The “Geo-Tomography” is now an essential tool to study geo-sciences. There are severalapplications of tomography in geophysics. e. g., seismology, geodesy, geomagnetism, gravity, etc. The tomography using cosmic ray, “Muons”, is a new application. In this paper, theauthor intends to give a general view of the geo-tomography and present the relation amongdifferent methods. Detailed description of each application is described by different authors inthis special volume. There are several different methods in tomography: Matrix method, ART or SIRT, CG, backprojection, backpropagation, p-tau trans form and Fourier method. These are overlappedeach other by some extents. The tomography initiated in the medical use and it is called “C omputed Tomography”. In the medical use, sets of (X-ray) parallel projections along lineswith a constant angle to the reference axis are used. In the filtered backprojection method, the convolution of the result of parallel projection to filter-function is integrated over wholeprojection angles. In the contrast with the medical projection method, geophysical applicationsof tomography tend to be limited in narrow projection angles. This narrow aperture will blurthe real image. Several methods have been used in the geo-tomography. DLSQ, SIRT and CG are themost powerful tools for traveltime tomography such as crosshole-VSP tomography and seismictravel time tomography. Recently, waveform inversion using high-frequency seismic wavessuggested its powerfulness to obtain the fine structure of the earth. However, since the waveforminversion has a nature of strong nonlinearity, it is necessary to use traveltime tomography withor in advance of the waveform inversion.
Tomographic inverse schemes, in particular travel-time tomography techniques, havebecome standard ones to image subsurface structures with respect to anomalies in seismicvelocities. In contrast to these ray-theoretical approaches, there exist wave-theoretical schemeswhere seismic waveforms are analyzed in terms of their relation to structural anomalies. In tomographic application of wave theories, Devaney (1984) proposed a method calleddiffraction tomography in which seismic wave-forms are composed of incident and scatteredwave-fields. Since several tens to hundred times much information might be included inseismic wave-forms, it is natural to think that there exists a strong necessity to utilize ofwave-forms in structural analyses. A theoretical jump from ray-theoretical travel-time to wave-theoretical diffraction tomographycan be examined by introducing a simple seismic scattering theory. Since thesetechniques are utilizing seismic signals, results obtained by these methods on the same datamight be considered as the derivation of the same physical properties of unknown targetmaterial in the subsurface. The resolution can also be compared between these two kindsapproaches in seismic tomography through the seismic scattering theory. The theory wasintroduced by a solution to the seismic scattering problem of a compressional plane wavetraveling in a homogeneous medium including a point scatterer, and three types of scatteredwaves were found generated depending on the contrasts in its lithological properties (the Lame's constants and the density) to the surrounding medium. They are equivalent towaves generated by three different kinds of seismic sources. Contrasts between the point scattererand the surrounding medium in bulk modulus, in density, and in rigidity work as a pole, asingle force, and a single couple, respectively. The relation of these parameters to observedscattered waves was found linear and thus invertible. The results obtained through this relationin the analysis of subsurface structure of Izu-Oshima volcano have shown the good resolutionwhich can only be achieved by wave-theoretical methods. It is concluded that seismic scatteringphenomena can be used for the following purposes:(1) to clarify the effects of inhomogeneitieson the observed seismic signals, (2) to find the inverse relation to the scatteringproblems, (3) to understand a link between the seismic methods, i. e., traveltime tomography, waveform tomography and reflection analyses.
We review our study for the P-wave velocity structure of the whole mantle, that areobtained by inverting first arrival times with better resolution under the Western Pacific. Itreveals the fate of subducting slabs of lithosphere and the figures of large-scale mantleupwellings.
This article introduces the mechanisms and principles of medical tomography. There arevarious tomographic imaging modalities for clinical practice that use X-rays, gamma rays fromradioisotopes, ultrasound, magnetic resonance, and electrophysiological effects. Conventional X-ray tomography provides a longitudinal cross-section. The X-ray tube andthe film are moved in such a way that regions in the focal plane register clearly and regionsoutside the focal plane tend to disappear due to blurring. X-ray computed tomography (X-ray CT) shows the structure of organs by imaging X-ray attenuation coefficient quantitatively.X-ray CT acquires projection data by rotating the X-ray tube and the detector array aroundthe patient, and the tomographic image is calculated using the theory of “reconstruction fromprojections”. This is the first application of the inversion analysis in medicine. In nuclear medicine, the functional activity of organs is evaluated by administering a radioisotopeto the patient, and mapping the distribution by measuring the emitted gamma ray radiation. Single photon emission tomography (SPECT) uses a scintillator camera to detect theradiation, generates projection images, and applies the theory of reconstruction from projectionsfor tomographic images. Seven pin-hole tomography generates a conventional longitudinalcross section image using a scintillator camera with a “seven pin-hole collimator”. Positronemission tomography (PET) maps the biochemical process of organs by administering positronemitting radioisotopes. PET measures a pair of gamma ray photons created by the annihilationof an electron and an emitted positron, and applies the theory of reconstruction from projections. Diagnostic ultrasound generates an animated image in real time by mapping the ultrasoundecho signal from acoustic interfaces in the patient's body. The velocity of blood flow can alsobe calculated from the Doppler shifted echo from the red blood cells. Magnetic resonance imaging (MRI) can acquire various kinds of tomographic images fromthe electromagnetic signal emitted by nuclear magnetic resonance of hydrogen and other nucleiin the patient. To control the signal emission, MRI applies a strong and uniform magneticfield, an additional gradient magnetic field, and irradiation of electromagnetic waves. Thetomogram is reconstructed from the electromagnetic signals using Fourier transform. Electronspin resonance (ESR) imaging is also discussed. The topogram in electroencephalography (EEG) is a rough surface mapping of electricactivity of neurons and thus, not strictly tomography. Recently, magnetic source imaging (MSI) of magnetoencephalography (MEG) has become available for research and clinical use. MEG shows activated regions in the brain by measuring the very weak magnetic field causedby the electrophysiological action of neurons.
The history of developments in electrical and electromagnetic exploration techniquesis briefly summarized. In electrical and electromagnetic exploration, subsurface resistivity distributionis obtained from measured data by inversion. The physical meaning of resistivityand the relationship between ground resistivity and other properties of the ground arediscussed. Many kinds of electrical and electromagnetic exploration techniques are classified withrespect to basic physical phenomena, the dimensions of the structure being and observationgeometries. Some essential parts of acquisition technique are also given. The author describes the problem of nonlinearity in electrical and electromagnetic exploration, and offers as a solution an iterative modification technique. Another difficulty in theinversion of electrical and electromagnetic data is complex sensitivity of data. To deal withthis problem, analysis is extended to an area of the ground beyond that from which datahas been measured. In addition, both in-line and cross-line data are used in crossholeexploration. Two practical inversion schemes are described. The conventional method for outliningsubsurface structures and making an initial model for inversion is resistivity back projection. Iterative inversion based on Bayes's theory can deal with both information from measured dataand prior in formation, and maximizes the likelihood of the inverted model. A numericalexperiment is presented to assess the reliability and resolution of the inverted model. The characteristics and uses of the following five examples of electrical and electromagneticexploration techniques are given: 1. 2D surface electrical exploration 2. 3D resistivity tomography 3. 2D CSAMT 4. 2D electromagnetic tomography 5. 2D radar tomography These examples show that the inversion technique is widely accepted in practical electricaland electromagnetic exploration activities and that inverted detailed resistivity images provideuseful information in many kinds of geological and geotechnical situations.
Waveform inversion is a technique to determine earth structure using the observed waveforms themselves, rather than intermediate parameters such as travel times, as the data to be inverted. This technique is widely employed in both exploration seismology and global seismology. Waveform inversion fully utilizes all of the information contained in the observed waveform, whereas seismic tomography using the times of the first arrivals uses only part of the available information. We review recent developments and applications of waveform inversion, mainly in the field of global seismology.
Crosswell seismic tomography is a new geophysical technique for investigating a subsurface structure. This method is characterized by the geometry that both a seismic source and a receiver are located in boreholes. Energy level of a downhole seismic source is relatively small in order to avoid the damage to well-bores. This restricts the distance between a source well and a receiver well to several hundred meters. However, observed seismic waves contain much higher frequency components than those of surface seismic method. This infers that the crosswell method has a potential to delineate detailed inter-well structure. The analysis of crosswell seismic tomography is to reconstruct inter-well velocity structure from traveltimes and ray paths of observed direct waves. Because ray paths of seismic waves depend on the velocity structure which would be the solution, the analysis is equivalent with solving non-linear equations as an inverse problem. The velocity structure is generally reconstructed by iteratively renewing a velocity model so that the traveltimes calculated from the velocity model converge to observed traveltimes. The crosswell seismic tomography has been applied to resource exploration and environmental studies through the research for investigating the relationship between seismic velocity and physical properties of rocks. The effect of EOR (Enhanced Oil Recovery) processes can be identified by the decrease of seismic velocity. Such a velocity change can be detected by comparing the results of crosswell experiments conducted in several stages of the EOR processes The crosswell tomography can construct detailed subsurface images in the volcanic area where surface seismic method is not available. This means that the crosswell method will be the best seismic approach to identify fracture zones which forms a geothermal reservoir in vol-canic rocks. In addition, the detection of fracture zones is extremely important to investigate environmental problem of underground waste disposal. Crosswell seismic tomography still has several research problems that should be overcome. Nevertheless, in the future the crosswell seismic method has the possibility to become the best seismic approach to investigate detailed subsurface structure and physical properties of rocks.
One potential use of cosmic-ray muons arriving nearly horizontally along the earth is a probe of the inner-structure of a gigantic geophysical substane, such as a volcanic mountain. A simple detection system comprising a plastic scintillator hodoscope which is expandable to a larger scale was developed. The first successful measurements of the inner-structure of Mt. Tsukuba as well as Mt. Asama are described. The natural extension towards tomographic measurement is considered. The future perspective of the application of the present method towards the prediction of volcanic eruption is discussed.
Subsurface exploration techniques using vertical seismic profile (VSP) are reviewed mainly on their principles and applications. VSP gives high-resolution and accurate images of seismic structure around a VSP well. The VSP measurement involves subsurface recording of seismic waves from a surface seismic source by means of geophones clamped in a drilled well. The VSP data set thus has the total seismic wavefields with downgoing waves (direct waves from the surface source and downgoing multiples) and upgoing waves (reflected waves toward the surface and upgoing multiples). The high-resolution images of subsurface reflectors produced by VSP data processing are particularly useful for reliable knowledge of fault positions around the VSP well. The depth accuracy of subsurface reflectors given by VSP is valuable in interpretation of surface-seismic data. The seismic tomography of velocity structure using only VSP data set gives a limited application because of its irregular and limited coverage of ray paths. The combination of VSP and surface-seismic data, however, provide a detailed image of reflector depths and velocity structure, based on an inversion formulation for seismic reflections. The VSP is also applied for delineating subsurface fracture systems and for evaluating fracture permeability. Measurements of shear-wave polarization anisotropy using downgoing shear-waves in VSP data gives clues to understand subsurface fractures. VSP observation of particular waves, say tube waves, generated by fluid-filled fractures is a promising method for a measurement of fracture permeability. Thus, the VSP technique is not only for imaging subsurface morphology but also for delineating rock properties including fractures.
Our understanding of three-dimensional mantle structure has been greatly advanced by surface wave tomography in the last decade. In the upper 300-400km, lateral heterogeneity of seismic wave velocity, attenuation, and seismic anisotropy is correlated well with surface tectonics: Slow velocity and high attenuation beneath island arcs, mountainous regions, and young ocean; fast velocity and low attenuation beneath shield and old ocean. Seismic anisotropy also shows a good correlation with plate motion. Such a correlation diminishes below 300-400km and the amplitude of velocity heterogeneity decreases with depth down to the mid mantle. In the deeper part of the lower mantle, the heterogeneity becomes stronger than that in the mid mantle and is dominated by a long-wavelength pattern: The circum-Pacific region is characterized by a fast velocity which may be cold subducted slabs and the South Pacific and Africa are dominated by low velocities which may represent super hot plumes rising from the core-mantle boundary.
We show a couple of methods of inversion of geodetic data to interpret crustal deformations from the viewpoint of kinematics. Geodetic data do not have sufficient resolving power because of their distribution and uncertainty. Therefore inversion of geodetic data is to find a way to overcome nonuniqueness. Currently the Monte Calro approach and inversion with a priori data are widely used among several ways. Especially introduction of a priori data solved this problem and stimulated development of methods to estimate fault slip or tectonic block motions and slip deficits on interface of plates. We show two illustrative examples of estimate of fault parameters by different schemes; the Kurile earthquake of October 4, 1994 and the Kobe earthquake of January 17, 1995. For the Kurile earthquake we apply a Monte-Carlo approach because of insufficient infor mation on fault geometry. We generate thousands of sets of parameters for fault geometry randomly in their possible ranges and estimate slip for each fault model and residual. So far obtained results suggest that a high-angled fault trending along arc is more preferable than that perpendicular to the trench on the basis of the consistency with CMT solutions and distribution of residuals. Fault parameters of the Kobe earthquake can be estimated by linear least squares method with a priori information, because of sufficient geodetic data and th eir geographically favorable distribution. We propose a six segment fault model trending along the known fault system to explain the observed coseismic displacements of the Kobe e arthquake. The inversion infers a couple of large slip zones (>1m) beneath the Nojima fault in Awaji island, north of the Akashi strait and northeastern Kobe. We also introduce models with block motion and slip deficit for the interseismic deformation of tectonic zones. In these models interseismic crustal defor mation can be represented as the sum of relative motion of blocks and displacement due to the slip deficit on the locked part of faults. The results for the Japanese islands indicate that significant strain partitioning is occurring there, which means relative plate motions ar e partly accommodated by intraplate faults. Furthermore the analysis of Japanese data infers significant aseismic slips along the Japan trench.
Inversion of potential fields such as gravity has inherent non-uniqueness when it is used for estimating subsurface density structure. The ambiguity could be overcome, at least partially, (1) by using a priori information (such as pointwise drilling data) and (2) by incorporating independent observations (such as geomagnetic anomaly and seismic data). We present several examples demonstrating how gravity inversion is applied for retrieving geologically interesting features (meteor crater, salt dome, volcano, active fault etc.). We emphasize that cooperative inversion should be used whenever possible to obtain better resolution on the underground structure. Recent advance of the gravity change theory enables us to discuss how to model seismic and volcanic events from gravity change data. Since gravity is sensitive to migration of matter under the ground, gravity inversion is useful in estimating flows of water and magma during such events. Joint inversion of gravity data with conventional crustal movement data proves to be quite effective in modeling the 1989 earthquake swarm and submarine eruption, off Ito.