Composite distribution inversion applied to crosshole tomography

Abstract

Crosshole tomography requires solution of a mixed‐determined inverse problem and addition of a priori information in the form of auxiliary constraints to achieve a stable solution. Composite distribution inversion (CDI) constraints are developed by assuming parameters are drawn from a composite distribution consisting of both normally and uniformly distributed parameters. Nonanomalous parameter estimates are assumed to be Gaussian while anomalous parameters are assumed uniform. The resulting constraints are sensitive to anomaly volume and are an alternative to the usual constraints of minimizing [Formula: see text] solution length or some measure of roughness. Damped least‐squares inversion, which minimizes solution length, distributes anomalous signal through poorly resolved areas to produce in attenuated and smoothed anomalies. Similar regularization methods, such as smoothness or flatness constraints, also degrade small spatial wavelength features and produce diffuse images of distinct anomalies. CDI constraints preserve small spatial wavelength features by encouraging small amplitude anomalies to assume the value of the reference model and by allowing truly anomalous parameter estimates to assume whatever value minimizes prediction error without incurring additional penalty. CDI tomograms are characterized by nearly ideal point‐spread functions, suggesting the possibility of better quantitative parameter estimates than are produced using most existing methods. CDI tomograms of both synthetic and field data are shown to produce less diffuse images with more accurate anomaly amplitude estimates than damped least‐squares methods. The CDI algorithm is potentially applicable to nontomographic inversion problems.

Multivariate analysis of cross‐hole georadar velocity and attenuation tomograms for aquifer zonation

“…Increasing these regularization constraints reduces the model variance and thus acts as a spatial low‐pass filter. Conversely, insufficient regularization fails to maintain sufficient a priori information to achieve a stable solution [e.g., Clippard et al , 1995]. In Figure 6c the resistivity discrepancies for clusters 3 and 4 can be explained by the previously discussed inherent assumptions of ray‐based methods for tomographic amplitude inversion.…”

Fourier reconstruction with sparse inversion

“…Trad et al (2003) gave an overview of the sparse Radon transform methods. Other interesting examples of sparse inversion in seismic data processing include cross‐hole tomography to detect hidden tunnels (Clippard et al 1995) and least‐squares migration to improve angle gathers (Liu et al 2003).…”

Ψηφιακή Ανάλυση Τομογραφικών Δεδομένων

“…Αντίστοιχα οι σεισµικοί δέκτες που τοποθετούνται µέσα σε γεωτρήσεις περικλείονται από αδιάβροχη συσκευασία και τοποθετούνται κατά µήκος καλωδίου ή συρµατόσχοινου. Στη συσκευασία τους περιλαµβάνεται µηχανισµός που τους προσαρµόζει στα τοιχώµατα της γεώτρησης [25] (clamping), ώστε να αυξηθεί αντίστοιχα η ευαισθησία τους. [26] αυτή που κυµαίνεται από 0.1 έως 0.5 ms. Όµως, σε πολλές από τις συνηθισµένες σεισµικές πηγές (εκρηκτικά, airguns), λόγω της κατασκευής τους, δεν είναι δυνατός ο ακριβής καθορισµός της χρονικής στιγµής της εκτόνωσής τους και το σφάλµα στο χρόνο εκτόνωσης µπορεί να κυµαίνεται από 3 έως 5 ms. Στις πρώτες µεθόδους τοµογραφικής ανάλυσης που αναπτύχθηκαν γινόταν επεξεργασία µόνο των χρόνων διαδροµής των σεισµικών κυµάτων κυρίως διότι ήταν πολύ πιο εύκολος [27] ο υπολογισµός τους δεδοµένου ότι µετά την πρώτη άφιξη καταγράφονται αφίξεις ανακλώµενων κυµάτων ή δευτερεύουσες αφίξεις.…”