopted in this study to calculate the pure path dispersion curves in this area. We obtained the group velocity maps of Rayleigh waves at thirty‐six periods from 10 to 150 seconds with this method, and inverted for the shear wave velocity structure at a few locations typical for some tectonic units. The division of different tectonic units and the characteristics of both velocity structure and the depth of low‐velocity layer in the upper mantle of different tectonic units in the study area were studied.

An alternative method for a reliable estimation of seismicity with an application in Greece and the surrounding area

AbstractAn alternative method is proposed for the robust estimation of a and b values of the Gutenberg-Richter relation. The main hypothesis is that b values depend on material properties and the seismotectonic setting and therefore should vary relatively smoothly in space. As far as the a values are concerned, more sharp variations are allowed because these values determine the seismicity level, once the b value is fixed. The study area is organized into a grid, and the a and b values are simultaneously determined for the whole grid by solving an appropriate linear system. Smooth b variations are imposed by introducing additional linear constraints, similar to the Occam's inversion used in tomography studies. The method is applied to Greece and the surrounding area, which is a high seismicity area. The results are in very good agreement with previous studies and further enhance our knowledge for the study area. Moreover, additional seismicity measures (return periods, probabilities, etc.) are estimated robustly because they depend on the a and b values obtained for this area.

Preliminary result of magnetotelluric soundings in the fold-thrust belt of Taiwan and possible detection of dehydration

Until the magnetotelluric (MT) soundings were conducted in the last two years, there was no systematic view of the deep electric conductivity in the fold-thrust belt of the Taiwan orogen, being a typical example of arc-continental collision. Presented in this paper are the initial results and preliminary interpretation of the MT survey in Taiwan. The determinant response of the impedance tensor was calculated for inversion and Occam's inversion which could generate smooth models was mainly used for interpreting MT data at each site. The existence of a conductive zone with depths of 10–20 km beneath the Island of Taiwan is undoubtedly the most important feature found in this study. The depths are well correlated with the inferred depth of dehydration reactions of Suppe (1981) and the top of the aseismic lower crust observed by Wang et al. (1994). Thus, the authors believe that the cause of this conductive zone is probably the fluids released from dehydration reactions. Additionally, close to the Lishan fault the MT data show strong distortions which may be the result of induction in more complex three-dimensional structures. Further multi-dimensional analysis of the data is required in the future for delineating a more realistic image of the subsurface heterogeneous structure.

Inverting AEM data using a damped eigenparameter method

Because of the non-uniqueness of the EM inversion problem, one must constrain the inversion procedure in some way to achieve a geologically valid model. All constraints are regarded as subjective except when they agree with the prejudices of the person using the inversion. Conventionally, constraints have included: inverting to models with a small number of parameters; forcing conformation with a priori geological information; or requiring smooth or minimal spatial derivatives with respect to conductivity (Occam inversion).We prefer to use the constraint philosophy of the damped eigenparameter method (also called the Jupp-Vozoff algorithm). After incorporating a priori geological knowledge in the starting model, this process constrains change to individual model parameters on the basis of the strength of their effect on the data when grouped into eigenparameters. The initial model can thus be regarded as a soft constraint. In this paper, we extend this inversion philosophy to the case where the number of unknown parameters exceeds the number of data points; i.e., an under-determined problem. Inverting to both undetermined and over-determined layered earth models, we have tested this method on two sets of synthetic AEM data: one generated from a 1D model, the other from a 2.5D model.

Comparison of induced polarization and controlled‐source audio‐magnetotellurics methods for massive chalcopyrite exploration in a volcanic area

In this paper, we compare and contrast the results of field experiments with the dipole‐dipole‐induced polarization (IP) and controlled‐source audio‐magnetotellurics (CSAMT) methods, along the same survey profiles, at a test area that was subject to extensive drilling and detailed geological investigation. The ore bodies are interbedded between two series of dacitic tuff. The depth and thickness of the massive chalcopyrite‐pyrite‐sphalerite body vary between 25 and 100 m and 0.5 and 16 m, respectively. Resistivity and IP phase measurements on the core samples collected from the test area provide some idea of the relative differences between the background rock units and the target. The resistivity of the chalcopyrite samples varies between 0.6 to 2 ohm-m and provides sufficient resistivity contrast with surrounding volcanic rock units for target detection. The results of dipole‐dipole IP profiling with a 50-m dipole length conducted along two profiles are presented in the form of apparent resistivity and phase pseudosections. CSAMT measurements were made at 13 frequencies from 2 Hz to 8192 Hz along three profiles. The receiver dipole length was 25 m. The CSAMT data are presented in the form of pseudosections using conventional and new definitions of apparent resistivity. The elliptical contours of low apparent resistivity generated by the transition‐field notch can be misleading with respect to the real anomaly of the ore body. These artificial anomaly patterns are suppressed by making use of an alternative apparent resistivity definition derived from the frequency‐normalized impedance. The qualitative interpretation based on the IP and CSAMT pseudosections shows that the location and the extension of the ore body are indicated better in the CSAMT apparent resistivity data computed from the alternative definition. The qualitative interpretation of the IP data is difficult because of the 3-D effect arising from the neighboring thicker parts of the ore body and pyrite particles within the basement. At the final stage, the far‐field range of the CSAMT apparent resistivity and phase data is identified by the visual inspection of the individual sounding diagrams. The models derived from the 2-D Occam inversion carried out on the far‐field data are compared with the drill‐hole information and are found to describe the actual geological situation.

Resolution of seismic waveform inversion: Bayes versus Occam

In Bayesian inference, probabilistic information about models is posited a priori. This information, which may very well include features in the null space of the forward problem, affects both the computed models and the resulting resolution estimates. In Occam's inversion, on the other hand, the goal is to construct the smoothest model consistent with the data. This is not to say that one believes a priori that models are really smooth, but rather that a more conservative interpretation of the data ought to be made by eliminating features of the model that are not required to fit the data. The length scale associated with the smoothing is an indirect measure of resolution. In some cases the mathematical machinery of Bayesian inference resembles that of Occam's inversion, but the goals and interpretations of the two methods are rather different. To understand better the similarities and differences of these two approaches, we show an application of both methods to the problem of inferring the Earth's subsurface elastic properties from reflection seismic data. On the one hand, by deriving a priori information about the Earth's layering from fine-scale borehole measurements, coupled with information about the noise in the data and the elastic forward modelling operator, we are able to compute the Bayesian a posteriori probability distribution on the space of models. Models pseudo-randomly simulated from this a posteriori probability will exhibit features that are implied by the a priori information as well as the data, even if the former are not well resolved by the data. Then we solve the Occam's inversion problem by determining the maximum model smoothness that allows for the data to be fit, without incorporating a priori information about the models. In this case we estimate the resolution in terms of the degree of model smoothness implied by the data. The main conclusions for the numerical experiments considered in this work are that the subsurface models derived from both techniques are quite similar but error estimates associated with such models are rather different, reflecting the role of the a priori information in the inverse calculation.

Occam's Inversion and the North American Central Plains Electrical Anomaly.

iterations excess structure was removed to reveal three discrete conductive zones of resistivity less than 1 Ωm at depths of 8–22 km in a relatively resistive background layer of 100–1000 Ωm. The inversion algorithm was modified to take advantage of the 1D structure of the shorter periods, which were inverted to obtain a model representative of surface sediments which extend to a depth of about 2 km. This surface structure was included in the long-period inversion by imposing a second penalty term in the regularized inversion, and the resulting model featured a broader, more complex conductive anomaly and a pronounced, westward-dipping fabric in the mid-to lower-crustal rocks. Graphitic rocks can account for the highly conductive parts of the models. In this paper we present the results of two-dimensional (2D), smooth inversions of the COPROD2 magnetotelluric (MT) data set (Jones and Savage, 1986; Jones, 1988) using the Occam’s inversion algorithm of Constable, Parker and Constable (1987), modified for 2D MT by deGrootHedlin and Constable (1990). The MT data were obtained over the North American Central Plains (NACP) and Thompson Belt electromagnetic anomalies in order to obtain a quantitative model of features previously identified in numerous geomagnetic depth sounding (GDS) surveys (see the summary by Jones and Craven, 1990). The GDS surveys indicated that the NACP anomaly is a large scale, linear feature extending from southeastern Wyoming northward to the exposed Canadian Shield in northern Saskatchewan, and from there extending eastward along the regional geological strike into the Hudson’s Bay basin. The alignment of zones of intense shearing and folding in the exposed Precambrian crust with both the northern and southern ends of the NACP anomaly led Camfield and Gough (1977) to suggest that the anomaly is associated with a Proterozoic plate boundary. Our aim here is to develop methods of interpretation of approximately 2D MT data sets using smooth inversion methods and to apply these techniques to determine the conductivity structure of the NACP anomaly. Although three-dimensionality is evident along the length of the conductivity anomaly in the GDS data (Alabi et al., 1975), as well as in MT observations recorded in two profiles to the north of the COPROD2 line (Jones and Craven, 1990), the NACP

Two-Dimensional Occam Model of COPROD2 Data. First Order Description of Resolution and Variance.

A two-dimensional Occam model of crustal electrical conductivity is derived based on data from 35 magnetotelluric stations on a profile in Saskatchewan, Canada. The model is discussed in relation to a first order description of the resolution and variance of the model parameters. Prior to the two-dimensional Occam's inversion, the data are analysed with respect to underestimated data errors. The analysis is based on separate D+ inversions of the E- and H-polarization responses and a procedure for adjusting the data errors is presented. The main features of the model are the presence of two conductive structures with vertically integrated conductivity exceeding 30, 000 S and 100, 000 S respectively. In addition to these main features, some minor conductive structures are inferred.

Inversion of long-offset TEM soundings near the borehole Münsterland 1, Germany, and comparison with MT measurements

SUMMARY Data from a long-offset transient electromagnetic (LOTEM) survey in northwest Germany around the borehole Munsterland 1 are interpreted using 1-D inversion. Special emphasis is given to the fact that the best-fitting model is not necessarily the most realistic one. We therefore investigate different inversion algorithms in order to obtain a more geologically meaningful result. The 1-D inversion results using a second-order Marquardt algorithm show a three-layer structure, with a conductor embedded between two more resistive layers. This is in good agreement with the known lithology and the well logs. ‘Profile inversion’ uses the result from one site as the starting model for the next. The application of the technique yields a smoother section than the individual inversions, and corresponds more closely to the (presumably) layered structure in the area. If desired, using a parameter weighting scheme makes it possible to force consistency at the cost of a larger misfit, yielding a smooth section even in a part of the area where the data are influenced by a 3-D anomaly. Occam inversion is a smoothness-constrained technique which is independent of the starting model. The result of the Occam inversion shows the same features as the Marquardt inversion, including effects which are attributed to 3-D distortions in the data. Joint inversions of the LOTEM data were carried out with magnetotelluric data from the same area. In that case, the LOTEM electric field is recognized as crucial for the resolution of the resistive layer in the section.