An Automated System For Picking Seismic Events

In this paper we introduce a. three stage approach for extracting secondary events from a. time section. First, a two dimensional local matched filtering scheme is used to reduce the time section to a collection of event tokens suitable for tracking with a Kalman filter. Second, a multiple hypothesis tracking system is used to analyse regions with crossing events. By using a dynamic model of event shape parameters, Kalman filters axe able to track events that deviate from pure hyperbolic form. Finally, based on events found through Kalman filtering, flexible templates are used to exploit similarity between events. Due to the global nature of the flexible template search bility can be identified. process, events with sections of poor visiI n t r o d u c t i o n There are several issues that must be considered when developing a pattern recognition system for event extraction from a time section. The time of arrival of a seismic pulse depends on the position and shape of the reflector and the average velocity of the pulse along the path traveled. If the average velocity of each pulse remains constant from trace to trace and if targets are small, events on the time section will have a hyperbolic shape. However, if the propagation medium is inhomogeneous, local deviations from hyperbolic form will occur. There are often multiple reflectors. Time sections are usually composed of a collection of seismic events that in general cross one another. Due to various noise factors, certai n areas of the time section will be very difficult to analyse. A robust event recognition system should take these issues into account. Huang [5] and others have used Hough and Radon transforms to search for events on time sections. However these methods for the most part rely on rigid templates which perform poorly in the of A* face of deviations used the the event from pure hyperbolic form. Geersearch algorithm, a heuristic tree search (see Lee [8]), to track events. Since the A* algorithm is a form of dynamic programing, it is unable to take advantage of local event shape. This makes it susceptible to crossing events. A number of researchers such as Le [7] and Lu [9] have proposed systems that extract seismic events by maximising the correlation between trace pulses. These systems operate under the assumption that there are no crossing events . This is inappropriate for the general case. In this paper we propose a three stage approach for extracting secondary events. Our approach consists of applying two dimensional matched filters, Kalman filters and flexible templates. The matched filters are used to exploit local trace coherency so as to reduce the time section to a collection of tokens that represent the time of arrival of each pulse and the local orientation of the event. Kalman filters use these tokens to track the events by incorporating a dynamic model for the shape parameters. When ambiguities occur due to crossing events, the system generates a set of hypotheses which follow multiple tracks until the proper segmentation decision becomes evident. Once a. track has been found, it is used to construct a flexible template to search for similar events elsewhere in the time section. T o k e n E x t r a c t i o n Figure 1 shows a portion of a. typical time section see Mason [10]. Figure 2 shows a reduction of the time section in Figure 1 into a set of event tokens. The first stage of this system is to reduce the discretized time section to a collection of tokens which is suitable for tracking with a Kalman filter. If it is decided that an event passes through pixel (i, j), a. token showing the local orientation of the event is associated with the pixel. Since there are crossing events, an individual pixel may have multiple tokens associated with it. In order to take advantage of pulse characteristics and local correlation between traces, a. bank of two dimensional matched filters is used to assign tokens to the pixels. All of the filters are localised both in space and frequency. Each filter is tuned to a pulse with a. specific scale and a specific 1ocal event orientation. By convolving the image with the matched filters, a. local spectrum can be assigned to each pixel. When an event is centered on pixel (i, j), there will be a, local spectral maxima. that is also a. local spatial maxima. in the direction perpendicular to the event. If there are multiple events passing through the pixel there will be multiple spectral maxima. A search algorithm is used to locate these event conditions. In this application the matched filter kernels axe created by the product of a, vertical and horizontal component. The vertical component is the second derivative of a Gaussian with standard deviation The horizontal component is a regular Gaussian with standard deviation (see Figure 3). The kernel is sheared by an angle to match a particular orientation and is varied to match a particular scale. The power of the kernel is normalised. In this application shear angles ranged from to radians and the choice of was from 1.25 to 2.5 pixels. M u l t i p l e H y p o t h e s i s K a l m a n T r a c k i n g Here we outline a. strategy for tracking an event through a time section with multiple crossing events. The multiple hypothesis algorithm as developed by Cox [3] for use in computer vision, is a method for extracting particular tracks conforming to a model from an image containing multiple tracks. By using the set of event tokens (see previous section) as input, this algorithm can be used to track events through a time section. The algorit hm analyses the time section from left, to right by placing a tracker on an event and letting it track through the time section. When the tracker encounters multiple valid tokens, a set, of hypotheses are generated which specifies how the tokens are to be processed. After the algorithm moves ahead 3 or 4 traces, it becomes evident which hypothesis was correct through the use of probabilistic reasoning. In this way the problem of tracking through crossing events can be handled efficiently. The extended Kalman filter approach, as it is used by Porrill [11] in the field of computer vision to extract ellipses from edge data, provides a natural framework for event tracking. The Kalman filter is a sequential estimator of a set of dynamic model parameters based on a. series of related observations. During each iteration of the filter process, an estimate of the model parameters is computed, a confidence measure of this estimate is calculated and a prediction of the next observation is made. The Kalman filter takes into ac-