Dr. Frank Forcella has numerous papers on the weed seed bank.  In short, integrated weed management can reduce weed seed bank numbers.  But, this is a long term strategy as weed seeds can have a long dormancy period in the soil.

Article Weed Seed Bank Dynamics

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Seed bank sampling is one method to quantify weed seed density/diversity. Obtain soil seed bank samples followed by cleaning to get weed seeds or germinating the seed bank samples under controlled conditions will do.

Management: Basically, control the above ground weeds before seed production or to be precise before seed dispersal. The idea is to avoid further replenishment of soil seed bank. In addition to that follow weed management practices that exhaust the existing soil seed bank (Ex. Tillage).

The first step would be to obtain soil samples (the seed bank samples) using core samplers or augers, to a depth that is guided by your study objectives.. with regards to sample size, many samples with a narrow diameter core or auger from the same plot give more accurate estimates than few samplers with a larger diameter... Once you collect your samples, you can go on to quantify your seeds using either of the following methods....

irregardless of the weaknesses of both methods, accuracies of up to 75 % have been obtained in most studies.... some workers recommend use of both methods in 1 trial..... 

Mesgaran, M. B., Mashhadi, H. R., Zand, E., & Alizade, E. (2007). Comparison of three methodologies for efficient seed extraction in studies of soil weed seedbanks. Weed Research, 47, 472 – 478.

Late season weed control is critical in reducing weed seed rain into the soil.... Weeds that escape control early and mid season profusely produce propagles which they deposit into the seed bank ... Moreover, these propagles are often dormant and have longevity in the soil which can be as high as 20 years.... These factor combined cater for the persistence and sustained presence of weeds in agricultural and none agricultural systems.... targeting weed seed production is the way to avoid seed bank build up... it should also be accompanied by use of eg stale seed bed technique,  where you irrigate your field to stimulate weed seed germination.... You then come in with your herbicides or tillage to control the emerged weeds..... This is done prior to coming in with your crop,,, SEE...

Walsh, M., Newman, P., & Stephen, P. (2013). Targeting Weed Seeds In-Crop: A New Weed Control Paradigm for Global Agriculture. Weed Technology, 27, 431 – 436.

Weed seed bank study can be carried out by putting an enclosure in a particular site, collecting soil samples from this enclosure, putting this sample in a tray and allowing seeds to grow and keeping a count of the weeds emerging. Record can be kept on different weed species and time of emergence etc.