1. An ultrasonic imaging apparatus comprising: an image data production device for scanning a subject with ultrasonic waves, receiving ultrasonic echoes from the subject, and producing image data composed of a plurality of frame image data items acquired successively from the subject during a scan time; a display device for displaying an image produced based on the image data; a storage device for preserving the image data; a continuous time field image data production device for producing continuous time field image data from the image data by adding up the plurality of frame image data items acquired successively during the scan time; a time-sequential change process image data production device for producing time-sequential change process image data, which represents a plurality of frame images showing a process that pixel values changes from one values to another with the passage of time during the scan time, from the image data; and a synthesis/output device for synthesizing an image represented by the continuous time field image data and each of the images represented by the time-sequential change process image data by superimposing the image represented by the continuous time field image data on each of the images represented by the time-sequential change process image data, and transmitting the resultant image to the display device by sequentially changing the images represented by the time-sequential change process image data with the passage of time during the scan time.